%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP179-3 : 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 : n018.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 27.51s 4.09s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP179-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.51 % Computer : n018.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Sun Sep 20 20:06:43 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.52 % Drodi V4.1.1
% 27.51/4.09 % Refutation found
% 27.51/4.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 27.51/4.09 % SZS output start CNFRefutation for theBenchmark
% 27.51/4.09 fof(f1,axiom,(
% 27.51/4.09 (![X]: (multiply(identity,X) = X ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f2,axiom,(
% 27.51/4.09 (![X]: (multiply(inverse(X),X) = identity ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f3,axiom,(
% 27.51/4.09 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f4,axiom,(
% 27.51/4.09 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f5,axiom,(
% 27.51/4.09 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f6,axiom,(
% 27.51/4.09 (![X,Y,Z]: (greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f7,axiom,(
% 27.51/4.09 (![X,Y,Z]: (least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f10,axiom,(
% 27.51/4.09 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f11,axiom,(
% 27.51/4.09 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f12,axiom,(
% 27.51/4.09 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f13,axiom,(
% 27.51/4.09 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f15,axiom,(
% 27.51/4.09 (![Y,Z,X]: (multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f16,hypothesis,(
% 27.51/4.09 inverse(identity) = identity ),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f17,hypothesis,(
% 27.51/4.09 (![X]: (inverse(inverse(X)) = X ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f18,hypothesis,(
% 27.51/4.09 (![X,Y]: (inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ))),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f19,negated_conjecture,(
% 27.51/4.09 least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)) ),
% 27.51/4.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 27.51/4.09 fof(f20,plain,(
% 27.51/4.09 ![X0]: (multiply(identity,X0)=X0)),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f1])).
% 27.51/4.09 fof(f21,plain,(
% 27.51/4.09 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f2])).
% 27.51/4.09 fof(f22,plain,(
% 27.51/4.09 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f3])).
% 27.51/4.09 fof(f23,plain,(
% 27.51/4.09 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f4])).
% 27.51/4.09 fof(f24,plain,(
% 27.51/4.09 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f5])).
% 27.51/4.09 fof(f25,plain,(
% 27.51/4.09 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(greatest_lower_bound(X0,X1),X2))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f6])).
% 27.51/4.09 fof(f26,plain,(
% 27.51/4.09 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,X2))=least_upper_bound(least_upper_bound(X0,X1),X2))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f7])).
% 27.51/4.09 fof(f29,plain,(
% 27.51/4.09 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f10])).
% 27.51/4.09 fof(f30,plain,(
% 27.51/4.09 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f11])).
% 27.51/4.09 fof(f31,plain,(
% 27.51/4.09 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f12])).
% 27.51/4.09 fof(f32,plain,(
% 27.51/4.09 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f13])).
% 27.51/4.09 fof(f34,plain,(
% 27.51/4.09 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,X1),X2)=greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f15])).
% 27.51/4.09 fof(f35,plain,(
% 27.51/4.09 inverse(identity)=identity),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f16])).
% 27.51/4.09 fof(f36,plain,(
% 27.51/4.09 ![X0]: (inverse(inverse(X0))=X0)),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f17])).
% 27.51/4.09 fof(f37,plain,(
% 27.51/4.09 ![X0,X1]: (inverse(multiply(X0,X1))=multiply(inverse(X1),inverse(X0)))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f18])).
% 27.51/4.09 fof(f38,plain,(
% 27.51/4.09 ~least_upper_bound(inverse(a),identity)=inverse(greatest_lower_bound(a,identity))),
% 27.51/4.09 inference(cnf_transformation,[status(thm)],[f19])).
% 27.51/4.09 fof(f39,definition,(
% 27.51/4.09 sF1_fnc=inverse(a)),
% 27.51/4.09 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 27.51/4.09 fof(f40,definition,(
% 27.51/4.09 sF0_fnc=least_upper_bound(sF1_fnc,identity)),
% 27.51/4.09 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 27.51/4.09 fof(f41,definition,(
% 27.51/4.09 sF3_fnc=greatest_lower_bound(a,identity)),
% 27.51/4.09 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 27.51/4.09 fof(f42,definition,(
% 27.51/4.09 sF2_fnc=inverse(sF3_fnc)),
% 27.51/4.09 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 27.51/4.09 fof(f43,plain,(
% 27.51/4.09 ~sF0_fnc=sF2_fnc),
% 27.51/4.09 inference(definition_folding,[],[f38,f42,f41,f40,f39])).
