%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP181-1 : 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 06:43:41 AM UTC 2025
% Result : Unsatisfiable 102.47s 102.56s
% Output : CNFRefutation 102.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% 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 : 115 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != b,
file('theBenchmark.p',prove_p12) ).
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,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('theBenchmark.p',p12_1) ).
cnf(c7,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
inference(equational,[status(thm)],[c6]) ).
cnf(c8,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('theBenchmark.p',p12_2) ).
cnf(c9,plain,
least_upper_bound(b,c) = least_upper_bound(a,c),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c11,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c12,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c13,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(equational,[status(thm)],[c5,c12]) ).
cnf(c15,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(c16,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c15]) ).
cnf(c17,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c18,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(c19,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c18]) ).
cnf(c25,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c26,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c10,c17]) ).
cnf(c28,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c10,c26]) ).
cnf(c31,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c26]) ).
cnf(c32,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c28,c31]) ).
cnf(c34,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c28,c32]) ).
cnf(c35,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c10,c31]) ).
cnf(c41,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c26,c31]) ).
cnf(c42,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c43,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c42]) ).
cnf(c46,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c47,plain,
greatest_lower_bound(multiply(X,Y),multiply(Z,Y)) = multiply(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c46]) ).
cnf(c48,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(greatest_lower_bound(identity,Y),X),
inference(equational,[status(thm)],[c3,c47]) ).
cnf(c49,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(greatest_lower_bound(Y,identity),X),
inference(equational,[status(thm)],[c3,c4,c47]) ).
cnf(c52,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c53,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c52]) ).
cnf(c54,plain,
greatest_lower_bound(X,multiply(X,Y)) = multiply(X,greatest_lower_bound(identity,Y)),
inference(equational,[status(thm)],[c28,c34,c53]) ).
cnf(c56,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c57,plain,
least_upper_bound(multiply(X,Y),multiply(Z,Y)) = multiply(least_upper_bound(X,Z),Y),
inference(equational,[status(thm)],[c56]) ).
cnf(c64,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c12,c19]) ).
cnf(c65,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Y),Z)) = least_upper_bound(X,Z),
inference(equational,[status(thm)],[c11,c16]) ).
cnf(c66,plain,
multiply(inverse(X),least_upper_bound(X,Y)) = least_upper_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c10,c43]) ).
cnf(c75,plain,
greatest_lower_bound(X,multiply(least_upper_bound(identity,Y),X)) = X,
inference(equational,[status(thm)],[c3,c12,c48]) ).
cnf(c84,plain,
least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(X,Z))) = least_upper_bound(Y,X),
inference(equational,[status(thm)],[c11,c25]) ).
cnf(c124,plain,
greatest_lower_bound(X,multiply(X,least_upper_bound(identity,Y))) = X,
inference(equational,[status(thm)],[c32,c54,c75]) ).
cnf(c156,plain,
multiply(X,least_upper_bound(identity,multiply(inverse(X),Y))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c26,c34,c66]) ).
cnf(c157,plain,
multiply(least_upper_bound(X,Y),inverse(Y)) = least_upper_bound(identity,multiply(X,inverse(Y))),
inference(equational,[status(thm)],[c5,c35,c57]) ).
cnf(c158,plain,
multiply(greatest_lower_bound(X,Y),inverse(Y)) = greatest_lower_bound(identity,multiply(X,inverse(Y))),
inference(equational,[status(thm)],[c4,c35,c47]) ).
cnf(c201,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c17,c35]) ).
cnf(c202,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c26,c32,c201]) ).
cnf(c204,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference(equational,[status(thm)],[c41,c202]) ).
cnf(c291,plain,
greatest_lower_bound(identity,multiply(b,inverse(c))) = greatest_lower_bound(identity,multiply(a,inverse(c))),
inference(equational,[status(thm)],[c7,c158]) ).
cnf(c296,plain,
least_upper_bound(identity,multiply(b,inverse(c))) = least_upper_bound(identity,multiply(a,inverse(c))),
inference(equational,[status(thm)],[c9,c157]) ).
cnf(c384,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,c13,c65]) ).
cnf(c458,plain,
multiply(inverse(greatest_lower_bound(X,identity)),greatest_lower_bound(Y,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c26,c49]) ).
cnf(c669,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)],[c49,c64]) ).
cnf(c913,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)],[c11,c384]) ).
cnf(c1033,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)],[c84,c669]) ).
cnf(c1143,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)],[c156,c458]) ).
cnf(c1144,plain,
multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X)) = X,
inference(equational,[status(thm)],[c124,c913,c1033,c1143]) ).
cnf(c1150,plain,
multiply(greatest_lower_bound(identity,X),least_upper_bound(identity,X)) = X,
inference(equational,[status(thm)],[c4,c1144]) ).
cnf(c1151,plain,
multiply(b,inverse(c)) = multiply(a,inverse(c)),
inference(equational,[status(thm)],[c291,c296,c1150]) ).
cnf(c1152,plain,
inverse(b) = inverse(a),
inference(equational,[status(thm)],[c26,c202,c204,c1151]) ).
cnf(c1153,plain,
b = a,
inference(equational,[status(thm)],[c34,c1152]) ).
cnf(g1,plain,
a = b,
inference(equational,[status(thm)],[c1153]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP181-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n010.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 08:14:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 102.47/102.56 % SZS status Unsatisfiable
% 102.47/102.56 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------