%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP181-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.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 134.11s 134.19s
% Output : CNFRefutation 134.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 12 RR)
% Number of literals : 63 ( 62 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != b,
file('theBenchmark.p',prove_p12) ).
cnf(c1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p12_1) ).
cnf(c3,axiom,
greatest_lower_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_gld) ).
cnf(c4,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c5,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',p12_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,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('theBenchmark.p',p12_4) ).
cnf(c9,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('theBenchmark.p',p12_5) ).
cnf(c11,plain,
least_upper_bound(b,c) = least_upper_bound(a,c),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c13,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c5,c12]) ).
cnf(c14,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c15,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c16,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(equational,[status(thm)],[c6,c15]) ).
cnf(c17,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c18,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('theBenchmark.p',p12_3) ).
cnf(c19,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(multiply(X,identity)) = inverse(X),
inference(equational,[status(thm)],[c1,c4,c19]) ).
cnf(c21,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c5,c20]) ).
cnf(c22,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(c23,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c22]) ).
cnf(c24,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(c25,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c24]) ).
cnf(c26,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c29,plain,
greatest_lower_bound(X,greatest_lower_bound(X,Y)) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c33,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c6,c25]) ).
cnf(c35,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c4,c12,c26]) ).
cnf(c40,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c4,c13,c26]) ).
cnf(c53,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c54,plain,
greatest_lower_bound(multiply(X,Y),multiply(Z,Y)) = multiply(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c53]) ).
cnf(c55,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(greatest_lower_bound(identity,Y),X),
inference(equational,[status(thm)],[c4,c54]) ).
cnf(c56,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(greatest_lower_bound(Y,identity),X),
inference(equational,[status(thm)],[c4,c7,c54]) ).
cnf(c59,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c60,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c59]) ).
cnf(c63,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c64,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c63]) ).
cnf(c65,plain,
greatest_lower_bound(X,multiply(X,Y)) = multiply(X,greatest_lower_bound(identity,Y)),
inference(equational,[status(thm)],[c21,c64]) ).
cnf(c68,plain,
multiply(inverse(X),greatest_lower_bound(Y,X)) = greatest_lower_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c7,c12,c64]) ).
cnf(c69,plain,
multiply(inverse(X),least_upper_bound(X,Y)) = least_upper_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c12,c60]) ).
cnf(c70,plain,
multiply(inverse(X),least_upper_bound(Y,X)) = least_upper_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c6,c12,c60]) ).
cnf(c71,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Y),Z)) = least_upper_bound(X,Z),
inference(equational,[status(thm)],[c14,c25]) ).
cnf(c72,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c15,c23]) ).
cnf(c105,plain,
least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(Z,X))) = least_upper_bound(Y,X),
inference(equational,[status(thm)],[c17,c33]) ).
cnf(c115,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(equational,[status(thm)],[c9,c68]) ).
cnf(c120,plain,
least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a)),
inference(equational,[status(thm)],[c11,c70]) ).
cnf(c134,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(identity,Y),X)) = greatest_lower_bound(X,multiply(Y,X)),
inference(equational,[status(thm)],[c29,c55]) ).
cnf(c143,plain,
greatest_lower_bound(X,multiply(X,least_upper_bound(identity,Y))) = X,
inference(equational,[status(thm)],[c15,c21,c65]) ).
cnf(c199,plain,
multiply(X,least_upper_bound(identity,multiply(inverse(X),Y))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c5,c35,c69]) ).
cnf(c495,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,c16,c71]) ).
cnf(c589,plain,
multiply(inverse(greatest_lower_bound(X,identity)),greatest_lower_bound(Y,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c35,c56]) ).
cnf(c841,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)],[c56,c72]) ).
cnf(c932,plain,
greatest_lower_bound(X,multiply(inverse(c),multiply(b,X))) = greatest_lower_bound(X,multiply(inverse(c),multiply(a,X))),
inference(equational,[status(thm)],[c26,c115,c134]) ).
cnf(c1148,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)],[c14,c495]) ).
cnf(c1317,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)],[c105,c841]) ).
cnf(c1391,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)],[c199,c589]) ).
cnf(c1392,plain,
multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X)) = X,
inference(equational,[status(thm)],[c143,c1148,c1317,c1391]) ).
cnf(c1404,plain,
multiply(greatest_lower_bound(identity,X),least_upper_bound(identity,X)) = X,
inference(equational,[status(thm)],[c7,c1392]) ).
cnf(c1405,plain,
multiply(inverse(c),b) = multiply(inverse(c),a),
inference(equational,[status(thm)],[c21,c120,c932,c1404]) ).
cnf(c1406,plain,
b = a,
inference(equational,[status(thm)],[c40,c1405]) ).
cnf(g1,plain,
a = b,
inference(equational,[status(thm)],[c1406]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP181-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.32 % Computer : n012.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon Jul 14 08:14:19 EDT 2025
% 0.13/0.32 % CPUTime :
% 134.11/134.19 % SZS status Unsatisfiable
% 134.11/134.19 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------