% 27.51/4.09 fof(f44,plain,(
% 27.51/4.09 sF0_fnc=least_upper_bound(identity,sF1_fnc)),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f24,f40])).
% 27.51/4.09 fof(f47,plain,(
% 27.51/4.09 multiply(sF2_fnc,sF3_fnc)=identity),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f42,f21])).
% 27.51/4.09 fof(f49,plain,(
% 27.51/4.09 inverse(sF2_fnc)=sF3_fnc),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f42,f36])).
% 27.51/4.09 fof(f50,plain,(
% 27.51/4.09 inverse(sF1_fnc)=a),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f39,f36])).
% 27.51/4.09 fof(f52,plain,(
% 27.51/4.09 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f36,f21])).
% 27.51/4.09 fof(f62,plain,(
% 27.51/4.09 multiply(a,sF1_fnc)=identity),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f50,f21])).
% 27.51/4.09 fof(f69,plain,(
% 27.51/4.09 ![X0]: (multiply(identity,X0)=multiply(sF2_fnc,multiply(sF3_fnc,X0)))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f47,f22])).
% 27.51/4.09 fof(f70,plain,(
% 27.51/4.09 ![X0]: (X0=multiply(sF2_fnc,multiply(sF3_fnc,X0)))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f20,f69])).
% 27.51/4.09 fof(f79,plain,(
% 27.51/4.09 least_upper_bound(a,sF3_fnc)=a),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f41,f29])).
% 27.51/4.09 fof(f80,plain,(
% 27.51/4.09 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X1,X0))=X0)),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f23,f29])).
% 27.51/4.09 fof(f84,plain,(
% 27.51/4.09 least_upper_bound(identity,sF3_fnc)=identity),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f41,f80])).
% 27.51/4.09 fof(f114,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(identity,X0)=multiply(X1,multiply(inverse(X1),X0)))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f52,f22])).
% 27.51/4.09 fof(f115,plain,(
% 27.51/4.09 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f20,f114])).
% 27.51/4.09 fof(f119,plain,(
% 27.51/4.09 greatest_lower_bound(identity,sF0_fnc)=identity),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f44,f30])).
% 27.51/4.09 fof(f122,plain,(
% 27.51/4.09 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X1,X0))=X0)),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f24,f30])).
% 27.51/4.09 fof(f130,plain,(
% 27.51/4.09 ![X0]: (greatest_lower_bound(identity,greatest_lower_bound(sF0_fnc,X0))=greatest_lower_bound(identity,X0))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f119,f25])).
% 27.51/4.09 fof(f144,plain,(
% 27.51/4.09 ![X0]: (least_upper_bound(identity,least_upper_bound(sF1_fnc,X0))=least_upper_bound(sF0_fnc,X0))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f44,f26])).
% 27.51/4.09 fof(f161,plain,(
% 27.51/4.09 greatest_lower_bound(sF3_fnc,a)=sF3_fnc),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f79,f122])).
% 27.51/4.09 fof(f175,plain,(
% 27.51/4.09 greatest_lower_bound(a,sF3_fnc)=sF3_fnc),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f23,f161])).
% 27.51/4.09 fof(f207,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(multiply(inverse(X0),X1),identity))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f21,f31])).
% 27.51/4.09 fof(f227,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(identity,multiply(inverse(X0),X1)))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f24,f207])).
% 27.51/4.09 fof(f265,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(inverse(X0),greatest_lower_bound(X0,X1))=greatest_lower_bound(identity,multiply(inverse(X0),X1)))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f21,f32])).
% 27.51/4.09 fof(f276,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(inverse(X0),greatest_lower_bound(X1,X0))=greatest_lower_bound(multiply(inverse(X0),X1),identity))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f21,f32])).
