%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP171-2 : 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 : n011.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 0.14s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP171-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:03:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.40 fof(f1,axiom,(
% 0.14/0.40 (![X]: (multiply(identity,X) = X ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f2,axiom,(
% 0.14/0.40 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f3,axiom,(
% 0.14/0.40 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f4,axiom,(
% 0.14/0.40 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f5,axiom,(
% 0.14/0.40 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f6,axiom,(
% 0.14/0.40 (![X,Y,Z]: (greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f10,axiom,(
% 0.14/0.40 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f11,axiom,(
% 0.14/0.40 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f13,axiom,(
% 0.14/0.40 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f16,hypothesis,(
% 0.14/0.40 least_upper_bound(identity,a) = a ),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f17,hypothesis,(
% 0.14/0.40 least_upper_bound(identity,b) = b ),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f18,negated_conjecture,(
% 0.14/0.40 greatest_lower_bound(identity,multiply(a,b)) != identity ),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f19,plain,(
% 0.14/0.40 ![X0]: (multiply(identity,X0)=X0)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.40 fof(f20,plain,(
% 0.14/0.40 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.40 fof(f21,plain,(
% 0.14/0.40 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.40 fof(f22,plain,(
% 0.14/0.40 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.40 fof(f23,plain,(
% 0.14/0.40 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/0.40 fof(f24,plain,(
% 0.14/0.40 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(greatest_lower_bound(X0,X1),X2))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/0.40 fof(f28,plain,(
% 0.14/0.40 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/0.40 fof(f29,plain,(
% 0.14/0.40 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/0.40 fof(f31,plain,(
% 0.14/0.40 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.40 fof(f34,plain,(
% 0.14/0.40 least_upper_bound(identity,a)=a),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/0.40 fof(f35,plain,(
% 0.14/0.40 least_upper_bound(identity,b)=b),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/0.40 fof(f36,plain,(
% 0.14/0.40 ~greatest_lower_bound(identity,multiply(a,b))=identity),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f18])).
% 0.14/0.40 fof(f37,definition,(
% 0.14/0.40 sF1_fnc=multiply(a,b)),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 0.14/0.40 fof(f38,definition,(
% 0.14/0.40 sF0_fnc=greatest_lower_bound(identity,sF1_fnc)),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.14/0.40 fof(f39,plain,(
% 0.14/0.40 ~sF0_fnc=identity),
% 0.14/0.40 inference(definition_folding,[],[f36,f38,f37])).
% 0.14/0.40 fof(f40,plain,(
% 0.14/0.40 least_upper_bound(a,identity)=a),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f23,f34])).
% 0.14/0.40 fof(f41,plain,(
% 0.14/0.40 least_upper_bound(b,identity)=b),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f23,f35])).
% 0.14/0.41 fof(f58,plain,(
% 0.14/0.41 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X1,X0))=X0)),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f22,f28])).
% 0.14/0.41 fof(f133,plain,(
% 0.14/0.41 ![X0,X1,X2]: (least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0)))=X0)),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f24,f58])).
% 0.14/0.41 fof(f146,plain,(
% 0.14/0.41 ![X0]: (multiply(a,greatest_lower_bound(b,X0))=greatest_lower_bound(sF1_fnc,multiply(a,X0)))),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f37,f31])).
% 0.14/0.41 fof(f203,plain,(
% 0.14/0.41 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f20,f21])).
% 0.14/0.41 fof(f206,plain,(
% 0.14/0.41 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f19,f203])).
% 0.14/0.41 fof(f207,plain,(
% 0.14/0.41 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f206,f206])).
% 0.14/0.41 fof(f208,plain,(
% 0.14/0.41 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f20,f206])).
% 0.14/0.41 fof(f218,plain,(
% 0.14/0.41 ![X0]: (X0=multiply(X0,identity))),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f207,f208])).
% 0.14/0.41 fof(f257,plain,(
% 0.14/0.41 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X1,X0))=X0)),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f23,f29])).
% 0.14/0.41 fof(f270,plain,(
% 0.14/0.41 greatest_lower_bound(identity,b)=identity),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f41,f257])).
% 0.14/0.41 fof(f271,plain,(
% 0.14/0.41 greatest_lower_bound(identity,a)=identity),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f40,f257])).
% 0.14/0.41 fof(f284,plain,(
% 0.14/0.41 greatest_lower_bound(b,identity)=identity),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f22,f270])).
% 0.14/0.41 fof(f285,plain,(
% 0.14/0.41 greatest_lower_bound(a,identity)=identity),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f22,f271])).
% 0.14/0.41 fof(f710,plain,(
% 0.14/0.41 multiply(a,identity)=greatest_lower_bound(sF1_fnc,multiply(a,identity))),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f284,f146])).
% 0.14/0.41 fof(f727,plain,(
% 0.14/0.41 a=greatest_lower_bound(sF1_fnc,multiply(a,identity))),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f218,f710])).
% 0.14/0.41 fof(f728,plain,(
% 0.14/0.41 a=greatest_lower_bound(sF1_fnc,a)),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f218,f727])).
% 0.14/0.41 fof(f729,plain,(
% 0.14/0.41 a=greatest_lower_bound(a,sF1_fnc)),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f22,f728])).
% 0.14/0.41 fof(f997,plain,(
% 0.14/0.41 ![X0]: (least_upper_bound(sF1_fnc,greatest_lower_bound(X0,a))=sF1_fnc)),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f729,f133])).
% 0.14/0.41 fof(f1042,plain,(
% 0.14/0.41 ![X0]: (least_upper_bound(sF1_fnc,greatest_lower_bound(a,X0))=sF1_fnc)),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f22,f997])).
% 0.14/0.41 fof(f1085,plain,(
% 0.14/0.41 least_upper_bound(sF1_fnc,identity)=sF1_fnc),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f285,f1042])).
% 0.14/0.41 fof(f1106,plain,(
% 0.14/0.41 least_upper_bound(identity,sF1_fnc)=sF1_fnc),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f23,f1085])).
% 0.14/0.41 fof(f1121,plain,(
% 0.14/0.41 greatest_lower_bound(identity,sF1_fnc)=identity),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f1106,f29])).
% 0.14/0.41 fof(f1127,plain,(
% 0.14/0.41 sF0_fnc=identity),
% 0.14/0.41 inference(backward_demodulation,[status(thm)],[f1121,f38])).
% 0.14/0.41 fof(f1128,plain,(
% 0.14/0.41 $false),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1127,f39])).
% 0.14/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.43 % Elapsed time: 0.051141 seconds
% 0.14/0.43 % CPU time: 0.202628 seconds
% 0.14/0.43 % Total memory used: 7.525 MB
% 0.14/0.43 % Net memory used: 7.461 MB
%------------------------------------------------------------------------------