%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP178-1 : 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 : n017.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 12:36:11 PM UTC 2026
% Result : Unsatisfiable 31.04s 4.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP178-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 19:59:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 31.04/4.40 % Refutation found
% 31.04/4.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 31.04/4.40 % SZS output start CNFRefutation for theBenchmark
% 31.04/4.40 fof(f1,axiom,(
% 31.04/4.40 (![X]: (multiply(identity,X) = X ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f2,axiom,(
% 31.04/4.40 (![X]: (multiply(inverse(X),X) = identity ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f3,axiom,(
% 31.04/4.40 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f4,axiom,(
% 31.04/4.40 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f5,axiom,(
% 31.04/4.40 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f6,axiom,(
% 31.04/4.40 (![X,Y,Z]: (greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f7,axiom,(
% 31.04/4.40 (![X,Y,Z]: (least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f10,axiom,(
% 31.04/4.40 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f11,axiom,(
% 31.04/4.40 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f13,axiom,(
% 31.04/4.40 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f15,axiom,(
% 31.04/4.40 (![Y,Z,X]: (multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ))),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f17,hypothesis,(
% 31.04/4.40 least_upper_bound(identity,b) = b ),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f18,hypothesis,(
% 31.04/4.40 least_upper_bound(identity,c) = c ),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f19,hypothesis,(
% 31.04/4.40 greatest_lower_bound(a,b) = identity ),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f20,negated_conjecture,(
% 31.04/4.40 greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) ),
% 31.04/4.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.04/4.40 fof(f21,plain,(
% 31.04/4.40 ![X0]: (multiply(identity,X0)=X0)),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f1])).
% 31.04/4.40 fof(f22,plain,(
% 31.04/4.40 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f2])).
% 31.04/4.40 fof(f23,plain,(
% 31.04/4.40 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f3])).
% 31.04/4.40 fof(f24,plain,(
% 31.04/4.40 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f4])).
% 31.04/4.40 fof(f25,plain,(
% 31.04/4.40 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f5])).
% 31.04/4.40 fof(f26,plain,(
% 31.04/4.40 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(greatest_lower_bound(X0,X1),X2))),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f6])).
% 31.04/4.40 fof(f27,plain,(
% 31.04/4.40 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,X2))=least_upper_bound(least_upper_bound(X0,X1),X2))),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f7])).
% 31.04/4.40 fof(f30,plain,(
% 31.04/4.40 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f10])).
% 31.04/4.40 fof(f31,plain,(
% 31.04/4.40 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f11])).
% 31.04/4.40 fof(f33,plain,(
% 31.04/4.40 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f13])).
% 31.04/4.40 fof(f35,plain,(
% 31.04/4.40 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,X1),X2)=greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)))),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f15])).
% 31.04/4.40 fof(f37,plain,(
% 31.04/4.40 least_upper_bound(identity,b)=b),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f17])).
% 31.04/4.40 fof(f38,plain,(
% 31.04/4.40 least_upper_bound(identity,c)=c),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f18])).
% 31.04/4.40 fof(f39,plain,(
% 31.04/4.40 greatest_lower_bound(a,b)=identity),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f19])).
% 31.04/4.40 fof(f40,plain,(
% 31.04/4.40 ~greatest_lower_bound(a,multiply(b,c))=greatest_lower_bound(a,c)),
% 31.04/4.40 inference(cnf_transformation,[status(thm)],[f20])).
% 31.04/4.40 fof(f41,definition,(
% 31.04/4.40 sF1_fnc=multiply(b,c)),
% 31.04/4.40 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 31.04/4.40 fof(f42,definition,(
% 31.04/4.40 sF0_fnc=greatest_lower_bound(a,sF1_fnc)),
% 31.04/4.40 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 31.04/4.40 fof(f43,definition,(
% 31.04/4.40 sF2_fnc=greatest_lower_bound(a,c)),
% 31.04/4.40 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 31.04/4.40 fof(f44,plain,(
% 31.04/4.40 ~sF0_fnc=sF2_fnc),
% 31.04/4.40 inference(definition_folding,[],[f40,f43,f42,f41])).
% 31.04/4.40 fof(f46,plain,(
% 31.04/4.40 least_upper_bound(b,identity)=b),
% 31.04/4.40 inference(forward_demodulation,[status(thm)],[f25,f37])).
% 31.04/4.40 fof(f47,plain,(
% 31.04/4.40 least_upper_bound(c,identity)=c),
% 31.04/4.40 inference(forward_demodulation,[status(thm)],[f25,f38])).