% 27.51/4.09 fof(f297,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(inverse(X0),greatest_lower_bound(X1,X0))=greatest_lower_bound(identity,multiply(inverse(X0),X1)))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f23,f276])).
% 27.51/4.09 fof(f413,plain,(
% 27.51/4.09 ![X0]: (X0=multiply(X0,identity))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f21,f115])).
% 27.51/4.09 fof(f548,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(greatest_lower_bound(identity,X0),X1)=greatest_lower_bound(X1,multiply(X0,X1)))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f20,f34])).
% 27.51/4.09 fof(f563,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(greatest_lower_bound(X0,identity),X1)=greatest_lower_bound(multiply(X0,X1),X1))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f20,f34])).
% 27.51/4.09 fof(f586,plain,(
% 27.51/4.09 ![X0,X1]: (multiply(greatest_lower_bound(X0,identity),X1)=greatest_lower_bound(X1,multiply(X0,X1)))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f23,f563])).
% 27.51/4.09 fof(f768,plain,(
% 27.51/4.09 ![X0]: (inverse(multiply(X0,sF3_fnc))=multiply(sF2_fnc,inverse(X0)))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f42,f37])).
% 27.51/4.09 fof(f769,plain,(
% 27.51/4.09 ![X0]: (inverse(multiply(X0,a))=multiply(sF1_fnc,inverse(X0)))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f39,f37])).
% 27.51/4.09 fof(f771,plain,(
% 27.51/4.09 ![X0]: (inverse(multiply(sF1_fnc,X0))=multiply(inverse(X0),a))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f50,f37])).
% 27.51/4.09 fof(f772,plain,(
% 27.51/4.09 ![X0]: (inverse(multiply(sF2_fnc,X0))=multiply(inverse(X0),sF3_fnc))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f49,f37])).
% 27.51/4.09 fof(f5249,plain,(
% 27.51/4.09 inverse(multiply(sF1_fnc,sF3_fnc))=multiply(sF2_fnc,a)),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f50,f768])).
% 27.51/4.09 fof(f5314,plain,(
% 27.51/4.09 inverse(multiply(sF2_fnc,a))=multiply(sF1_fnc,sF3_fnc)),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f49,f769])).
% 27.51/4.09 fof(f6840,plain,(
% 27.51/4.09 multiply(inverse(sF3_fnc),identity)=least_upper_bound(identity,multiply(inverse(sF3_fnc),identity))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f84,f227])).
% 27.51/4.09 fof(f6841,plain,(
% 27.51/4.09 multiply(inverse(sF1_fnc),sF0_fnc)=least_upper_bound(identity,multiply(inverse(sF1_fnc),identity))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f44,f227])).
% 27.51/4.09 fof(f6925,plain,(
% 27.51/4.09 inverse(sF3_fnc)=least_upper_bound(identity,multiply(inverse(sF3_fnc),identity))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f413,f6840])).
% 27.51/4.09 fof(f6926,plain,(
% 27.51/4.09 sF2_fnc=least_upper_bound(identity,multiply(inverse(sF3_fnc),identity))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f42,f6925])).
% 27.51/4.09 fof(f6927,plain,(
% 27.51/4.09 sF2_fnc=least_upper_bound(identity,inverse(sF3_fnc))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f413,f6926])).
% 27.51/4.09 fof(f6928,plain,(
% 27.51/4.09 sF2_fnc=least_upper_bound(identity,sF2_fnc)),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f42,f6927])).
% 27.51/4.09 fof(f6929,plain,(
% 27.51/4.09 multiply(a,sF0_fnc)=least_upper_bound(identity,multiply(inverse(sF1_fnc),identity))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f50,f6841])).
% 27.51/4.09 fof(f6930,plain,(
% 27.51/4.09 multiply(a,sF0_fnc)=least_upper_bound(identity,inverse(sF1_fnc))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f413,f6929])).
% 27.51/4.09 fof(f6931,plain,(
% 27.51/4.09 multiply(a,sF0_fnc)=least_upper_bound(identity,a)),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f50,f6930])).
% 27.51/4.09 fof(f6934,plain,(
% 27.51/4.09 multiply(a,sF0_fnc)=least_upper_bound(a,identity)),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f24,f6931])).
