%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP183-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 06:43:42 AM UTC 2025
% Result : Unsatisfiable 36.32s 36.45s
% Output : CNFRefutation 36.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 61 ( 61 unt; 0 nHn; 4 RR)
% Number of literals : 61 ( 60 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity,
file('theBenchmark.p',prove_p20) ).
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,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c7,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c8,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c9,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c11,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(c12,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,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(c14,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c16,plain,
least_upper_bound(X,least_upper_bound(X,Y)) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c19,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c20,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c6,c15]) ).
cnf(c22,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c6,c20]) ).
cnf(c25,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c20]) ).
cnf(c26,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c22,c25]) ).
cnf(c27,plain,
inverse(identity) = identity,
inference(equational,[status(thm)],[c6,c26]) ).
cnf(c28,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c22,c26]) ).
cnf(c29,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c6,c25]) ).
cnf(c30,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c20,c25]) ).
cnf(c31,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c32,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c33,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c58,plain,
least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,greatest_lower_bound(Y,Z))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c7,c12]) ).
cnf(c63,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c15,c29]) ).
cnf(c64,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c20,c26,c63]) ).
cnf(c65,plain,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c20,c64]) ).
cnf(c72,plain,
least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,greatest_lower_bound(X,Z))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c19,c58]) ).
cnf(c265,plain,
least_upper_bound(multiply(inverse(least_upper_bound(X,Y)),X),multiply(inverse(least_upper_bound(X,Y)),Y)) = identity,
inference(equational,[status(thm)],[c6,c31]) ).
cnf(c266,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X,Y)),X)) = identity,
inference(equational,[status(thm)],[c5,c16,c265]) ).
cnf(c271,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X,Y)),Y)) = multiply(inverse(least_upper_bound(X,Y)),Y),
inference(equational,[status(thm)],[c4,c9,c265]) ).
cnf(c272,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X,identity))) = inverse(least_upper_bound(X,identity)),
inference(equational,[status(thm)],[c26,c271]) ).
cnf(c282,plain,
least_upper_bound(X,multiply(inverse(least_upper_bound(Y,Z)),multiply(Y,X))) = X,
inference(equational,[status(thm)],[c3,c15,c33,c266]) ).
cnf(c283,plain,
least_upper_bound(X,inverse(least_upper_bound(inverse(X),Y))) = X,
inference(equational,[status(thm)],[c6,c26,c282]) ).
cnf(c284,plain,
least_upper_bound(inverse(X),inverse(least_upper_bound(X,Y))) = inverse(X),
inference(equational,[status(thm)],[c26,c29,c282]) ).
cnf(c286,plain,
least_upper_bound(inverse(X),inverse(least_upper_bound(Y,X))) = inverse(X),
inference(equational,[status(thm)],[c5,c284]) ).
cnf(c288,plain,
greatest_lower_bound(X,inverse(least_upper_bound(inverse(X),Y))) = inverse(least_upper_bound(inverse(X),Y)),
inference(equational,[status(thm)],[c4,c9,c283]) ).
cnf(c291,plain,
least_upper_bound(inverse(X),inverse(greatest_lower_bound(X,Y))) = inverse(greatest_lower_bound(X,Y)),
inference(equational,[status(thm)],[c5,c7,c286]) ).
cnf(c292,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,X))) = inverse(greatest_lower_bound(identity,X)),
inference(equational,[status(thm)],[c27,c291]) ).
cnf(c294,plain,
least_upper_bound(inverse(X),inverse(greatest_lower_bound(Y,X))) = inverse(greatest_lower_bound(Y,X)),
inference(equational,[status(thm)],[c5,c10,c286]) ).
cnf(c451,plain,
greatest_lower_bound(multiply(inverse(greatest_lower_bound(X,Y)),X),multiply(inverse(greatest_lower_bound(X,Y)),Y)) = identity,
inference(equational,[status(thm)],[c6,c32]) ).
cnf(c647,plain,
inverse(least_upper_bound(multiply(X,Y),multiply(X,Z))) = multiply(inverse(least_upper_bound(Y,Z)),inverse(X)),
inference(equational,[status(thm)],[c31,c65]) ).
cnf(c648,plain,
inverse(least_upper_bound(X,multiply(X,Y))) = multiply(inverse(least_upper_bound(identity,Y)),inverse(X)),
inference(equational,[status(thm)],[c26,c647]) ).
cnf(c649,plain,
inverse(least_upper_bound(identity,inverse(X))) = multiply(inverse(least_upper_bound(identity,X)),X),
inference(equational,[status(thm)],[c5,c6,c28,c648]) ).
cnf(c651,plain,
inverse(least_upper_bound(X,multiply(X,Y))) = multiply(inverse(least_upper_bound(Y,identity)),inverse(X)),
inference(equational,[status(thm)],[c5,c26,c647]) ).
cnf(c665,plain,
inverse(least_upper_bound(multiply(X,Y),multiply(Z,Y))) = multiply(inverse(Y),inverse(least_upper_bound(X,Z))),
inference(equational,[status(thm)],[c33,c65]) ).
cnf(c666,plain,
inverse(least_upper_bound(identity,multiply(X,inverse(Y)))) = multiply(Y,inverse(least_upper_bound(Y,X))),
inference(equational,[status(thm)],[c28,c29,c665]) ).
cnf(c667,plain,
multiply(X,inverse(least_upper_bound(X,identity))) = multiply(inverse(least_upper_bound(identity,X)),X),
inference(equational,[status(thm)],[c5,c26,c27,c649,c651,c666]) ).
cnf(c668,plain,
multiply(inverse(least_upper_bound(identity,X)),X) = multiply(X,inverse(least_upper_bound(identity,X))),
inference(equational,[status(thm)],[c5,c15,c26,c29,c30,c649,c667]) ).
cnf(c751,plain,
least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(X,inverse(least_upper_bound(Y,identity)))) = greatest_lower_bound(identity,X),
inference(equational,[status(thm)],[c72,c272]) ).
cnf(c752,plain,
least_upper_bound(greatest_lower_bound(identity,X),multiply(X,inverse(least_upper_bound(identity,X)))) = greatest_lower_bound(identity,X),
inference(equational,[status(thm)],[c5,c288,c649,c668,c751]) ).
cnf(c753,plain,
inverse(greatest_lower_bound(identity,X)) = least_upper_bound(identity,inverse(X)),
inference(equational,[status(thm)],[c3,c5,c14,c28,c29,c33,c65,c286,c292,c294,c752]) ).
cnf(c767,plain,
greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(identity,inverse(X))) = identity,
inference(equational,[status(thm)],[c3,c4,c6,c26,c33,c451,c753]) ).
cnf(c775,plain,
greatest_lower_bound(least_upper_bound(identity,X),least_upper_bound(identity,inverse(X))) = identity,
inference(equational,[status(thm)],[c5,c767]) ).
cnf(g1,plain,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = identity,
inference(equational,[status(thm)],[c4,c5,c753,c775]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP183-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.31 % CPULimit : 300
% 0.17/0.31 % WCLimit : 300
% 0.17/0.31 % DateTime : Mon Jul 14 08:14:34 EDT 2025
% 0.17/0.31 % CPUTime :
% 36.32/36.45 % SZS status Unsatisfiable
% 36.32/36.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------