%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP190-1 : 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 : 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 12:36:14 PM UTC 2026
% Result : Unsatisfiable 5.69s 1.29s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP190-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % Computer : n008.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Sun Sep 20 20:06:39 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 5.69/1.29 % Refutation found
% 5.69/1.29 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.69/1.29 % SZS output start CNFRefutation for theBenchmark
% 5.69/1.29 fof(f1,axiom,(
% 5.69/1.29 (![X]: (multiply(identity,X) = X ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f2,axiom,(
% 5.69/1.29 (![X]: (multiply(inverse(X),X) = identity ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f3,axiom,(
% 5.69/1.29 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f4,axiom,(
% 5.69/1.29 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f5,axiom,(
% 5.69/1.29 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f7,axiom,(
% 5.69/1.29 (![X,Y,Z]: (least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f10,axiom,(
% 5.69/1.29 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f11,axiom,(
% 5.69/1.29 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f12,axiom,(
% 5.69/1.29 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f14,axiom,(
% 5.69/1.29 (![Y,Z,X]: (multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ))),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f16,hypothesis,(
% 5.69/1.29 least_upper_bound(a,b) = a ),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f17,negated_conjecture,(
% 5.69/1.29 least_upper_bound(inverse(a),inverse(b)) != inverse(b) ),
% 5.69/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.69/1.29 fof(f18,plain,(
% 5.69/1.29 ![X0]: (multiply(identity,X0)=X0)),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f1])).
% 5.69/1.29 fof(f19,plain,(
% 5.69/1.29 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f2])).
% 5.69/1.29 fof(f20,plain,(
% 5.69/1.29 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f3])).
% 5.69/1.29 fof(f21,plain,(
% 5.69/1.29 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f4])).
% 5.69/1.29 fof(f22,plain,(
% 5.69/1.29 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f5])).
% 5.69/1.29 fof(f24,plain,(
% 5.69/1.29 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,X2))=least_upper_bound(least_upper_bound(X0,X1),X2))),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 5.69/1.29 fof(f27,plain,(
% 5.69/1.29 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 5.69/1.29 fof(f28,plain,(
% 5.69/1.29 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 5.69/1.29 fof(f29,plain,(
% 5.69/1.29 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 5.69/1.29 fof(f31,plain,(
% 5.69/1.29 ![X0,X1,X2]: (multiply(least_upper_bound(X0,X1),X2)=least_upper_bound(multiply(X0,X2),multiply(X1,X2)))),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 5.69/1.29 fof(f33,plain,(
% 5.69/1.29 least_upper_bound(a,b)=a),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f16])).
% 5.69/1.29 fof(f34,plain,(
% 5.69/1.29 ~least_upper_bound(inverse(a),inverse(b))=inverse(b)),
% 5.69/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 5.69/1.29 fof(f35,definition,(
% 5.69/1.29 sF1_fnc=inverse(a)),
% 5.69/1.29 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 5.69/1.29 fof(f36,definition,(
% 5.69/1.29 sF2_fnc=inverse(b)),
% 5.69/1.29 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 5.69/1.29 fof(f37,definition,(
% 5.69/1.29 sF0_fnc=least_upper_bound(sF1_fnc,sF2_fnc)),
% 5.69/1.29 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 5.69/1.29 fof(f38,plain,(
% 5.69/1.29 ~sF0_fnc=sF2_fnc),
% 5.69/1.29 inference(definition_folding,[],[f34,f37,f36,f35])).
% 5.69/1.29 fof(f43,plain,(
% 5.69/1.29 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,X2))=least_upper_bound(X2,least_upper_bound(X0,X1)))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f22,f24])).
% 5.69/1.29 fof(f55,plain,(
% 5.69/1.29 multiply(sF2_fnc,b)=identity),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f36,f19])).
% 5.69/1.29 fof(f56,plain,(
% 5.69/1.29 multiply(sF1_fnc,a)=identity),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f35,f19])).
% 5.69/1.29 fof(f58,plain,(
% 5.69/1.29 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f19,f20])).
% 5.69/1.29 fof(f62,plain,(
% 5.69/1.29 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f18,f58])).
% 5.69/1.29 fof(f79,plain,(
% 5.69/1.29 ![X0]: (multiply(identity,X0)=multiply(sF2_fnc,multiply(b,X0)))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f55,f20])).
% 5.69/1.29 fof(f80,plain,(
% 5.69/1.29 ![X0]: (X0=multiply(sF2_fnc,multiply(b,X0)))),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f18,f79])).
% 5.69/1.29 fof(f93,plain,(
% 5.69/1.29 ![X0]: (multiply(sF1_fnc,least_upper_bound(X0,a))=least_upper_bound(multiply(sF1_fnc,X0),identity))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f56,f29])).
