%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP184-4 : 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 : n016.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 12.26s 2.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP184-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.87 % Computer : n016.cluster.edu
% 0.16/0.87 % Model : x86_64 x86_64
% 0.16/0.87 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.87 % Memory : 8046.5625MB
% 0.16/0.87 % OS : Linux 6.8.0-71-generic
% 0.16/0.87 % CPULimit : 300
% 0.16/0.87 % WCLimit : 300
% 0.16/0.87 % DateTime : Sun Sep 20 20:09:38 UTC 2026
% 0.16/0.87 % CPUTime :
% 0.16/0.88 % Drodi V4.1.1
% 12.26/2.98 % Refutation found
% 12.26/2.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.26/2.98 % SZS output start CNFRefutation for theBenchmark
% 12.26/2.98 fof(f1,axiom,(
% 12.26/2.98 (![X]: (multiply(identity,X) = X ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f2,axiom,(
% 12.26/2.98 (![X]: (multiply(inverse(X),X) = identity ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f3,axiom,(
% 12.26/2.98 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f4,axiom,(
% 12.26/2.98 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f5,axiom,(
% 12.26/2.98 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f12,axiom,(
% 12.26/2.98 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f14,axiom,(
% 12.26/2.98 (![Y,Z,X]: (multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f16,hypothesis,(
% 12.26/2.98 inverse(identity) = identity ),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f17,hypothesis,(
% 12.26/2.98 (![X]: (inverse(inverse(X)) = X ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f18,hypothesis,(
% 12.26/2.98 (![X,Y]: (inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f19,hypothesis,(
% 12.26/2.98 (![X,Y]: (inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ))),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f21,negated_conjecture,(
% 12.26/2.98 multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
% 12.26/2.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.26/2.98 fof(f22,plain,(
% 12.26/2.98 ![X0]: (multiply(identity,X0)=X0)),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f1])).
% 12.26/2.98 fof(f23,plain,(
% 12.26/2.98 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f2])).
% 12.26/2.98 fof(f24,plain,(
% 12.26/2.98 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f3])).
% 12.26/2.98 fof(f25,plain,(
% 12.26/2.98 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f4])).
% 12.26/2.98 fof(f26,plain,(
% 12.26/2.98 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f5])).
% 12.26/2.98 fof(f33,plain,(
% 12.26/2.98 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f12])).
% 12.26/2.98 fof(f35,plain,(
% 12.26/2.98 ![X0,X1,X2]: (multiply(least_upper_bound(X0,X1),X2)=least_upper_bound(multiply(X0,X2),multiply(X1,X2)))),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f14])).
% 12.26/2.98 fof(f37,plain,(
% 12.26/2.98 inverse(identity)=identity),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f16])).
% 12.26/2.98 fof(f38,plain,(
% 12.26/2.98 ![X0]: (inverse(inverse(X0))=X0)),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f17])).
% 12.26/2.98 fof(f39,plain,(
% 12.26/2.98 ![X0,X1]: (inverse(multiply(X0,X1))=multiply(inverse(X1),inverse(X0)))),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f18])).
% 12.26/2.98 fof(f40,plain,(
% 12.26/2.98 ![X0,X1]: (inverse(greatest_lower_bound(X0,X1))=least_upper_bound(inverse(X0),inverse(X1)))),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f19])).
% 12.26/2.98 fof(f42,plain,(
% 12.26/2.98 ~multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity)))=multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))),
% 12.26/2.98 inference(cnf_transformation,[status(thm)],[f21])).
