%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP183-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 122.98s 122.89s
% Output : CNFRefutation 122.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 77 ( 77 unt; 0 nHn; 4 RR)
% Number of literals : 77 ( 76 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 : 157 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
file('theBenchmark.p',prove_20x) ).
cnf(c1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p20x_1) ).
cnf(c2,axiom,
least_upper_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_lub) ).
cnf(c4,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c5,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',p20x_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,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c9,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c11,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c12,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(equational,[status(thm)],[c7,c10]) ).
cnf(c14,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('theBenchmark.p',p20x_3) ).
cnf(c15,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(multiply(X,identity)) = inverse(X),
inference(equational,[status(thm)],[c1,c4,c15]) ).
cnf(c17,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c18,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(c19,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c18]) ).
cnf(c20,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(c24,plain,
least_upper_bound(X,least_upper_bound(X,Y)) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c2,c19]) ).
cnf(c25,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c26,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c28,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c6,c19]) ).
cnf(c29,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c4,c8,c20]) ).
cnf(c30,plain,
least_upper_bound(X,least_upper_bound(Y,X)) = least_upper_bound(Y,X),
inference(equational,[status(thm)],[c2,c28]) ).
cnf(c33,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c5,c15,c29]) ).
cnf(c35,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c36,plain,
greatest_lower_bound(multiply(X,Y),multiply(Z,Y)) = multiply(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c35]) ).
cnf(c38,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(greatest_lower_bound(Y,identity),X),
inference(equational,[status(thm)],[c4,c7,c36]) ).
cnf(c41,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c42,plain,
least_upper_bound(multiply(X,Y),multiply(Z,Y)) = multiply(least_upper_bound(X,Z),Y),
inference(equational,[status(thm)],[c41]) ).
cnf(c43,plain,
least_upper_bound(X,multiply(Y,X)) = multiply(least_upper_bound(identity,Y),X),
inference(equational,[status(thm)],[c4,c42]) ).
cnf(c44,plain,
least_upper_bound(X,multiply(Y,X)) = multiply(least_upper_bound(Y,identity),X),
inference(equational,[status(thm)],[c4,c6,c42]) ).
cnf(c46,plain,
multiply(least_upper_bound(X,inverse(Y)),Y) = least_upper_bound(identity,multiply(X,Y)),
inference(equational,[status(thm)],[c6,c8,c42]) ).
cnf(c47,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c48,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c47]) ).
cnf(c49,plain,
least_upper_bound(X,multiply(X,Y)) = multiply(X,least_upper_bound(identity,Y)),
inference(equational,[status(thm)],[c17,c48]) ).
cnf(c51,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c52,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c51]) ).
cnf(c57,plain,
multiply(inverse(X),least_upper_bound(X,Y)) = least_upper_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c8,c48]) ).
cnf(c59,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c11,c22]) ).
cnf(c60,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Y),Z)) = least_upper_bound(X,Z),
inference(equational,[status(thm)],[c10,c19]) ).
cnf(c69,plain,
multiply(least_upper_bound(identity,X),inverse(X)) = least_upper_bound(identity,inverse(X)),
inference(equational,[status(thm)],[c6,c9,c43]) ).
cnf(c70,plain,
least_upper_bound(identity,inverse(least_upper_bound(X,identity))) = identity,
inference(equational,[status(thm)],[c9,c30,c69]) ).
cnf(c71,plain,
least_upper_bound(identity,inverse(least_upper_bound(identity,X))) = identity,
inference(equational,[status(thm)],[c9,c24,c69]) ).
cnf(c90,plain,
least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(Z,X))) = least_upper_bound(Y,X),
inference(equational,[status(thm)],[c13,c28]) ).
cnf(c108,plain,
least_upper_bound(X,multiply(least_upper_bound(Y,identity),X)) = least_upper_bound(X,multiply(Y,X)),
inference(equational,[status(thm)],[c24,c44]) ).
cnf(c113,plain,
greatest_lower_bound(X,multiply(X,least_upper_bound(identity,Y))) = X,
inference(equational,[status(thm)],[c11,c49]) ).
cnf(c157,plain,
multiply(X,least_upper_bound(identity,multiply(inverse(X),Y))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c5,c29,c57]) ).
cnf(c172,plain,
least_upper_bound(inverse(X),inverse(multiply(X,Y))) = multiply(least_upper_bound(identity,inverse(Y)),inverse(X)),
inference(equational,[status(thm)],[c15,c43]) ).
cnf(c189,plain,
multiply(least_upper_bound(identity,X),inverse(least_upper_bound(X,identity))) = identity,
inference(equational,[status(thm)],[c17,c69,c70,c108]) ).
