%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP166-2 : 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 : n018.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 12:36:08 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 20:05:14 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.38 fof(f1,axiom,(
% 0.12/0.38 (![X]: (multiply(identity,X) = X ))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f2,axiom,(
% 0.12/0.38 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f3,axiom,(
% 0.12/0.38 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f4,axiom,(
% 0.12/0.38 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f13,axiom,(
% 0.12/0.38 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f17,hypothesis,(
% 0.12/0.38 greatest_lower_bound(b,identity) = identity ),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f18,negated_conjecture,(
% 0.12/0.38 greatest_lower_bound(a,multiply(a,b)) != a ),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f19,plain,(
% 0.12/0.38 ![X0]: (multiply(identity,X0)=X0)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.38 fof(f20,plain,(
% 0.12/0.38 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.38 fof(f21,plain,(
% 0.12/0.38 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.38 fof(f22,plain,(
% 0.12/0.38 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.38 fof(f31,plain,(
% 0.12/0.38 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f13])).
% 0.12/0.38 fof(f35,plain,(
% 0.12/0.38 greatest_lower_bound(b,identity)=identity),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.38 fof(f36,plain,(
% 0.12/0.38 ~greatest_lower_bound(a,multiply(a,b))=a),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f18])).
% 0.12/0.38 fof(f37,definition,(
% 0.12/0.38 sF1_fnc=multiply(a,b)),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.12/0.38 fof(f38,definition,(
% 0.12/0.38 sF0_fnc=greatest_lower_bound(a,sF1_fnc)),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.12/0.38 fof(f39,plain,(
% 0.12/0.38 ~sF0_fnc=a),
% 0.12/0.38 inference(definition_folding,[],[f36,f38,f37])).
% 0.12/0.38 fof(f256,plain,(
% 0.12/0.38 ![X0]: (multiply(a,greatest_lower_bound(b,X0))=greatest_lower_bound(sF1_fnc,multiply(a,X0)))),
% 0.12/0.38 inference(paramodulation,[status(thm)],[f37,f31])).
% 0.12/0.38 fof(f320,plain,(
% 0.12/0.38 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.12/0.38 inference(paramodulation,[status(thm)],[f20,f21])).
% 0.12/0.38 fof(f323,plain,(
% 0.12/0.38 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f19,f320])).
% 0.12/0.38 fof(f433,plain,(
% 0.12/0.38 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 0.12/0.38 inference(paramodulation,[status(thm)],[f323,f323])).
% 0.12/0.38 fof(f434,plain,(
% 0.12/0.38 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 0.12/0.38 inference(paramodulation,[status(thm)],[f20,f323])).
% 0.12/0.38 fof(f444,plain,(
% 0.12/0.38 ![X0]: (X0=multiply(X0,identity))),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f433,f434])).
% 0.12/0.38 fof(f710,plain,(
% 0.12/0.38 multiply(a,identity)=greatest_lower_bound(sF1_fnc,multiply(a,identity))),
% 0.12/0.38 inference(paramodulation,[status(thm)],[f35,f256])).
% 0.12/0.38 fof(f732,plain,(
% 0.12/0.38 a=greatest_lower_bound(sF1_fnc,multiply(a,identity))),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f444,f710])).
% 0.12/0.38 fof(f733,plain,(
% 0.12/0.38 a=greatest_lower_bound(sF1_fnc,a)),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f444,f732])).
% 0.12/0.38 fof(f734,plain,(
% 0.12/0.38 sF0_fnc=a),
% 0.12/0.38 inference(backward_demodulation,[status(thm)],[f735,f38])).
% 0.12/0.38 fof(f735,plain,(
% 0.12/0.38 a=greatest_lower_bound(a,sF1_fnc)),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f22,f733])).
% 0.12/0.38 fof(f756,plain,(
% 0.12/0.38 $false),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f734,f39])).
% 0.12/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.39 % Elapsed time: 0.036874 seconds
% 0.12/0.39 % CPU time: 0.155370 seconds
% 0.12/0.39 % Total memory used: 5.720 MB
% 0.12/0.39 % Net memory used: 5.687 MB
%------------------------------------------------------------------------------