%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP190-2 : 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 : n004.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 4.17s 1.01s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:05:51 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 4.17/1.01 % Refutation found
% 4.17/1.01 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.17/1.01 % SZS output start CNFRefutation for theBenchmark
% 4.17/1.01 fof(f1,axiom,(
% 4.17/1.01 (![X]: (multiply(identity,X) = X ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f2,axiom,(
% 4.17/1.01 (![X]: (multiply(inverse(X),X) = identity ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f3,axiom,(
% 4.17/1.01 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f5,axiom,(
% 4.17/1.01 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f6,axiom,(
% 4.17/1.01 (![X,Y,Z]: (greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f9,axiom,(
% 4.17/1.01 (![X]: (greatest_lower_bound(X,X) = X ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f11,axiom,(
% 4.17/1.01 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f13,axiom,(
% 4.17/1.01 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f15,axiom,(
% 4.17/1.01 (![Y,Z,X]: (multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ))),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f16,hypothesis,(
% 4.17/1.01 least_upper_bound(a,b) = a ),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f17,negated_conjecture,(
% 4.17/1.01 greatest_lower_bound(inverse(a),inverse(b)) != inverse(a) ),
% 4.17/1.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.17/1.01 fof(f18,plain,(
% 4.17/1.01 ![X0]: (multiply(identity,X0)=X0)),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f1])).
% 4.17/1.01 fof(f19,plain,(
% 4.17/1.01 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f2])).
% 4.17/1.01 fof(f20,plain,(
% 4.17/1.01 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f3])).
% 4.17/1.01 fof(f22,plain,(
% 4.17/1.01 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f5])).
% 4.17/1.01 fof(f23,plain,(
% 4.17/1.01 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(greatest_lower_bound(X0,X1),X2))),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f6])).
% 4.17/1.01 fof(f26,plain,(
% 4.17/1.01 ![X0]: (greatest_lower_bound(X0,X0)=X0)),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f9])).
% 4.17/1.01 fof(f28,plain,(
% 4.17/1.01 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f11])).
% 4.17/1.01 fof(f30,plain,(
% 4.17/1.01 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f13])).
% 4.17/1.01 fof(f32,plain,(
% 4.17/1.01 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,X1),X2)=greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)))),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f15])).
% 4.17/1.01 fof(f33,plain,(
% 4.17/1.01 least_upper_bound(a,b)=a),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f16])).
% 4.17/1.01 fof(f34,plain,(
% 4.17/1.01 ~greatest_lower_bound(inverse(a),inverse(b))=inverse(a)),
% 4.17/1.01 inference(cnf_transformation,[status(thm)],[f17])).
% 4.17/1.01 fof(f35,definition,(
% 4.17/1.01 sF1_fnc=inverse(a)),
% 4.17/1.01 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 4.17/1.01 fof(f36,definition,(
% 4.17/1.01 sF2_fnc=inverse(b)),
% 4.17/1.01 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 4.17/1.01 fof(f37,definition,(
% 4.17/1.01 sF0_fnc=greatest_lower_bound(sF1_fnc,sF2_fnc)),
% 4.17/1.01 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 4.17/1.01 fof(f38,plain,(
% 4.17/1.01 ~sF0_fnc=sF1_fnc),
% 4.17/1.01 inference(definition_folding,[],[f34,f37,f36,f35])).
% 4.17/1.01 fof(f49,plain,(
% 4.17/1.01 ![X0]: (greatest_lower_bound(sF1_fnc,greatest_lower_bound(sF2_fnc,X0))=greatest_lower_bound(sF0_fnc,X0))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f37,f23])).
% 4.17/1.01 fof(f62,plain,(
% 4.17/1.01 multiply(sF1_fnc,a)=identity),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f35,f19])).
% 4.17/1.01 fof(f71,plain,(
% 4.17/1.01 ![X0]: (multiply(identity,X0)=multiply(sF1_fnc,multiply(a,X0)))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f62,f20])).
% 4.17/1.01 fof(f73,plain,(
% 4.17/1.01 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f19,f20])).
% 4.17/1.01 fof(f77,plain,(
% 4.17/1.01 ![X0]: (X0=multiply(sF1_fnc,multiply(a,X0)))),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f18,f71])).
% 4.17/1.01 fof(f79,plain,(
% 4.17/1.01 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f18,f73])).
% 4.17/1.01 fof(f80,plain,(
% 4.17/1.01 a=least_upper_bound(b,a)),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f33,f22])).
% 4.17/1.01 fof(f118,plain,(
% 4.17/1.01 greatest_lower_bound(sF1_fnc,sF2_fnc)=greatest_lower_bound(sF0_fnc,sF2_fnc)),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f26,f49])).
% 4.17/1.01 fof(f122,plain,(
% 4.17/1.01 sF0_fnc=greatest_lower_bound(sF0_fnc,sF2_fnc)),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f37,f118])).
% 4.17/1.01 fof(f126,plain,(
% 4.17/1.01 greatest_lower_bound(b,a)=b),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f80,f28])).
% 4.17/1.01 fof(f139,plain,(
% 4.17/1.01 ![X0,X1]: (multiply(inverse(X0),greatest_lower_bound(X0,X1))=greatest_lower_bound(identity,multiply(inverse(X0),X1)))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f19,f30])).
