%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP167-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 06:43:37 AM UTC 2025
% Result : Unsatisfiable 104.43s 104.61s
% Output : CNFRefutation 104.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 3 RR)
% Number of literals : 43 ( 42 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 : 92 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('theBenchmark.p',prove_p19) ).
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(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(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(c28,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c22,c26]) ).
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,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c31]) ).
cnf(c33,plain,
least_upper_bound(X,multiply(X,Y)) = multiply(X,least_upper_bound(identity,Y)),
inference(equational,[status(thm)],[c22,c28,c32]) ).
cnf(c35,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c36,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c35]) ).
cnf(c39,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c40,plain,
least_upper_bound(multiply(X,Y),multiply(Z,Y)) = multiply(least_upper_bound(X,Z),Y),
inference(equational,[status(thm)],[c39]) ).
cnf(c42,plain,
least_upper_bound(X,multiply(Y,X)) = multiply(least_upper_bound(Y,identity),X),
inference(equational,[status(thm)],[c3,c5,c40]) ).
cnf(c52,plain,
multiply(inverse(X),greatest_lower_bound(X,Y)) = greatest_lower_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c6,c36]) ).
cnf(c55,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(c56,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c72,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,least_upper_bound(X,Z))) = greatest_lower_bound(Y,X),
inference(equational,[status(thm)],[c8,c19]) ).
cnf(c97,plain,
least_upper_bound(X,multiply(X,greatest_lower_bound(identity,Y))) = X,
inference(equational,[status(thm)],[c7,c26,c33]) ).
cnf(c130,plain,
multiply(X,greatest_lower_bound(identity,multiply(inverse(X),Y))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c20,c28,c52]) ).
cnf(c329,plain,
least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(least_upper_bound(X,Z),Y)) = greatest_lower_bound(least_upper_bound(X,Z),Y),
inference(equational,[status(thm)],[c5,c10,c56]) ).
cnf(c402,plain,
multiply(inverse(least_upper_bound(X,identity)),least_upper_bound(Y,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c20,c42]) ).
cnf(c554,plain,
least_upper_bound(X,multiply(least_upper_bound(Y,identity),greatest_lower_bound(X,Z))) = least_upper_bound(X,multiply(Y,greatest_lower_bound(X,Z))),
inference(equational,[status(thm)],[c42,c55]) ).
cnf(c771,plain,
least_upper_bound(X,greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z))) = greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c8,c329]) ).
cnf(c867,plain,
least_upper_bound(X,multiply(least_upper_bound(Y,identity),greatest_lower_bound(Z,X))) = least_upper_bound(X,multiply(Y,greatest_lower_bound(Z,X))),
inference(equational,[status(thm)],[c72,c554]) ).
cnf(c963,plain,
greatest_lower_bound(least_upper_bound(X,identity),least_upper_bound(Y,multiply(X,Y))) = multiply(least_upper_bound(X,identity),greatest_lower_bound(identity,Y)),
inference(equational,[status(thm)],[c130,c402]) ).
cnf(c964,plain,
multiply(least_upper_bound(X,identity),greatest_lower_bound(identity,X)) = X,
inference(equational,[status(thm)],[c97,c771,c867,c963]) ).
cnf(c969,plain,
multiply(least_upper_bound(X,identity),greatest_lower_bound(X,identity)) = X,
inference(equational,[status(thm)],[c4,c964]) ).
cnf(g1,plain,
a = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(equational,[status(thm)],[c969]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP167-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:13:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 104.43/104.61 % SZS status Unsatisfiable
% 104.43/104.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------