%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP174-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:32:58 PM UTC 2026
% Result : Unsatisfiable 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
greatest_lower_bound(identity,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
identity != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
greatest_lower_bound(identity,a) = a,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
identity != a,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f38,plain,
least_upper_bound(identity,a) = identity,
inference(paramodulation,[status(thm)],[f34,f28]) ).
fof(f125,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f20,f21]) ).
fof(f129,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f19,f125]) ).
fof(f131,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f129,f129]) ).
fof(f132,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f20,f129]) ).
fof(f135,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f131,f132]) ).
fof(f171,plain,
least_upper_bound(identity,inverse(a)) = identity,
inference(paramodulation,[status(thm)],[f35,f28]) ).
fof(f180,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f20,f131]) ).
fof(f597,plain,
! [X0,X1] : multiply(X0,least_upper_bound(X1,inverse(X0))) = least_upper_bound(multiply(X0,X1),identity),
inference(paramodulation,[status(thm)],[f180,f30]) ).
fof(f619,plain,
! [X0,X1] : multiply(X0,least_upper_bound(X1,inverse(X0))) = least_upper_bound(identity,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f597]) ).
fof(f1159,plain,
multiply(a,identity) = least_upper_bound(identity,multiply(a,identity)),
inference(paramodulation,[status(thm)],[f171,f619]) ).
fof(f1190,plain,
a = least_upper_bound(identity,multiply(a,identity)),
inference(forward_demodulation,[status(thm)],[f135,f1159]) ).
fof(f1191,plain,
a = least_upper_bound(identity,a),
inference(forward_demodulation,[status(thm)],[f135,f1190]) ).
fof(f1192,plain,
a = identity,
inference(forward_demodulation,[status(thm)],[f38,f1191]) ).
fof(f1193,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1192,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP174-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n008.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Sun Sep 20 20:05:06 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.38 % Drodi V4.1.1
% 0.14/10.41 % Refutation found
% 0.14/10.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.42 % Elapsed time: 0.042158 seconds
% 0.14/10.42 % CPU time: 0.208654 seconds
% 0.14/10.42 % Total memory used: 7.760 MB
% 0.14/10.42 % Net memory used: 7.550 MB
%------------------------------------------------------------------------------