%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP184-3 : 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 : n012.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 12:36:12 PM UTC 2026
% Result : Unsatisfiable 54.66s 7.28s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP184-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 20 20:04:53 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 54.66/7.28 % Refutation found
% 54.66/7.28 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 54.66/7.28 % SZS output start CNFRefutation for theBenchmark
% 54.66/7.28 fof(f1,axiom,(
% 54.66/7.28 (![X]: (multiply(identity,X) = X ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f2,axiom,(
% 54.66/7.28 (![X]: (multiply(inverse(X),X) = identity ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f3,axiom,(
% 54.66/7.28 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f4,axiom,(
% 54.66/7.28 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f5,axiom,(
% 54.66/7.28 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f12,axiom,(
% 54.66/7.28 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f13,axiom,(
% 54.66/7.28 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f14,axiom,(
% 54.66/7.28 (![Y,Z,X]: (multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f15,axiom,(
% 54.66/7.28 (![Y,Z,X]: (multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ))),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f16,negated_conjecture,(
% 54.66/7.28 multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 54.66/7.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 54.66/7.28 fof(f17,plain,(
% 54.66/7.28 ![X0]: (multiply(identity,X0)=X0)),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f1])).
% 54.66/7.28 fof(f18,plain,(
% 54.66/7.28 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f2])).
% 54.66/7.28 fof(f19,plain,(
% 54.66/7.28 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f3])).
% 54.66/7.28 fof(f20,plain,(
% 54.66/7.28 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f4])).
% 54.66/7.28 fof(f21,plain,(
% 54.66/7.28 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f5])).
% 54.66/7.28 fof(f28,plain,(
% 54.66/7.28 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f12])).
% 54.66/7.28 fof(f29,plain,(
% 54.66/7.28 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f13])).
% 54.66/7.28 fof(f30,plain,(
% 54.66/7.28 ![X0,X1,X2]: (multiply(least_upper_bound(X0,X1),X2)=least_upper_bound(multiply(X0,X2),multiply(X1,X2)))),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f14])).
% 54.66/7.28 fof(f31,plain,(
% 54.66/7.28 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,X1),X2)=greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)))),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f15])).
% 54.66/7.28 fof(f32,plain,(
% 54.66/7.28 ~multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))=multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))),
% 54.66/7.28 inference(cnf_transformation,[status(thm)],[f16])).
% 54.66/7.28 fof(f33,definition,(
% 54.66/7.28 sF1_fnc=least_upper_bound(a,identity)),
% 54.66/7.28 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 54.66/7.28 fof(f34,definition,(
% 54.66/7.28 sF3_fnc=greatest_lower_bound(a,identity)),
% 54.66/7.28 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 54.66/7.28 fof(f35,definition,(
% 54.66/7.28 sF2_fnc=inverse(sF3_fnc)),
% 54.66/7.28 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 54.66/7.28 fof(f36,definition,(
% 54.66/7.28 sF0_fnc=multiply(sF1_fnc,sF2_fnc)),
% 54.66/7.28 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 54.66/7.28 fof(f37,definition,(
% 54.66/7.28 sF5_fnc=inverse(sF3_fnc)),
% 54.66/7.28 introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition])).
% 54.66/7.30 fof(f38,definition,(
% 54.66/7.30 sF4_fnc=multiply(sF5_fnc,sF1_fnc)),
% 54.66/7.30 introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition])).
% 54.66/7.30 fof(f39,plain,(
% 54.66/7.30 ~sF0_fnc=sF4_fnc),
% 54.66/7.30 inference(definition_folding,[],[f32,f38,f37,f36,f35,f34,f33])).
% 54.66/7.30 fof(f40,plain,(
% 54.66/7.30 sF5_fnc=sF2_fnc),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f35,f37])).
% 54.66/7.30 fof(f41,plain,(
% 54.66/7.30 sF4_fnc=multiply(sF2_fnc,sF1_fnc)),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f40,f38])).
% 54.66/7.30 fof(f42,plain,(
% 54.66/7.30 multiply(sF2_fnc,sF3_fnc)=identity),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f35,f18])).
% 54.66/7.30 fof(f70,plain,(
% 54.66/7.30 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f18,f19])).
% 54.66/7.30 fof(f72,plain,(
% 54.66/7.30 ![X0]: (multiply(identity,X0)=multiply(sF2_fnc,multiply(sF3_fnc,X0)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f42,f19])).
% 54.66/7.30 fof(f77,plain,(
% 54.66/7.30 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f17,f70])).
% 54.66/7.30 fof(f78,plain,(
% 54.66/7.30 ![X0]: (X0=multiply(sF2_fnc,multiply(sF3_fnc,X0)))),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f17,f72])).
% 54.66/7.30 fof(f117,plain,(
% 54.66/7.30 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f77,f77])).
% 54.66/7.30 fof(f118,plain,(
% 54.66/7.30 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f18,f77])).
% 54.66/7.30 fof(f125,plain,(
% 54.66/7.30 ![X0]: (X0=multiply(X0,identity))),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f117,f118])).
% 54.66/7.30 fof(f240,plain,(
% 54.66/7.30 ![X0]: (multiply(X0,identity)=inverse(inverse(X0)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f125,f117])).
% 54.66/7.30 fof(f249,plain,(
% 54.66/7.30 ![X0]: (X0=inverse(inverse(X0)))),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f125,f240])).
% 54.66/7.30 fof(f257,plain,(
% 54.66/7.30 sF3_fnc=inverse(sF2_fnc)),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f35,f249])).