% 27.51/4.09 fof(f7985,plain,(
% 27.51/4.09 multiply(inverse(a),sF3_fnc)=greatest_lower_bound(identity,multiply(inverse(a),identity))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f41,f265])).
% 27.51/4.09 fof(f8132,plain,(
% 27.51/4.09 inverse(multiply(sF2_fnc,a))=greatest_lower_bound(identity,multiply(inverse(a),identity))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f772,f7985])).
% 27.51/4.09 fof(f8133,plain,(
% 27.51/4.09 multiply(sF1_fnc,sF3_fnc)=greatest_lower_bound(identity,multiply(inverse(a),identity))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f5314,f8132])).
% 27.51/4.09 fof(f8134,plain,(
% 27.51/4.09 multiply(sF1_fnc,sF3_fnc)=greatest_lower_bound(identity,inverse(a))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f413,f8133])).
% 27.51/4.09 fof(f8142,plain,(
% 27.51/4.09 inverse(greatest_lower_bound(identity,sF1_fnc))=multiply(sF2_fnc,a)),
% 27.51/4.09 inference(backward_demodulation,[status(thm)],[f8143,f5249])).
% 27.51/4.09 fof(f8143,plain,(
% 27.51/4.09 multiply(sF1_fnc,sF3_fnc)=greatest_lower_bound(identity,sF1_fnc)),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f39,f8134])).
% 27.51/4.09 fof(f8497,plain,(
% 27.51/4.09 multiply(inverse(sF3_fnc),sF3_fnc)=greatest_lower_bound(identity,multiply(inverse(sF3_fnc),a))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f175,f297])).
% 27.51/4.09 fof(f8625,plain,(
% 27.51/4.09 inverse(multiply(sF2_fnc,sF3_fnc))=greatest_lower_bound(identity,multiply(inverse(sF3_fnc),a))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f772,f8497])).
% 27.51/4.09 fof(f8626,plain,(
% 27.51/4.09 inverse(identity)=greatest_lower_bound(identity,multiply(inverse(sF3_fnc),a))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f47,f8625])).
% 27.51/4.09 fof(f8627,plain,(
% 27.51/4.09 identity=greatest_lower_bound(identity,multiply(inverse(sF3_fnc),a))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f35,f8626])).
% 27.51/4.09 fof(f8628,plain,(
% 27.51/4.09 identity=greatest_lower_bound(identity,inverse(multiply(sF1_fnc,sF3_fnc)))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f771,f8627])).
% 27.51/4.09 fof(f8629,plain,(
% 27.51/4.09 identity=greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,sF1_fnc)))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f8143,f8628])).
% 27.51/4.09 fof(f8630,plain,(
% 27.51/4.09 identity=greatest_lower_bound(identity,multiply(sF2_fnc,a))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f8142,f8629])).
% 27.51/4.09 fof(f16092,plain,(
% 27.51/4.09 ![X0]: (multiply(identity,X0)=greatest_lower_bound(X0,multiply(multiply(sF2_fnc,a),X0)))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f8630,f548])).
% 27.51/4.09 fof(f16257,plain,(
% 27.51/4.09 ![X0]: (X0=greatest_lower_bound(X0,multiply(multiply(sF2_fnc,a),X0)))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f20,f16092])).
% 27.51/4.09 fof(f16258,plain,(
% 27.51/4.09 ![X0]: (X0=greatest_lower_bound(X0,multiply(sF2_fnc,multiply(a,X0))))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f22,f16257])).
% 27.51/4.09 fof(f18268,plain,(
% 27.51/4.09 ![X0]: (multiply(sF3_fnc,X0)=greatest_lower_bound(X0,multiply(a,X0)))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f41,f586])).
% 27.51/4.09 fof(f18830,plain,(
% 27.51/4.09 sF1_fnc=greatest_lower_bound(sF1_fnc,multiply(sF2_fnc,identity))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f62,f16258])).
% 27.51/4.09 fof(f18894,plain,(
% 27.51/4.09 sF1_fnc=greatest_lower_bound(sF1_fnc,sF2_fnc)),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f413,f18830])).
