%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP172-2 : 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 : n003.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 12:36:10 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n003.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 20 20:05:00 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f1,axiom,(
% 0.09/0.39 (![X]: (multiply(identity,X) = X ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f2,axiom,(
% 0.09/0.39 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f3,axiom,(
% 0.09/0.39 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f4,axiom,(
% 0.09/0.39 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f5,axiom,(
% 0.09/0.39 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f6,axiom,(
% 0.09/0.39 (![X,Y,Z]: (greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f10,axiom,(
% 0.09/0.39 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f11,axiom,(
% 0.09/0.39 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f12,axiom,(
% 0.09/0.39 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f16,hypothesis,(
% 0.09/0.39 greatest_lower_bound(identity,a) = identity ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f17,hypothesis,(
% 0.09/0.39 greatest_lower_bound(identity,b) = identity ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f18,negated_conjecture,(
% 0.09/0.39 least_upper_bound(identity,multiply(a,b)) != multiply(a,b) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f19,plain,(
% 0.09/0.39 ![X0]: (multiply(identity,X0)=X0)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.39 fof(f20,plain,(
% 0.09/0.39 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/0.39 fof(f21,plain,(
% 0.09/0.39 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.39 fof(f22,plain,(
% 0.09/0.39 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.09/0.39 fof(f23,plain,(
% 0.09/0.39 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.09/0.39 fof(f24,plain,(
% 0.09/0.39 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(greatest_lower_bound(X0,X1),X2))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.09/0.39 fof(f28,plain,(
% 0.09/0.39 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/0.39 fof(f29,plain,(
% 0.09/0.39 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/0.39 fof(f30,plain,(
% 0.09/0.39 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.39 fof(f34,plain,(
% 0.09/0.39 greatest_lower_bound(identity,a)=identity),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f16])).
% 0.09/0.39 fof(f35,plain,(
% 0.09/0.39 greatest_lower_bound(identity,b)=identity),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.39 fof(f36,plain,(
% 0.09/0.39 ~least_upper_bound(identity,multiply(a,b))=multiply(a,b)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.39 fof(f37,definition,(
% 0.09/0.39 sF1_fnc=multiply(a,b)),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.09/0.39 fof(f38,definition,(
% 0.09/0.39 sF0_fnc=least_upper_bound(identity,sF1_fnc)),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.09/0.39 fof(f39,plain,(
% 0.09/0.39 ~sF0_fnc=sF1_fnc),
% 0.09/0.39 inference(definition_folding,[],[f36,f38,f37])).
% 0.09/0.39 fof(f51,plain,(
% 0.09/0.39 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f20,f21])).
% 0.09/0.39 fof(f52,plain,(
% 0.09/0.39 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f19,f51])).
% 0.09/0.39 fof(f56,plain,(
% 0.09/0.39 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X1,X0))=X0)),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f23,f29])).
% 0.09/0.39 fof(f70,plain,(
% 0.09/0.39 identity=greatest_lower_bound(b,identity)),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f35,f22])).
% 0.09/0.39 fof(f80,plain,(
% 0.09/0.39 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X1,X0))=X0)),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f22,f28])).
% 0.09/0.39 fof(f92,plain,(
% 0.09/0.39 ![X0]: (greatest_lower_bound(identity,greatest_lower_bound(a,X0))=greatest_lower_bound(identity,X0))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f34,f24])).
% 0.09/0.39 fof(f138,plain,(
% 0.09/0.39 least_upper_bound(b,identity)=b),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f70,f28])).
% 0.09/0.39 fof(f154,plain,(
% 0.09/0.39 ![X0]: (multiply(a,least_upper_bound(b,X0))=least_upper_bound(sF1_fnc,multiply(a,X0)))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f37,f30])).
% 0.09/0.39 fof(f240,plain,(
% 0.09/0.39 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f52,f52])).
% 0.09/0.39 fof(f241,plain,(
% 0.09/0.39 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f20,f52])).
% 0.09/0.39 fof(f251,plain,(
% 0.09/0.39 ![X0]: (X0=multiply(X0,identity))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f240,f241])).
% 0.09/0.39 fof(f426,plain,(
% 0.09/0.39 multiply(a,b)=least_upper_bound(sF1_fnc,multiply(a,identity))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f138,f154])).
% 0.09/0.39 fof(f442,plain,(
% 0.09/0.39 sF1_fnc=least_upper_bound(sF1_fnc,multiply(a,identity))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f37,f426])).
% 0.09/0.39 fof(f443,plain,(
% 0.09/0.39 sF1_fnc=least_upper_bound(sF1_fnc,a)),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f251,f442])).
% 0.09/0.39 fof(f463,plain,(
% 0.09/0.39 greatest_lower_bound(a,sF1_fnc)=a),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f443,f56])).
% 0.09/0.39 fof(f531,plain,(
% 0.09/0.39 greatest_lower_bound(identity,a)=greatest_lower_bound(identity,sF1_fnc)),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f463,f92])).
% 0.09/0.39 fof(f536,plain,(
% 0.09/0.39 identity=greatest_lower_bound(identity,sF1_fnc)),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f34,f531])).
% 0.09/0.39 fof(f540,plain,(
% 0.09/0.39 least_upper_bound(sF1_fnc,identity)=sF1_fnc),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f536,f80])).
% 0.09/0.39 fof(f545,plain,(
% 0.09/0.39 least_upper_bound(identity,sF1_fnc)=sF1_fnc),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f23,f540])).
% 0.09/0.39 fof(f553,plain,(
% 0.09/0.39 sF0_fnc=sF1_fnc),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f38,f545])).
% 0.09/0.39 fof(f554,plain,(
% 0.09/0.39 $false),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f553,f39])).
% 0.09/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.40 % Elapsed time: 0.055091 seconds
% 0.09/0.40 % CPU time: 0.257510 seconds
% 0.09/0.40 % Total memory used: 9.889 MB
% 0.09/0.40 % Net memory used: 9.810 MB
%------------------------------------------------------------------------------