% 4.17/1.01 fof(f165,plain,(
% 4.17/1.01 ![X0]: (multiply(greatest_lower_bound(sF1_fnc,X0),a)=greatest_lower_bound(identity,multiply(X0,a)))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f62,f32])).
% 4.17/1.01 fof(f716,plain,(
% 4.17/1.01 ![X0]: (multiply(a,X0)=multiply(inverse(sF1_fnc),X0))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f77,f79])).
% 4.17/1.01 fof(f720,plain,(
% 4.17/1.01 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f79,f79])).
% 4.17/1.01 fof(f721,plain,(
% 4.17/1.01 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f19,f79])).
% 4.17/1.01 fof(f736,plain,(
% 4.17/1.01 ![X0]: (X0=multiply(X0,identity))),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f720,f721])).
% 4.17/1.01 fof(f2546,plain,(
% 4.17/1.01 multiply(a,identity)=inverse(sF1_fnc)),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f736,f716])).
% 4.17/1.01 fof(f2561,plain,(
% 4.17/1.01 a=inverse(sF1_fnc)),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f736,f2546])).
% 4.17/1.01 fof(f2822,plain,(
% 4.17/1.01 multiply(inverse(b),b)=greatest_lower_bound(identity,multiply(inverse(b),a))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f126,f139])).
% 4.17/1.01 fof(f2827,plain,(
% 4.17/1.01 multiply(inverse(sF0_fnc),sF0_fnc)=greatest_lower_bound(identity,multiply(inverse(sF0_fnc),sF2_fnc))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f122,f139])).
% 4.17/1.01 fof(f2834,plain,(
% 4.17/1.01 multiply(inverse(sF1_fnc),sF0_fnc)=greatest_lower_bound(identity,multiply(inverse(sF1_fnc),sF2_fnc))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f37,f139])).
% 4.17/1.01 fof(f2874,plain,(
% 4.17/1.01 identity=greatest_lower_bound(identity,multiply(inverse(b),a))),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f19,f2822])).
% 4.17/1.01 fof(f2875,plain,(
% 4.17/1.01 identity=greatest_lower_bound(identity,multiply(sF2_fnc,a))),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f36,f2874])).
% 4.17/1.01 fof(f2880,plain,(
% 4.17/1.01 identity=greatest_lower_bound(identity,multiply(inverse(sF0_fnc),sF2_fnc))),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f19,f2827])).
% 4.17/1.01 fof(f2888,plain,(
% 4.17/1.01 multiply(a,sF0_fnc)=greatest_lower_bound(identity,multiply(inverse(sF1_fnc),sF2_fnc))),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f2561,f2834])).
% 4.17/1.01 fof(f2889,plain,(
% 4.17/1.01 multiply(a,sF0_fnc)=greatest_lower_bound(identity,multiply(a,sF2_fnc))),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f2561,f2888])).
% 4.17/1.01 fof(f5181,plain,(
% 4.17/1.01 multiply(sF0_fnc,a)=greatest_lower_bound(identity,multiply(sF2_fnc,a))),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f37,f165])).
% 4.17/1.01 fof(f5220,plain,(
% 4.17/1.01 multiply(sF0_fnc,a)=identity),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f2875,f5181])).
% 4.17/1.01 fof(f5284,plain,(
% 4.17/1.01 a=multiply(inverse(sF0_fnc),identity)),
% 4.17/1.01 inference(paramodulation,[status(thm)],[f5220,f79])).
% 4.17/1.01 fof(f5305,plain,(
% 4.17/1.01 identity=greatest_lower_bound(identity,multiply(a,sF2_fnc))),
% 4.17/1.01 inference(backward_demodulation,[status(thm)],[f5310,f2880])).
% 4.17/1.01 fof(f5310,plain,(
% 4.17/1.01 a=inverse(sF0_fnc)),
% 4.17/1.01 inference(forward_demodulation,[status(thm)],[f736,f5284])).
% 4.17/1.01 fof(f5319,plain,(
% 4.17/1.01 multiply(a,sF0_fnc)=identity),
% 4.33/1.02 inference(backward_demodulation,[status(thm)],[f5305,f2889])).
% 4.33/1.02 fof(f5331,plain,(
% 4.33/1.02 sF0_fnc=multiply(sF1_fnc,identity)),
% 4.33/1.02 inference(paramodulation,[status(thm)],[f5319,f77])).
% 4.33/1.02 fof(f5354,plain,(
% 4.33/1.02 sF0_fnc=sF1_fnc),
% 4.33/1.02 inference(forward_demodulation,[status(thm)],[f736,f5331])).
% 4.33/1.02 fof(f5355,plain,(
% 4.33/1.02 $false),
% 4.33/1.02 inference(forward_subsumption_resolution,[status(thm)],[f5354,f38])).
% 4.33/1.02 % SZS output end CNFRefutation for theBenchmark.p
% 4.33/1.03 % Elapsed time: 0.671344 seconds
% 4.33/1.03 % CPU time: 5.164738 seconds
% 4.33/1.03 % Total memory used: 87.597 MB
% 4.33/1.03 % Net memory used: 86.141 MB
%------------------------------------------------------------------------------