% 12.26/2.98 fof(f43,definition,(
% 12.26/2.98 sF1_fnc=least_upper_bound(a,identity)),
% 12.26/2.98 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 12.26/2.98 fof(f44,definition,(
% 12.26/2.98 sF3_fnc=greatest_lower_bound(a,identity)),
% 12.26/2.98 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 12.26/2.98 fof(f45,definition,(
% 12.26/2.98 sF2_fnc=inverse(sF3_fnc)),
% 12.26/2.98 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 12.26/2.98 fof(f46,definition,(
% 12.26/2.98 sF0_fnc=multiply(sF1_fnc,sF2_fnc)),
% 12.26/2.98 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 12.26/2.98 fof(f47,definition,(
% 12.26/2.98 sF5_fnc=inverse(sF3_fnc)),
% 12.26/2.98 introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition])).
% 12.26/2.98 fof(f48,definition,(
% 12.26/2.98 sF4_fnc=multiply(sF5_fnc,sF1_fnc)),
% 12.26/2.98 introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition])).
% 12.26/2.98 fof(f49,plain,(
% 12.26/2.98 ~sF0_fnc=sF4_fnc),
% 12.26/2.98 inference(definition_folding,[],[f42,f48,f47,f46,f45,f44,f43])).
% 12.26/2.98 fof(f50,plain,(
% 12.26/2.98 sF5_fnc=sF2_fnc),
% 12.26/2.98 inference(forward_demodulation,[status(thm)],[f45,f47])).
% 12.26/2.98 fof(f51,plain,(
% 12.26/2.98 sF4_fnc=multiply(sF2_fnc,sF1_fnc)),
% 12.26/2.98 inference(forward_demodulation,[status(thm)],[f50,f48])).
% 12.26/2.98 fof(f54,plain,(
% 12.26/2.98 inverse(sF2_fnc)=sF3_fnc),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f45,f38])).
% 12.26/2.98 fof(f57,plain,(
% 12.26/2.98 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f38,f23])).
% 12.26/2.98 fof(f59,plain,(
% 12.26/2.98 multiply(sF2_fnc,sF3_fnc)=identity),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f45,f23])).
% 12.26/2.98 fof(f60,plain,(
% 12.26/2.98 sF3_fnc=greatest_lower_bound(identity,a)),
% 12.26/2.98 inference(backward_demodulation,[status(thm)],[f25,f44])).
% 12.26/2.98 fof(f65,plain,(
% 12.26/2.98 sF1_fnc=least_upper_bound(identity,a)),
% 12.26/2.98 inference(backward_demodulation,[status(thm)],[f26,f43])).
% 12.26/2.98 fof(f80,plain,(
% 12.26/2.98 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f23,f24])).
% 12.26/2.98 fof(f82,plain,(
% 12.26/2.98 ![X0]: (multiply(sF4_fnc,X0)=multiply(sF2_fnc,multiply(sF1_fnc,X0)))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f51,f24])).
% 12.26/2.98 fof(f83,plain,(
% 12.26/2.98 ![X0]: (multiply(sF0_fnc,X0)=multiply(sF1_fnc,multiply(sF2_fnc,X0)))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f46,f24])).
% 12.26/2.98 fof(f87,plain,(
% 12.26/2.98 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 12.26/2.98 inference(forward_demodulation,[status(thm)],[f22,f80])).
% 12.26/2.98 fof(f112,plain,(
% 12.26/2.98 ![X0,X1]: (multiply(identity,X0)=multiply(X1,multiply(inverse(X1),X0)))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f57,f24])).
% 12.26/2.98 fof(f113,plain,(
% 12.26/2.98 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 12.26/2.98 inference(forward_demodulation,[status(thm)],[f22,f112])).
% 12.26/2.98 fof(f215,plain,(
% 12.26/2.98 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(multiply(inverse(X0),X1),identity))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f23,f33])).
% 12.26/2.98 fof(f235,plain,(
% 12.26/2.98 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(identity,multiply(inverse(X0),X1)))),
% 12.26/2.98 inference(forward_demodulation,[status(thm)],[f26,f215])).
% 12.26/2.98 fof(f340,plain,(
% 12.26/2.98 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f23,f87])).