% 31.04/4.40 fof(f48,plain,(
% 31.04/4.40 greatest_lower_bound(b,a)=identity),
% 31.04/4.40 inference(forward_demodulation,[status(thm)],[f24,f39])).
% 31.04/4.40 fof(f49,plain,(
% 31.04/4.40 sF2_fnc=greatest_lower_bound(c,a)),
% 31.04/4.40 inference(forward_demodulation,[status(thm)],[f24,f43])).
% 31.04/4.40 fof(f69,plain,(
% 31.04/4.40 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X1,X0))=X0)),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f24,f30])).
% 31.04/4.40 fof(f94,plain,(
% 31.04/4.40 ![X0]: (greatest_lower_bound(b,greatest_lower_bound(a,X0))=greatest_lower_bound(identity,X0))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f48,f26])).
% 31.04/4.40 fof(f96,plain,(
% 31.04/4.40 ![X0]: (greatest_lower_bound(a,greatest_lower_bound(sF1_fnc,X0))=greatest_lower_bound(sF0_fnc,X0))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f42,f26])).
% 31.04/4.40 fof(f113,plain,(
% 31.04/4.40 ![X0]: (multiply(b,greatest_lower_bound(c,X0))=greatest_lower_bound(sF1_fnc,multiply(b,X0)))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f41,f33])).
% 31.04/4.40 fof(f139,plain,(
% 31.04/4.40 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f22,f23])).
% 31.04/4.40 fof(f141,plain,(
% 31.04/4.40 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 31.04/4.40 inference(forward_demodulation,[status(thm)],[f21,f139])).
% 31.04/4.40 fof(f142,plain,(
% 31.04/4.40 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f141,f141])).
% 31.04/4.40 fof(f143,plain,(
% 31.04/4.40 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f22,f141])).
% 31.04/4.40 fof(f147,plain,(
% 31.04/4.40 ![X0,X1,X2]: (multiply(inverse(X0),greatest_lower_bound(X1,multiply(X0,X2)))=greatest_lower_bound(multiply(inverse(X0),X1),X2))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f141,f33])).
% 31.04/4.40 fof(f150,plain,(
% 31.04/4.40 ![X0]: (X0=multiply(X0,identity))),
% 31.04/4.40 inference(forward_demodulation,[status(thm)],[f142,f143])).
% 31.04/4.40 fof(f195,plain,(
% 31.04/4.40 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X1,X0))=X0)),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f25,f31])).
% 31.04/4.40 fof(f203,plain,(
% 31.04/4.40 greatest_lower_bound(identity,c)=identity),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f47,f195])).
% 31.04/4.40 fof(f220,plain,(
% 31.04/4.40 greatest_lower_bound(c,identity)=identity),
% 31.04/4.40 inference(forward_demodulation,[status(thm)],[f24,f203])).
% 31.04/4.40 fof(f277,plain,(
% 31.04/4.40 ![X0,X1]: (multiply(X0,multiply(inverse(X0),X1))=X1)),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f141,f142])).
% 31.04/4.40 fof(f326,plain,(
% 31.04/4.40 ![X0,X1,X2]: (greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0)))=X0)),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f27,f195])).
% 31.04/4.40 fof(f827,plain,(
% 31.04/4.40 ![X0]: (multiply(greatest_lower_bound(b,X0),c)=greatest_lower_bound(sF1_fnc,multiply(X0,c)))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f41,f35])).
% 31.04/4.40 fof(f1210,plain,(
% 31.04/4.40 greatest_lower_bound(b,sF0_fnc)=greatest_lower_bound(identity,sF1_fnc)),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f42,f94])).
% 31.04/4.40 fof(f2356,plain,(
% 31.04/4.40 multiply(b,identity)=greatest_lower_bound(sF1_fnc,multiply(b,identity))),
% 31.04/4.40 inference(paramodulation,[status(thm)],[f220,f113])).
% 31.04/4.40 fof(f2380,plain,(
% 31.04/4.40 b=greatest_lower_bound(sF1_fnc,multiply(b,identity))),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f150,f2356])).
% 31.04/4.49 fof(f2381,plain,(
% 31.04/4.49 b=greatest_lower_bound(sF1_fnc,b)),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f150,f2380])).
% 31.04/4.49 fof(f2382,plain,(
% 31.04/4.49 b=greatest_lower_bound(b,sF1_fnc)),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f24,f2381])).
