%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:36:09 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.78s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n005.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 20:03:39 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.78 % Refutation found
% 0.14/5.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.78 % SZS output start CNFRefutation for theBenchmark
% 0.14/5.78 fof(f1,axiom,(
% 0.14/5.78 (![X]: (multiply(identity,X) = X ))),
% 0.14/5.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.78 fof(f2,axiom,(
% 0.14/5.78 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.14/5.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.78 fof(f3,axiom,(
% 0.14/5.78 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.14/5.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.78 fof(f5,axiom,(
% 0.14/5.78 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 0.14/5.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.78 fof(f12,axiom,(
% 0.14/5.78 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 0.14/5.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.78 fof(f14,axiom,(
% 0.14/5.78 (![Y,Z,X]: (multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ))),
% 0.14/5.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.78 fof(f16,hypothesis,(
% 0.14/5.78 least_upper_bound(inverse(a),inverse(b)) = inverse(b) ),
% 0.14/5.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.78 fof(f17,negated_conjecture,(
% 0.14/5.78 least_upper_bound(a,b) != a ),
% 0.14/5.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.78 fof(f18,plain,(
% 0.14/5.78 ![X0]: (multiply(identity,X0)=X0)),
% 0.14/5.78 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/5.78 fof(f19,plain,(
% 0.14/5.78 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.14/5.78 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/5.78 fof(f20,plain,(
% 0.14/5.78 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.14/5.78 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/5.78 fof(f22,plain,(
% 0.14/5.78 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 0.14/5.78 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/5.78 fof(f29,plain,(
% 0.14/5.78 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 0.14/5.78 inference(cnf_transformation,[status(thm)],[f12])).
% 0.14/5.78 fof(f31,plain,(
% 0.14/5.78 ![X0,X1,X2]: (multiply(least_upper_bound(X0,X1),X2)=least_upper_bound(multiply(X0,X2),multiply(X1,X2)))),
% 0.14/5.78 inference(cnf_transformation,[status(thm)],[f14])).
% 0.14/5.78 fof(f33,plain,(
% 0.14/5.78 least_upper_bound(inverse(a),inverse(b))=inverse(b)),
% 0.14/5.78 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/5.78 fof(f34,plain,(
% 0.14/5.78 ~least_upper_bound(a,b)=a),
% 0.14/5.78 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/5.78 fof(f35,definition,(
% 0.14/5.78 sF0_fnc=least_upper_bound(a,b)),
% 0.14/5.78 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.14/5.78 fof(f36,plain,(
% 0.14/5.78 ~sF0_fnc=a),
% 0.14/5.78 inference(definition_folding,[],[f34,f35])).
% 0.14/5.78 fof(f38,plain,(
% 0.14/5.78 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.14/5.78 inference(paramodulation,[status(thm)],[f19,f20])).
% 0.14/5.78 fof(f42,plain,(
% 0.14/5.78 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.14/5.78 inference(forward_demodulation,[status(thm)],[f18,f38])).
% 0.14/5.78 fof(f112,plain,(
% 0.14/5.78 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(multiply(inverse(X0),X1),identity))),
% 0.14/5.78 inference(paramodulation,[status(thm)],[f19,f29])).
% 0.14/5.78 fof(f126,plain,(
% 0.14/5.78 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(identity,multiply(inverse(X0),X1)))),
% 0.14/5.78 inference(forward_demodulation,[status(thm)],[f22,f112])).
% 0.14/5.78 fof(f168,plain,(
% 0.14/5.78 ![X0,X1]: (multiply(least_upper_bound(X0,inverse(X1)),X1)=least_upper_bound(multiply(X0,X1),identity))),
% 0.14/5.78 inference(paramodulation,[status(thm)],[f19,f31])).
% 0.14/5.78 fof(f177,plain,(
% 0.14/5.78 ![X0,X1]: (multiply(least_upper_bound(X0,inverse(X1)),X1)=least_upper_bound(identity,multiply(X0,X1)))),
% 0.14/5.78 inference(forward_demodulation,[status(thm)],[f22,f168])).
% 0.14/5.78 fof(f236,plain,(
% 0.14/5.78 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 0.14/5.78 inference(paramodulation,[status(thm)],[f19,f42])).
% 0.14/5.78 fof(f4002,plain,(
% 0.14/5.78 multiply(inverse(b),b)=least_upper_bound(identity,multiply(inverse(a),b))),
% 0.14/5.78 inference(paramodulation,[status(thm)],[f33,f177])).
% 0.14/5.78 fof(f4037,plain,(
% 0.14/5.78 identity=least_upper_bound(identity,multiply(inverse(a),b))),
% 0.14/5.78 inference(forward_demodulation,[status(thm)],[f19,f4002])).
% 0.14/5.78 fof(f4038,plain,(
% 0.14/5.78 identity=multiply(inverse(a),least_upper_bound(b,a))),
% 0.14/5.79 inference(forward_demodulation,[status(thm)],[f126,f4037])).
% 0.14/5.79 fof(f4039,plain,(
% 0.14/5.79 identity=multiply(inverse(a),least_upper_bound(a,b))),
% 0.14/5.79 inference(forward_demodulation,[status(thm)],[f22,f4038])).
% 0.14/5.79 fof(f4040,plain,(
% 0.14/5.79 identity=multiply(inverse(a),sF0_fnc)),
% 0.14/5.79 inference(forward_demodulation,[status(thm)],[f35,f4039])).
% 0.14/5.79 fof(f4108,plain,(
% 0.14/5.79 sF0_fnc=multiply(inverse(inverse(a)),identity)),
% 0.14/5.79 inference(paramodulation,[status(thm)],[f4040,f42])).
% 0.14/5.79 fof(f4140,plain,(
% 0.14/5.79 sF0_fnc=a),
% 0.14/5.79 inference(forward_demodulation,[status(thm)],[f236,f4108])).
% 0.14/5.79 fof(f4141,plain,(
% 0.14/5.79 $false),
% 0.14/5.79 inference(forward_subsumption_resolution,[status(thm)],[f4140,f36])).
% 0.14/5.79 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.80 % Elapsed time: 0.408536 seconds
% 0.14/5.80 % CPU time: 3.151564 seconds
% 0.14/5.80 % Total memory used: 52.781 MB
% 0.14/5.80 % Net memory used: 51.833 MB
%------------------------------------------------------------------------------