%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP181-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 62.67s 62.79s
% Output : CNFRefutation 62.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 50 ( 50 unt; 0 nHn; 12 RR)
% Number of literals : 50 ( 49 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 : 79 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != b,
file('theBenchmark.p',prove_p12x) ).
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(c4,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c5,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c6,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('theBenchmark.p',p12x_1) ).
cnf(c7,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('theBenchmark.p',p12x_2) ).
cnf(c9,plain,
least_upper_bound(b,c) = least_upper_bound(a,c),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c12,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c17,axiom,
inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)),
file('theBenchmark.p',p12x_4) ).
cnf(c18,plain,
greatest_lower_bound(inverse(X),inverse(Y)) = inverse(least_upper_bound(X,Y)),
inference(equational,[status(thm)],[c17]) ).
cnf(c21,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(c22,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c21]) ).
cnf(c23,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c24,plain,
least_upper_bound(X,least_upper_bound(X,Y)) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c30,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c10,c23]) ).
cnf(c32,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c10,c30]) ).
cnf(c35,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c30]) ).
cnf(c36,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c32,c35]) ).
cnf(c37,plain,
inverse(identity) = identity,
inference(equational,[status(thm)],[c10,c36]) ).
cnf(c38,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c32,c36]) ).
cnf(c44,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c30,c35]) ).
cnf(c45,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c46,plain,
least_upper_bound(multiply(X,Y),multiply(Z,Y)) = multiply(least_upper_bound(X,Z),Y),
inference(equational,[status(thm)],[c45]) ).
cnf(c47,plain,
least_upper_bound(X,multiply(Y,X)) = multiply(least_upper_bound(identity,Y),X),
inference(equational,[status(thm)],[c3,c46]) ).
cnf(c51,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c52,plain,
greatest_lower_bound(multiply(X,Y),multiply(Z,Y)) = multiply(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c51]) ).
cnf(c54,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(greatest_lower_bound(Y,identity),X),
inference(equational,[status(thm)],[c3,c4,c52]) ).
cnf(c55,plain,
multiply(greatest_lower_bound(inverse(X),Y),X) = greatest_lower_bound(identity,multiply(Y,X)),
inference(equational,[status(thm)],[c10,c52]) ).
cnf(c57,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c58,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c57]) ).
cnf(c59,plain,
least_upper_bound(X,multiply(X,Y)) = multiply(X,least_upper_bound(identity,Y)),
inference(equational,[status(thm)],[c32,c38,c58]) ).
cnf(c61,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c62,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c61]) ).
cnf(c66,plain,
greatest_lower_bound(identity,inverse(X)) = inverse(least_upper_bound(identity,X)),
inference(equational,[status(thm)],[c18,c37]) ).
cnf(c68,plain,
multiply(inverse(X),least_upper_bound(Y,X)) = least_upper_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c5,c10,c58]) ).
cnf(c70,plain,
multiply(inverse(X),greatest_lower_bound(Y,X)) = greatest_lower_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c4,c10,c62]) ).
cnf(c83,plain,
multiply(least_upper_bound(identity,X),X) = multiply(X,least_upper_bound(identity,X)),
inference(equational,[status(thm)],[c47,c59]) ).
cnf(c112,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(equational,[status(thm)],[c7,c70]) ).
cnf(c113,plain,
least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a)),
inference(equational,[status(thm)],[c9,c68]) ).
cnf(c199,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(inverse(least_upper_bound(identity,Y)),multiply(Y,X)),
inference(equational,[status(thm)],[c4,c30,c54,c66]) ).
cnf(c288,plain,
multiply(greatest_lower_bound(inverse(X),Y),multiply(X,Z)) = multiply(greatest_lower_bound(identity,multiply(Y,X)),Z),
inference(equational,[status(thm)],[c23,c55]) ).
cnf(c333,plain,
multiply(inverse(least_upper_bound(identity,X)),multiply(X,Y)) = multiply(greatest_lower_bound(identity,X),Y),
inference(equational,[status(thm)],[c10,c23,c30,c36,c199,c288]) ).
cnf(c334,plain,
multiply(greatest_lower_bound(identity,X),least_upper_bound(identity,X)) = X,
inference(equational,[status(thm)],[c3,c12,c24,c83,c333]) ).
cnf(c335,plain,
multiply(inverse(c),b) = multiply(inverse(c),a),
inference(equational,[status(thm)],[c112,c113,c334]) ).
cnf(c336,plain,
b = a,
inference(equational,[status(thm)],[c44,c335]) ).
cnf(g1,plain,
a = b,
inference(equational,[status(thm)],[c336]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP181-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n004.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 08:14:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 62.67/62.79 % SZS status Unsatisfiable
% 62.67/62.79 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------