% 31.04/4.49 fof(f2414,plain,(
% 31.04/4.49 least_upper_bound(sF1_fnc,b)=sF1_fnc),
% 31.04/4.49 inference(paramodulation,[status(thm)],[f2382,f69])).
% 31.04/4.49 fof(f2422,plain,(
% 31.04/4.49 least_upper_bound(b,sF1_fnc)=sF1_fnc),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f25,f2414])).
% 31.04/4.49 fof(f2686,plain,(
% 31.04/4.49 ![X0]: (greatest_lower_bound(identity,least_upper_bound(X0,b))=identity)),
% 31.04/4.49 inference(paramodulation,[status(thm)],[f46,f326])).
% 31.04/4.49 fof(f2841,plain,(
% 31.04/4.49 ![X0]: (greatest_lower_bound(identity,least_upper_bound(b,X0))=identity)),
% 31.04/4.49 inference(paramodulation,[status(thm)],[f25,f2686])).
% 31.04/4.49 fof(f3004,plain,(
% 31.04/4.49 greatest_lower_bound(identity,sF1_fnc)=identity),
% 31.04/4.49 inference(paramodulation,[status(thm)],[f2422,f2841])).
% 31.04/4.49 fof(f3033,plain,(
% 31.04/4.49 greatest_lower_bound(b,sF0_fnc)=identity),
% 31.04/4.49 inference(backward_demodulation,[status(thm)],[f3004,f1210])).
% 31.04/4.49 fof(f18373,plain,(
% 31.04/4.49 multiply(identity,c)=greatest_lower_bound(sF1_fnc,multiply(sF0_fnc,c))),
% 31.04/4.49 inference(paramodulation,[status(thm)],[f3033,f827])).
% 31.04/4.49 fof(f18429,plain,(
% 31.04/4.49 c=greatest_lower_bound(sF1_fnc,multiply(sF0_fnc,c))),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f21,f18373])).
% 31.04/4.49 fof(f21968,plain,(
% 31.04/4.49 greatest_lower_bound(a,c)=greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,c))),
% 31.04/4.49 inference(paramodulation,[status(thm)],[f18429,f96])).
% 31.04/4.49 fof(f21987,plain,(
% 31.04/4.49 greatest_lower_bound(c,a)=greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,c))),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f24,f21968])).
% 31.04/4.49 fof(f21988,plain,(
% 31.04/4.49 sF2_fnc=greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,c))),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f49,f21987])).
% 31.04/4.49 fof(f30071,plain,(
% 31.04/4.49 multiply(inverse(sF0_fnc),sF2_fnc)=greatest_lower_bound(multiply(inverse(sF0_fnc),sF0_fnc),c)),
% 31.04/4.49 inference(paramodulation,[status(thm)],[f21988,f147])).
% 31.04/4.49 fof(f30090,plain,(
% 31.04/4.49 multiply(inverse(sF0_fnc),sF2_fnc)=greatest_lower_bound(c,multiply(inverse(sF0_fnc),sF0_fnc))),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f24,f30071])).
% 31.04/4.49 fof(f30091,plain,(
% 31.04/4.49 multiply(inverse(sF0_fnc),sF2_fnc)=greatest_lower_bound(c,identity)),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f22,f30090])).
% 31.04/4.49 fof(f30098,plain,(
% 31.04/4.49 multiply(inverse(sF0_fnc),sF2_fnc)=identity),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f220,f30091])).
% 31.04/4.49 fof(f30123,plain,(
% 31.04/4.49 multiply(sF0_fnc,identity)=sF2_fnc),
% 31.04/4.49 inference(paramodulation,[status(thm)],[f30098,f277])).
% 31.04/4.49 fof(f30162,plain,(
% 31.04/4.49 sF0_fnc=sF2_fnc),
% 31.04/4.49 inference(forward_demodulation,[status(thm)],[f150,f30123])).
% 31.04/4.49 fof(f30163,plain,(
% 31.04/4.49 $false),
% 31.04/4.49 inference(forward_subsumption_resolution,[status(thm)],[f30162,f44])).
% 31.04/4.49 % SZS output end CNFRefutation for theBenchmark.p
% 29.75/4.51 % Elapsed time: 4.117714 seconds
% 29.75/4.51 % CPU time: 32.472361 seconds
% 29.75/4.51 % Total memory used: 405.026 MB
% 29.75/4.51 % Net memory used: 398.672 MB
%------------------------------------------------------------------------------