% 12.26/2.98 fof(f357,plain,(
% 12.26/2.98 ![X0]: (X0=multiply(X0,identity))),
% 12.26/2.98 inference(forward_demodulation,[status(thm)],[f38,f340])).
% 12.26/2.98 fof(f635,plain,(
% 12.26/2.98 ![X0,X1]: (multiply(least_upper_bound(X0,inverse(X1)),X1)=least_upper_bound(multiply(X0,X1),identity))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f23,f35])).
% 12.26/2.98 fof(f636,plain,(
% 12.26/2.98 ![X0,X1]: (multiply(least_upper_bound(X0,identity),X1)=least_upper_bound(multiply(X0,X1),X1))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f22,f35])).
% 12.26/2.98 fof(f662,plain,(
% 12.26/2.98 ![X0,X1]: (multiply(least_upper_bound(X0,inverse(X1)),X1)=least_upper_bound(identity,multiply(X0,X1)))),
% 12.26/2.98 inference(forward_demodulation,[status(thm)],[f26,f635])).
% 12.26/2.98 fof(f663,plain,(
% 12.26/2.98 ![X0,X1]: (multiply(least_upper_bound(X0,identity),X1)=least_upper_bound(X1,multiply(X0,X1)))),
% 12.26/2.98 inference(forward_demodulation,[status(thm)],[f26,f636])).
% 12.26/2.98 fof(f1119,plain,(
% 12.26/2.98 ![X0,X1]: (inverse(X0)=multiply(X1,inverse(multiply(X0,X1))))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f39,f113])).
% 12.26/2.98 fof(f1146,plain,(
% 12.26/2.98 ![X0]: (inverse(greatest_lower_bound(identity,X0))=least_upper_bound(identity,inverse(X0)))),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f37,f40])).
% 12.26/2.98 fof(f1286,plain,(
% 12.26/2.98 multiply(sF0_fnc,sF3_fnc)=multiply(sF1_fnc,identity)),
% 12.26/2.98 inference(paramodulation,[status(thm)],[f59,f83])).
% 12.26/2.98 fof(f1302,plain,(
% 12.26/2.98 multiply(sF0_fnc,sF3_fnc)=sF1_fnc),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f357,f1286])).
% 12.26/3.02 fof(f2734,plain,(
% 12.26/3.02 inverse(sF0_fnc)=multiply(sF3_fnc,inverse(sF1_fnc))),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f1302,f1119])).
% 12.26/3.02 fof(f2744,plain,(
% 12.26/3.02 ![X0,X1]: (inverse(inverse(X0))=multiply(inverse(X1),inverse(inverse(multiply(X1,X0)))))),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f39,f1119])).
% 12.26/3.02 fof(f2793,plain,(
% 12.26/3.02 ![X0,X1]: (X0=multiply(inverse(X1),inverse(inverse(multiply(X1,X0)))))),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f38,f2744])).
% 12.26/3.02 fof(f2794,plain,(
% 12.26/3.02 ![X0,X1]: (X0=inverse(multiply(inverse(multiply(X1,X0)),X1)))),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f39,f2793])).
% 12.26/3.02 fof(f3135,plain,(
% 12.26/3.02 ![X0,X1]: (inverse(X0)=multiply(inverse(multiply(X1,X0)),X1))),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f2794,f38])).
% 12.26/3.02 fof(f38963,plain,(
% 12.26/3.02 inverse(sF3_fnc)=least_upper_bound(identity,inverse(a))),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f60,f1146])).
% 12.26/3.02 fof(f39106,plain,(
% 12.26/3.02 sF2_fnc=least_upper_bound(identity,inverse(a))),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f45,f38963])).
% 12.26/3.02 fof(f39370,plain,(
% 12.26/3.02 multiply(sF2_fnc,a)=least_upper_bound(identity,multiply(identity,a))),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f39106,f662])).
% 12.26/3.02 fof(f39381,plain,(
% 12.26/3.02 multiply(inverse(inverse(a)),sF2_fnc)=least_upper_bound(identity,multiply(inverse(inverse(a)),identity))),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f39106,f235])).
