%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP186-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 06:43:43 AM UTC 2025
% Result : Unsatisfiable 42.55s 42.66s
% Output : CNFRefutation 42.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 4 RR)
% Number of literals : 81 ( 80 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 169 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
file('theBenchmark.p',prove_p23) ).
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(c18,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c5,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(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(c34,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c35,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Y),Z)) = least_upper_bound(X,Z),
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c43,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(Z,X))) = greatest_lower_bound(Y,X),
inference(equational,[status(thm)],[c9,c19]) ).
cnf(c54,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,least_upper_bound(Y,Z))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c55,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(c57,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(greatest_lower_bound(X,Y),Z))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c58,plain,
least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(least_upper_bound(X,Y),Z))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c59,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c15,c29]) ).
cnf(c60,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c20,c26,c59]) ).
cnf(c61,plain,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c20,c60]) ).
cnf(c63,plain,
least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(Y,greatest_lower_bound(Z,X))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c4,c12,c55]) ).
cnf(c64,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(Z,greatest_lower_bound(X,Y)))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c5,c57]) ).
cnf(c69,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(Y,least_upper_bound(X,Z))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c18,c54]) ).
cnf(c70,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(Y,X)) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c1,c69]) ).
cnf(c71,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(Y,least_upper_bound(Z,X))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c5,c14,c54]) ).
cnf(c72,plain,
least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(least_upper_bound(Y,X),Z))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c5,c58]) ).
cnf(c83,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(greatest_lower_bound(X,Z),Y)) = least_upper_bound(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c4,c9,c35]) ).
cnf(c90,plain,
greatest_lower_bound(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(Z,X)) = least_upper_bound(Z,X),
inference(equational,[status(thm)],[c43,c64,c71]) ).
cnf(c91,plain,
least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(Z,least_upper_bound(Y,X)))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c4,c72]) ).
cnf(c115,plain,
least_upper_bound(greatest_lower_bound(least_upper_bound(X,Y),Z),greatest_lower_bound(Z,X)) = greatest_lower_bound(least_upper_bound(X,Y),Z),
inference(equational,[status(thm)],[c8,c63]) ).
cnf(c123,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(Y,greatest_lower_bound(X,Z))) = least_upper_bound(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c5,c83]) ).
cnf(c131,plain,
least_upper_bound(X,greatest_lower_bound(least_upper_bound(Y,Z),least_upper_bound(Z,greatest_lower_bound(Y,least_upper_bound(X,Z))))) = least_upper_bound(Z,X),
inference(equational,[status(thm)],[c14,c70,c90,c91,c123]) ).
cnf(c277,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(c278,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X,Y)),X)) = identity,
inference(equational,[status(thm)],[c5,c16,c277]) ).
cnf(c296,plain,
least_upper_bound(X,multiply(inverse(least_upper_bound(Y,Z)),multiply(Y,X))) = X,
inference(equational,[status(thm)],[c3,c15,c33,c278]) ).
cnf(c297,plain,
least_upper_bound(X,inverse(least_upper_bound(inverse(X),Y))) = X,
inference(equational,[status(thm)],[c6,c26,c296]) ).
cnf(c298,plain,
least_upper_bound(inverse(X),inverse(least_upper_bound(X,Y))) = inverse(X),
inference(equational,[status(thm)],[c26,c29,c296]) ).
cnf(c300,plain,
least_upper_bound(inverse(X),inverse(least_upper_bound(Y,X))) = inverse(X),
inference(equational,[status(thm)],[c131,c298]) ).
cnf(c302,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,c297]) ).
cnf(c305,plain,
least_upper_bound(inverse(X),inverse(greatest_lower_bound(Y,X))) = inverse(greatest_lower_bound(Y,X)),
inference(equational,[status(thm)],[c5,c10,c300]) ).
cnf(c308,plain,
least_upper_bound(inverse(X),inverse(greatest_lower_bound(X,Y))) = inverse(greatest_lower_bound(X,Y)),
inference(equational,[status(thm)],[c5,c7,c300]) ).
