%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:36:13 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.31s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 20:05:08 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.03/0.31 % Refutation found
% 0.03/0.31 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.31 % SZS output start CNFRefutation for theBenchmark
% 0.03/0.31 fof(f1,axiom,(
% 0.03/0.31 (![X]: (multiply(identity,X) = X ))),
% 0.03/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.31 fof(f2,axiom,(
% 0.03/0.31 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.03/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.31 fof(f3,axiom,(
% 0.03/0.31 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.03/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.31 fof(f5,axiom,(
% 0.03/0.31 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 0.03/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.31 fof(f12,axiom,(
% 0.03/0.31 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 0.03/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.31 fof(f16,negated_conjecture,(
% 0.03/0.31 least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)) ),
% 0.03/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.31 fof(f17,plain,(
% 0.03/0.31 ![X0]: (multiply(identity,X0)=X0)),
% 0.03/0.31 inference(cnf_transformation,[status(thm)],[f1])).
% 0.03/0.31 fof(f18,plain,(
% 0.03/0.31 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.03/0.31 inference(cnf_transformation,[status(thm)],[f2])).
% 0.03/0.31 fof(f19,plain,(
% 0.03/0.31 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.03/0.31 inference(cnf_transformation,[status(thm)],[f3])).
% 0.03/0.31 fof(f21,plain,(
% 0.03/0.31 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 0.03/0.31 inference(cnf_transformation,[status(thm)],[f5])).
% 0.03/0.31 fof(f28,plain,(
% 0.03/0.31 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 0.03/0.31 inference(cnf_transformation,[status(thm)],[f12])).
% 0.03/0.31 fof(f32,plain,(
% 0.03/0.31 ~least_upper_bound(multiply(a,b),identity)=multiply(a,least_upper_bound(inverse(a),b))),
% 0.03/0.31 inference(cnf_transformation,[status(thm)],[f16])).
% 0.03/0.31 fof(f40,plain,(
% 0.03/0.31 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.03/0.31 inference(paramodulation,[status(thm)],[f18,f19])).
% 0.03/0.31 fof(f44,plain,(
% 0.03/0.31 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.03/0.31 inference(forward_demodulation,[status(thm)],[f17,f40])).
% 0.03/0.31 fof(f52,plain,(
% 0.03/0.31 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 0.03/0.31 inference(paramodulation,[status(thm)],[f44,f44])).
% 0.03/0.31 fof(f71,plain,(
% 0.03/0.31 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 0.03/0.31 inference(paramodulation,[status(thm)],[f18,f52])).
% 0.03/0.31 fof(f137,plain,(
% 0.03/0.31 ![X0,X1]: (multiply(X0,least_upper_bound(inverse(X0),X1))=least_upper_bound(identity,multiply(X0,X1)))),
% 0.03/0.31 inference(paramodulation,[status(thm)],[f71,f28])).
% 0.03/0.31 fof(f154,plain,(
% 0.03/0.31 ~least_upper_bound(multiply(a,b),identity)=least_upper_bound(identity,multiply(a,b))),
% 0.03/0.31 inference(backward_demodulation,[status(thm)],[f137,f32])).
% 0.03/0.31 fof(f160,plain,(
% 0.03/0.31 $false),
% 0.03/0.31 inference(forward_subsumption_resolution,[status(thm)],[f154,f21])).
% 0.03/0.31 % SZS output end CNFRefutation for theBenchmark.p
% 0.03/0.32 % Elapsed time: 0.017900 seconds
% 0.03/0.32 % CPU time: 0.040584 seconds
% 0.03/0.32 % Total memory used: 2.826 MB
% 0.03/0.32 % Net memory used: 2.809 MB
%------------------------------------------------------------------------------