cnf(c225,plain,
multiply(inverse(X),greatest_lower_bound(multiply(X,Y),Z)) = greatest_lower_bound(Y,multiply(inverse(X),Z)),
inference(equational,[status(thm)],[c29,c52]) ).
cnf(c318,plain,
multiply(least_upper_bound(X,identity),inverse(least_upper_bound(identity,X))) = identity,
inference(equational,[status(thm)],[c1,c25,c189]) ).
cnf(c349,plain,
multiply(X,inverse(least_upper_bound(identity,multiply(Y,X)))) = inverse(least_upper_bound(Y,inverse(X))),
inference(equational,[status(thm)],[c33,c46]) ).
cnf(c386,plain,
least_upper_bound(multiply(X,Y),multiply(Z,multiply(W,Y))) = multiply(least_upper_bound(X,multiply(Z,W)),Y),
inference(equational,[status(thm)],[c20,c42]) ).
cnf(c392,plain,
multiply(least_upper_bound(X,multiply(Y,Z)),inverse(Z)) = least_upper_bound(multiply(X,inverse(Z)),Y),
inference(equational,[status(thm)],[c9,c17,c386]) ).
cnf(c422,plain,
multiply(least_upper_bound(X,inverse(multiply(Y,Z))),Y) = least_upper_bound(multiply(X,Y),inverse(Z)),
inference(equational,[status(thm)],[c5,c15,c392]) ).
cnf(c437,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)],[c7,c12,c60]) ).
cnf(c513,plain,
multiply(inverse(greatest_lower_bound(X,identity)),greatest_lower_bound(Y,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c29,c38]) ).
cnf(c516,plain,
multiply(inverse(greatest_lower_bound(multiply(X,Y),Z)),X) = inverse(greatest_lower_bound(Y,multiply(inverse(X),Z))),
inference(equational,[status(thm)],[c26,c225]) ).
cnf(c558,plain,
least_upper_bound(inverse(X),inverse(multiply(X,Y))) = multiply(least_upper_bound(identity,Y),inverse(multiply(X,Y))),
inference(equational,[status(thm)],[c6,c33,c43]) ).
cnf(c735,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(Y,identity),least_upper_bound(X,Z))) = greatest_lower_bound(X,multiply(Y,least_upper_bound(X,Z))),
inference(equational,[status(thm)],[c38,c59]) ).
cnf(c964,plain,
multiply(least_upper_bound(identity,X),inverse(multiply(Y,X))) = multiply(least_upper_bound(identity,inverse(X)),inverse(Y)),
inference(equational,[status(thm)],[c172,c558]) ).
cnf(c995,plain,
greatest_lower_bound(X,least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z))) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)),
inference(equational,[status(thm)],[c10,c437]) ).
cnf(c1120,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(Y,identity),least_upper_bound(Z,X))) = greatest_lower_bound(X,multiply(Y,least_upper_bound(Z,X))),
inference(equational,[status(thm)],[c90,c735]) ).
cnf(c1203,plain,
least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(Y,multiply(X,Y))) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,Y)),
inference(equational,[status(thm)],[c157,c513]) ).
cnf(c1204,plain,
multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X)) = X,
inference(equational,[status(thm)],[c113,c995,c1120,c1203]) ).
cnf(c1206,plain,
least_upper_bound(identity,inverse(X)) = inverse(greatest_lower_bound(X,identity)),
inference(equational,[status(thm)],[c4,c24,c69,c71,c964,c1204]) ).
cnf(c1208,plain,
inverse(greatest_lower_bound(X,inverse(Y))) = least_upper_bound(Y,inverse(X)),
inference(equational,[status(thm)],[c4,c17,c422,c516,c1206]) ).
cnf(c1212,plain,
inverse(least_upper_bound(X,inverse(Y))) = greatest_lower_bound(Y,inverse(X)),
inference(equational,[status(thm)],[c5,c1208]) ).
cnf(c1215,plain,
multiply(greatest_lower_bound(X,identity),least_upper_bound(X,identity)) = X,
inference(equational,[status(thm)],[c6,c1204]) ).
cnf(c1257,plain,
greatest_lower_bound(least_upper_bound(X,identity),inverse(greatest_lower_bound(X,identity))) = identity,
inference(equational,[status(thm)],[c318,c349,c1212,c1215]) ).
cnf(g1,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) = identity,
inference(equational,[status(thm)],[c6,c1206,c1257]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP183-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.10/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:14:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 122.98/122.89 % SZS status Unsatisfiable
% 122.98/122.89 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------