cnf(c309,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(identity,X))) = inverse(greatest_lower_bound(identity,X)),
inference(equational,[status(thm)],[c27,c308]) ).
cnf(c677,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,c61]) ).
cnf(c678,plain,
inverse(least_upper_bound(X,multiply(X,Y))) = multiply(inverse(least_upper_bound(identity,Y)),inverse(X)),
inference(equational,[status(thm)],[c26,c677]) ).
cnf(c679,plain,
inverse(least_upper_bound(identity,inverse(X))) = multiply(inverse(least_upper_bound(identity,X)),X),
inference(equational,[status(thm)],[c5,c6,c28,c678]) ).
cnf(c680,plain,
inverse(least_upper_bound(identity,multiply(inverse(X),Y))) = multiply(inverse(least_upper_bound(X,Y)),X),
inference(equational,[status(thm)],[c6,c28,c677]) ).
cnf(c681,plain,
inverse(least_upper_bound(X,multiply(X,Y))) = multiply(inverse(least_upper_bound(Y,identity)),inverse(X)),
inference(equational,[status(thm)],[c5,c26,c677]) ).
cnf(c687,plain,
inverse(greatest_lower_bound(multiply(X,Y),multiply(Z,Y))) = multiply(inverse(Y),inverse(greatest_lower_bound(X,Z))),
inference(equational,[status(thm)],[c34,c61]) ).
cnf(c688,plain,
inverse(greatest_lower_bound(identity,multiply(X,inverse(Y)))) = multiply(Y,inverse(greatest_lower_bound(Y,X))),
inference(equational,[status(thm)],[c28,c29,c687]) ).
cnf(c695,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,c61]) ).
cnf(c696,plain,
inverse(least_upper_bound(identity,multiply(X,inverse(Y)))) = multiply(Y,inverse(least_upper_bound(Y,X))),
inference(equational,[status(thm)],[c28,c29,c695]) ).
cnf(c697,plain,
multiply(X,inverse(least_upper_bound(X,identity))) = multiply(inverse(least_upper_bound(identity,X)),X),
inference(equational,[status(thm)],[c5,c26,c27,c679,c681,c696]) ).
cnf(c698,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,c679,c697]) ).
cnf(c699,plain,
inverse(least_upper_bound(X,multiply(Y,X))) = multiply(inverse(X),inverse(least_upper_bound(identity,Y))),
inference(equational,[status(thm)],[c3,c695]) ).
cnf(c700,plain,
multiply(X,inverse(least_upper_bound(identity,X))) = multiply(inverse(least_upper_bound(X,identity)),X),
inference(equational,[status(thm)],[c3,c27,c679,c680,c698,c699]) ).
cnf(c702,plain,
multiply(inverse(least_upper_bound(X,identity)),X) = multiply(X,inverse(least_upper_bound(X,identity))),
inference(equational,[status(thm)],[c5,c700]) ).
cnf(c761,plain,
least_upper_bound(inverse(least_upper_bound(X,identity)),multiply(X,inverse(least_upper_bound(X,identity)))) = identity,
inference(equational,[status(thm)],[c5,c26,c277,c702]) ).
cnf(c832,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)],[c115,c761]) ).
cnf(c833,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,c302,c679,c698,c832]) ).
cnf(c834,plain,
inverse(greatest_lower_bound(identity,X)) = least_upper_bound(identity,inverse(X)),
inference(equational,[status(thm)],[c3,c5,c14,c28,c29,c33,c61,c300,c305,c309,c833]) ).
cnf(c844,plain,
multiply(X,inverse(greatest_lower_bound(X,Y))) = least_upper_bound(identity,multiply(X,inverse(Y))),
inference(equational,[status(thm)],[c28,c61,c688,c834]) ).
cnf(g1,plain,
least_upper_bound(multiply(a,b),identity) = multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
inference(equational,[status(thm)],[c5,c28,c844]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP186-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:15:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 42.55/42.66 % SZS status Unsatisfiable
% 42.55/42.66 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------