% 12.26/3.02 fof(f39404,plain,(
% 12.26/3.02 multiply(sF2_fnc,a)=least_upper_bound(identity,a)),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f22,f39370])).
% 12.26/3.02 fof(f39405,plain,(
% 12.26/3.02 multiply(sF2_fnc,a)=sF1_fnc),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f65,f39404])).
% 12.26/3.02 fof(f39411,plain,(
% 12.26/3.02 multiply(a,sF2_fnc)=least_upper_bound(identity,multiply(inverse(inverse(a)),identity))),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f38,f39381])).
% 12.26/3.02 fof(f39412,plain,(
% 12.26/3.02 multiply(a,sF2_fnc)=multiply(least_upper_bound(inverse(inverse(a)),identity),identity)),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f663,f39411])).
% 12.26/3.02 fof(f39413,plain,(
% 12.26/3.02 multiply(a,sF2_fnc)=least_upper_bound(inverse(inverse(a)),identity)),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f357,f39412])).
% 12.26/3.02 fof(f39414,plain,(
% 12.26/3.02 multiply(a,sF2_fnc)=least_upper_bound(identity,inverse(inverse(a)))),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f26,f39413])).
% 12.26/3.02 fof(f39415,plain,(
% 12.26/3.02 multiply(a,sF2_fnc)=least_upper_bound(identity,a)),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f38,f39414])).
% 12.26/3.02 fof(f39416,plain,(
% 12.26/3.02 multiply(a,sF2_fnc)=sF1_fnc),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f65,f39415])).
% 12.26/3.02 fof(f39598,plain,(
% 12.26/3.02 inverse(sF2_fnc)=multiply(inverse(sF1_fnc),a)),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f39416,f3135])).
% 12.26/3.02 fof(f39662,plain,(
% 12.26/3.02 sF3_fnc=multiply(inverse(sF1_fnc),a)),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f54,f39598])).
% 12.26/3.02 fof(f40253,plain,(
% 12.26/3.02 a=multiply(sF1_fnc,sF3_fnc)),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f39662,f113])).
% 12.26/3.02 fof(f40376,plain,(
% 12.26/3.02 multiply(sF4_fnc,sF3_fnc)=multiply(sF2_fnc,a)),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f40253,f82])).
% 12.26/3.02 fof(f40440,plain,(
% 12.26/3.02 multiply(sF4_fnc,sF3_fnc)=sF1_fnc),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f39405,f40376])).
% 12.26/3.02 fof(f40528,plain,(
% 12.26/3.02 inverse(sF4_fnc)=multiply(sF3_fnc,inverse(sF1_fnc))),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f40440,f1119])).
% 12.26/3.02 fof(f40583,plain,(
% 12.26/3.02 inverse(sF4_fnc)=inverse(sF0_fnc)),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f2734,f40528])).
% 12.26/3.02 fof(f40649,plain,(
% 12.26/3.02 inverse(inverse(sF0_fnc))=sF4_fnc),
% 12.26/3.02 inference(paramodulation,[status(thm)],[f40583,f38])).
% 12.26/3.02 fof(f40689,plain,(
% 12.26/3.02 sF0_fnc=sF4_fnc),
% 12.26/3.02 inference(forward_demodulation,[status(thm)],[f38,f40649])).
% 12.26/3.02 fof(f40690,plain,(
% 12.26/3.02 $false),
% 12.26/3.02 inference(forward_subsumption_resolution,[status(thm)],[f40689,f49])).
% 12.26/3.02 % SZS output end CNFRefutation for theBenchmark.p
% 15.49/3.06 % Elapsed time: 2.168138 seconds
% 15.49/3.06 % CPU time: 16.907593 seconds
% 15.49/3.06 % Total memory used: 170.028 MB
% 15.49/3.06 % Net memory used: 167.154 MB
%------------------------------------------------------------------------------