% 54.66/7.30 fof(f353,plain,(
% 54.66/7.30 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X2),multiply(X0,X1)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f21,f28])).
% 54.66/7.30 fof(f409,plain,(
% 54.66/7.30 multiply(sF3_fnc,sF2_fnc)=identity),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f257,f18])).
% 54.66/7.30 fof(f778,plain,(
% 54.66/7.30 ![X0]: (multiply(sF1_fnc,greatest_lower_bound(sF2_fnc,X0))=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,X0)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f36,f29])).
% 54.66/7.30 fof(f897,plain,(
% 54.66/7.30 ![X0,X1]: (multiply(least_upper_bound(X0,identity),X1)=least_upper_bound(multiply(X0,X1),X1))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f17,f30])).
% 54.66/7.30 fof(f937,plain,(
% 54.66/7.30 ![X0,X1]: (multiply(least_upper_bound(X0,identity),X1)=least_upper_bound(X1,multiply(X0,X1)))),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f21,f897])).
% 54.66/7.30 fof(f1613,plain,(
% 54.66/7.30 ![X0,X1]: (multiply(greatest_lower_bound(X0,identity),X1)=greatest_lower_bound(multiply(X0,X1),X1))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f17,f31])).
% 54.66/7.30 fof(f1656,plain,(
% 54.66/7.30 ![X0,X1]: (multiply(greatest_lower_bound(X0,identity),X1)=greatest_lower_bound(X1,multiply(X0,X1)))),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f20,f1613])).
% 54.66/7.30 fof(f9378,plain,(
% 54.66/7.30 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=multiply(X0,least_upper_bound(X2,X1)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f28,f353])).
% 54.66/7.30 fof(f25849,plain,(
% 54.66/7.30 ![X0]: (multiply(sF1_fnc,X0)=least_upper_bound(X0,multiply(a,X0)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f33,f937])).
% 54.66/7.30 fof(f38609,plain,(
% 54.66/7.30 ![X0]: (multiply(sF3_fnc,X0)=greatest_lower_bound(X0,multiply(a,X0)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f34,f1656])).
% 54.66/7.30 fof(f49972,plain,(
% 54.66/7.30 ![X0]: (multiply(sF1_fnc,multiply(a,X0))=multiply(a,least_upper_bound(multiply(a,X0),X0)))),
% 54.66/7.30 inference(paramodulation,[status(thm)],[f353,f25849])).
% 54.66/7.30 fof(f50072,plain,(
% 54.66/7.30 ![X0]: (multiply(sF1_fnc,multiply(a,X0))=multiply(a,least_upper_bound(X0,multiply(a,X0))))),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f9378,f49972])).
% 54.66/7.30 fof(f50073,plain,(
% 54.66/7.30 ![X0]: (multiply(sF1_fnc,multiply(a,X0))=multiply(a,multiply(sF1_fnc,X0)))),
% 54.66/7.30 inference(forward_demodulation,[status(thm)],[f25849,f50072])).
% 54.66/7.30 fof(f56268,plain,(
% 54.66/7.30 multiply(sF1_fnc,multiply(sF3_fnc,sF2_fnc))=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc)))),
% 44.01/7.48 inference(paramodulation,[status(thm)],[f38609,f778])).
% 44.01/7.48 fof(f56392,plain,(
% 44.01/7.48 multiply(sF1_fnc,identity)=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc)))),
% 44.01/7.48 inference(forward_demodulation,[status(thm)],[f409,f56268])).
% 44.01/7.48 fof(f56393,plain,(
% 44.01/7.48 sF1_fnc=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc)))),
% 44.01/7.48 inference(forward_demodulation,[status(thm)],[f125,f56392])).
% 44.01/7.48 fof(f56394,plain,(
% 44.01/7.48 sF1_fnc=greatest_lower_bound(sF0_fnc,multiply(a,multiply(sF1_fnc,sF2_fnc)))),
% 44.01/7.48 inference(forward_demodulation,[status(thm)],[f50073,f56393])).
% 44.01/7.48 fof(f56395,plain,(
% 44.01/7.48 sF1_fnc=greatest_lower_bound(sF0_fnc,multiply(a,sF0_fnc))),
% 44.01/7.48 inference(forward_demodulation,[status(thm)],[f36,f56394])).
% 44.01/7.48 fof(f56419,plain,(
% 44.01/7.48 sF1_fnc=multiply(sF3_fnc,sF0_fnc)),
% 44.01/7.48 inference(forward_demodulation,[status(thm)],[f38609,f56395])).
% 44.01/7.48 fof(f56554,plain,(
% 44.01/7.48 sF0_fnc=multiply(sF2_fnc,sF1_fnc)),
% 44.01/7.48 inference(paramodulation,[status(thm)],[f56419,f78])).
% 44.01/7.48 fof(f56655,plain,(
% 44.01/7.48 sF4_fnc=sF0_fnc),
% 44.01/7.48 inference(backward_demodulation,[status(thm)],[f56554,f41])).
% 44.01/7.48 fof(f57116,plain,(
% 44.01/7.48 $false),
% 44.01/7.48 inference(forward_subsumption_resolution,[status(thm)],[f56655,f39])).
% 44.01/7.48 % SZS output end CNFRefutation for theBenchmark.p
% 6.87/7.52 % Elapsed time: 7.214297 seconds
% 6.87/7.52 % CPU time: 56.773777 seconds
% 6.87/7.52 % Total memory used: 712.324 MB
% 6.87/7.52 % Net memory used: 701.775 MB
%------------------------------------------------------------------------------