%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP181-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 06:43:41 AM UTC 2025
% Result : Unsatisfiable 60.44s 61.01s
% Output : CNFRefutation 60.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 12 RR)
% Number of literals : 35 ( 34 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 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != b,
file('theBenchmark.p',prove_p12x) ).
cnf(c1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p12x_1) ).
cnf(c4,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c5,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',p12x_2) ).
cnf(c6,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c7,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c8,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('theBenchmark.p',p12x_4) ).
cnf(c9,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('theBenchmark.p',p12x_5) ).
cnf(c11,plain,
least_upper_bound(b,c) = least_upper_bound(a,c),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c13,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c5,c12]) ).
cnf(c25,axiom,
inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)),
file('theBenchmark.p',p12x_7) ).
cnf(c26,plain,
greatest_lower_bound(inverse(X),inverse(Y)) = inverse(least_upper_bound(X,Y)),
inference(equational,[status(thm)],[c25]) ).
cnf(c27,plain,
greatest_lower_bound(identity,inverse(X)) = inverse(least_upper_bound(identity,X)),
inference(equational,[status(thm)],[c1,c26]) ).
cnf(c32,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c45,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c4,c12,c32]) ).
cnf(c50,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c4,c13,c32]) ).
cnf(c56,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c57,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c56]) ).
cnf(c60,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c61,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c60]) ).
cnf(c71,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c72,plain,
greatest_lower_bound(multiply(X,Y),multiply(Z,Y)) = multiply(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c71]) ).
cnf(c76,plain,
multiply(greatest_lower_bound(X,inverse(Y)),Y) = greatest_lower_bound(identity,multiply(X,Y)),
inference(equational,[status(thm)],[c7,c12,c72]) ).
cnf(c77,plain,
multiply(inverse(least_upper_bound(identity,X)),X) = greatest_lower_bound(identity,X),
inference(equational,[status(thm)],[c4,c27,c76]) ).
cnf(c81,plain,
multiply(inverse(X),greatest_lower_bound(Y,X)) = greatest_lower_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c7,c12,c61]) ).
cnf(c83,plain,
multiply(inverse(X),least_upper_bound(Y,X)) = least_upper_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c6,c12,c57]) ).
cnf(c148,plain,
multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,X)) = X,
inference(equational,[status(thm)],[c5,c45,c77]) ).
cnf(c153,plain,
least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a)),
inference(equational,[status(thm)],[c11,c83]) ).
cnf(c154,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(equational,[status(thm)],[c9,c81]) ).
cnf(c155,plain,
multiply(inverse(c),b) = multiply(inverse(c),a),
inference(equational,[status(thm)],[c148,c153,c154]) ).
cnf(c156,plain,
b = a,
inference(equational,[status(thm)],[c50,c155]) ).
cnf(g1,plain,
a = b,
inference(equational,[status(thm)],[c156]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP181-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Jul 14 08:14:49 EDT 2025
% 0.14/0.34 % CPUTime :
% 60.44/61.01 % SZS status Unsatisfiable
% 60.44/61.01 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------