% 27.51/4.09 fof(f18980,plain,(
% 27.51/4.09 least_upper_bound(sF2_fnc,sF1_fnc)=sF2_fnc),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f18894,f80])).
% 27.51/4.09 fof(f19007,plain,(
% 27.51/4.09 least_upper_bound(sF1_fnc,sF2_fnc)=sF2_fnc),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f24,f18980])).
% 27.51/4.09 fof(f19480,plain,(
% 27.51/4.09 least_upper_bound(identity,sF2_fnc)=least_upper_bound(sF0_fnc,sF2_fnc)),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f19007,f144])).
% 27.51/4.09 fof(f19502,plain,(
% 27.51/4.09 sF2_fnc=least_upper_bound(sF0_fnc,sF2_fnc)),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f6928,f19480])).
% 27.51/4.09 fof(f19550,plain,(
% 27.51/4.09 greatest_lower_bound(sF0_fnc,sF2_fnc)=sF0_fnc),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f19502,f30])).
% 27.51/4.09 fof(f19575,plain,(
% 27.51/4.09 multiply(inverse(sF2_fnc),sF0_fnc)=greatest_lower_bound(identity,multiply(inverse(sF2_fnc),sF0_fnc))),
% 27.51/4.09 inference(paramodulation,[status(thm)],[f19550,f297])).
% 27.51/4.09 fof(f19597,plain,(
% 27.51/4.09 multiply(sF3_fnc,sF0_fnc)=greatest_lower_bound(identity,multiply(inverse(sF2_fnc),sF0_fnc))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f49,f19575])).
% 27.51/4.09 fof(f19598,plain,(
% 27.51/4.09 multiply(sF3_fnc,sF0_fnc)=greatest_lower_bound(identity,multiply(sF3_fnc,sF0_fnc))),
% 27.51/4.09 inference(forward_demodulation,[status(thm)],[f49,f19597])).
% 27.51/4.09 fof(f22714,plain,(
% 27.51/4.09 greatest_lower_bound(identity,multiply(sF3_fnc,sF0_fnc))=greatest_lower_bound(identity,multiply(a,sF0_fnc))),
% 28.18/4.16 inference(paramodulation,[status(thm)],[f18268,f130])).
% 28.18/4.16 fof(f22834,plain,(
% 28.18/4.16 multiply(sF3_fnc,sF0_fnc)=greatest_lower_bound(identity,multiply(a,sF0_fnc))),
% 28.18/4.16 inference(forward_demodulation,[status(thm)],[f19598,f22714])).
% 28.18/4.16 fof(f22835,plain,(
% 28.18/4.16 multiply(sF3_fnc,sF0_fnc)=greatest_lower_bound(identity,least_upper_bound(a,identity))),
% 28.18/4.16 inference(forward_demodulation,[status(thm)],[f6934,f22834])).
% 28.18/4.16 fof(f22858,plain,(
% 28.18/4.16 multiply(sF3_fnc,sF0_fnc)=identity),
% 28.18/4.16 inference(forward_demodulation,[status(thm)],[f122,f22835])).
% 28.18/4.16 fof(f23343,plain,(
% 28.18/4.16 sF0_fnc=multiply(sF2_fnc,identity)),
% 28.18/4.16 inference(paramodulation,[status(thm)],[f22858,f70])).
% 28.18/4.16 fof(f23391,plain,(
% 28.18/4.16 sF0_fnc=sF2_fnc),
% 28.18/4.16 inference(forward_demodulation,[status(thm)],[f413,f23343])).
% 28.18/4.16 fof(f23392,plain,(
% 28.18/4.16 $false),
% 28.18/4.16 inference(forward_subsumption_resolution,[status(thm)],[f23391,f43])).
% 28.18/4.16 % SZS output end CNFRefutation for theBenchmark.p
% 28.18/4.19 % Elapsed time: 3.653212 seconds
% 28.18/4.19 % CPU time: 28.781954 seconds
% 28.18/4.19 % Total memory used: 339.119 MB
% 28.18/4.19 % Net memory used: 333.581 MB
%------------------------------------------------------------------------------