% 5.69/1.29 fof(f120,plain,(
% 5.69/1.29 ![X0]: (multiply(least_upper_bound(X0,sF2_fnc),b)=least_upper_bound(multiply(X0,b),identity))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f55,f31])).
% 5.69/1.29 fof(f131,plain,(
% 5.69/1.29 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X0,X1),X2)))=least_upper_bound(X0,X1))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f24,f27])).
% 5.69/1.29 fof(f133,plain,(
% 5.69/1.29 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X1,X0))=X0)),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f21,f27])).
% 5.69/1.29 fof(f155,plain,(
% 5.69/1.29 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X1,X0))=X0)),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f22,f28])).
% 5.69/1.29 fof(f251,plain,(
% 5.69/1.29 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2))=least_upper_bound(X2,X0))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f133,f43])).
% 5.69/1.29 fof(f470,plain,(
% 5.69/1.29 greatest_lower_bound(b,a)=b),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f33,f155])).
% 5.69/1.29 fof(f500,plain,(
% 5.69/1.29 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f62,f62])).
% 5.69/1.29 fof(f501,plain,(
% 5.69/1.29 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f19,f62])).
% 5.69/1.29 fof(f514,plain,(
% 5.69/1.29 ![X0]: (X0=multiply(X0,identity))),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f500,f501])).
% 5.69/1.29 fof(f770,plain,(
% 5.69/1.29 greatest_lower_bound(a,b)=b),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f21,f470])).
% 5.69/1.29 fof(f2319,plain,(
% 5.69/1.29 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),greatest_lower_bound(X0,X2)))=least_upper_bound(X0,greatest_lower_bound(X1,X0)))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f133,f131])).
% 5.69/1.29 fof(f2424,plain,(
% 5.69/1.29 ![X0,X1,X2]: (least_upper_bound(greatest_lower_bound(X0,X1),X0)=least_upper_bound(X0,greatest_lower_bound(X2,X0)))),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f251,f2319])).
% 5.69/1.29 fof(f2427,plain,(
% 5.69/1.29 ![X0,X1]: (least_upper_bound(greatest_lower_bound(X0,X1),X0)=X0)),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f133,f2424])).
% 5.69/1.29 fof(f2632,plain,(
% 5.69/1.29 least_upper_bound(b,a)=a),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f770,f2427])).
% 5.69/1.29 fof(f5053,plain,(
% 5.69/1.29 multiply(least_upper_bound(sF1_fnc,sF2_fnc),b)=multiply(sF1_fnc,least_upper_bound(b,a))),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f93,f120])).
% 5.69/1.29 fof(f5087,plain,(
% 5.69/1.29 multiply(sF0_fnc,b)=multiply(sF1_fnc,least_upper_bound(b,a))),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f37,f5053])).
% 5.69/1.29 fof(f5088,plain,(
% 5.69/1.29 multiply(sF0_fnc,b)=multiply(sF1_fnc,a)),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f2632,f5087])).
% 5.69/1.29 fof(f5089,plain,(
% 5.69/1.29 multiply(sF0_fnc,b)=identity),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f56,f5088])).
% 5.69/1.29 fof(f5148,plain,(
% 5.69/1.29 b=multiply(inverse(sF0_fnc),identity)),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f5089,f62])).
% 5.69/1.29 fof(f5168,plain,(
% 5.69/1.29 b=inverse(sF0_fnc)),
% 5.69/1.29 inference(forward_demodulation,[status(thm)],[f514,f5148])).
% 5.69/1.29 fof(f5210,plain,(
% 5.69/1.29 multiply(b,sF0_fnc)=identity),
% 5.69/1.29 inference(paramodulation,[status(thm)],[f5168,f19])).
% 5.69/1.31 fof(f5227,plain,(
% 5.69/1.31 sF0_fnc=multiply(sF2_fnc,identity)),
% 5.69/1.31 inference(paramodulation,[status(thm)],[f5210,f80])).
% 5.69/1.31 fof(f5256,plain,(
% 5.69/1.31 sF0_fnc=sF2_fnc),
% 5.69/1.31 inference(forward_demodulation,[status(thm)],[f514,f5227])).
% 5.69/1.31 fof(f5257,plain,(
% 5.69/1.31 $false),
% 5.69/1.31 inference(forward_subsumption_resolution,[status(thm)],[f5256,f38])).
% 5.69/1.31 % SZS output end CNFRefutation for theBenchmark.p
% 0.73/1.35 % Elapsed time: 0.848304 seconds
% 0.73/1.35 % CPU time: 6.288814 seconds
% 0.73/1.35 % Total memory used: 66.812 MB
% 0.73/1.35 % Net memory used: 65.664 MB
%------------------------------------------------------------------------------