%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP167-4 : 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 12:36:09 PM UTC 2026
% Result : Unsatisfiable 96.17s 12.59s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n016.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun Sep 20 20:07:52 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.35 % Drodi V4.1.1
% 96.17/12.59 % Refutation found
% 96.17/12.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 96.17/12.59 % SZS output start CNFRefutation for theBenchmark
% 96.17/12.59 fof(f1,axiom,(
% 96.17/12.59 (![X]: (multiply(identity,X) = X ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f2,axiom,(
% 96.17/12.59 (![X]: (multiply(inverse(X),X) = identity ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f3,axiom,(
% 96.17/12.59 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f4,axiom,(
% 96.17/12.59 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f5,axiom,(
% 96.17/12.59 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f6,axiom,(
% 96.17/12.59 (![X,Y,Z]: (greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f7,axiom,(
% 96.17/12.59 (![X,Y,Z]: (least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f10,axiom,(
% 96.17/12.59 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f11,axiom,(
% 96.17/12.59 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f12,axiom,(
% 96.17/12.59 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f13,axiom,(
% 96.17/12.59 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f14,axiom,(
% 96.17/12.59 (![Y,Z,X]: (multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f15,axiom,(
% 96.17/12.59 (![Y,Z,X]: (multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f17,axiom,(
% 96.17/12.59 (![X]: (inverse(inverse(X)) = X ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f18,axiom,(
% 96.17/12.59 (![X,Y]: (inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ))),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f19,negated_conjecture,(
% 96.17/12.59 a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) ),
% 96.17/12.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 96.17/12.59 fof(f20,plain,(
% 96.17/12.59 ![X0]: (multiply(identity,X0)=X0)),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f1])).
% 96.17/12.59 fof(f21,plain,(
% 96.17/12.59 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f2])).
% 96.17/12.59 fof(f22,plain,(
% 96.17/12.59 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f3])).
% 96.17/12.59 fof(f23,plain,(
% 96.17/12.59 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f4])).
% 96.17/12.59 fof(f24,plain,(
% 96.17/12.59 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f5])).
% 96.17/12.59 fof(f25,plain,(
% 96.17/12.59 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(greatest_lower_bound(X0,X1),X2))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f6])).
% 96.17/12.59 fof(f26,plain,(
% 96.17/12.59 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,X2))=least_upper_bound(least_upper_bound(X0,X1),X2))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f7])).
% 96.17/12.59 fof(f29,plain,(
% 96.17/12.59 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f10])).
% 96.17/12.59 fof(f30,plain,(
% 96.17/12.59 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f11])).
% 96.17/12.59 fof(f31,plain,(
% 96.17/12.59 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f12])).
% 96.17/12.59 fof(f32,plain,(
% 96.17/12.59 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f13])).
% 96.17/12.59 fof(f33,plain,(
% 96.17/12.59 ![X0,X1,X2]: (multiply(least_upper_bound(X0,X1),X2)=least_upper_bound(multiply(X0,X2),multiply(X1,X2)))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f14])).
% 96.17/12.59 fof(f34,plain,(
% 96.17/12.59 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,X1),X2)=greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f15])).
% 96.17/12.59 fof(f36,plain,(
% 96.17/12.59 ![X0]: (inverse(inverse(X0))=X0)),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f17])).
% 96.17/12.59 fof(f37,plain,(
% 96.17/12.59 ![X0,X1]: (inverse(multiply(X0,X1))=multiply(inverse(X1),inverse(X0)))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f18])).
% 96.17/12.59 fof(f38,plain,(
% 96.17/12.59 ~a=multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity))),
% 96.17/12.59 inference(cnf_transformation,[status(thm)],[f19])).
% 96.17/12.59 fof(f39,definition,(
% 96.17/12.59 sF1_fnc=least_upper_bound(a,identity)),
% 96.17/12.59 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 96.17/12.59 fof(f40,definition,(
% 96.17/12.59 sF2_fnc=greatest_lower_bound(a,identity)),
% 96.17/12.59 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 96.17/12.59 fof(f41,definition,(
% 96.17/12.59 sF0_fnc=multiply(sF1_fnc,sF2_fnc)),
% 96.17/12.59 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 96.17/12.59 fof(f42,plain,(
% 96.17/12.59 ~a=sF0_fnc),
% 96.17/12.59 inference(definition_folding,[],[f38,f41,f40,f39])).
% 96.17/12.59 fof(f44,plain,(
% 96.17/12.59 least_upper_bound(a,sF2_fnc)=a),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f40,f29])).
% 96.17/12.59 fof(f47,plain,(
% 96.17/12.59 greatest_lower_bound(a,sF1_fnc)=a),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f39,f30])).
% 96.17/12.59 fof(f56,plain,(
% 96.17/12.59 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X1,X0))=X0)),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f23,f29])).
% 96.17/12.59 fof(f60,plain,(
% 96.17/12.59 least_upper_bound(identity,sF2_fnc)=identity),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f40,f56])).
% 96.17/12.59 fof(f75,plain,(
% 96.17/12.59 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X1,X0))=X0)),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f24,f30])).
% 96.17/12.59 fof(f81,plain,(
% 96.17/12.59 greatest_lower_bound(identity,sF1_fnc)=identity),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f39,f75])).
% 96.17/12.59 fof(f82,plain,(
% 96.17/12.59 ![X0,X1]: (greatest_lower_bound(greatest_lower_bound(X0,X1),X1)=greatest_lower_bound(X0,X1))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f56,f75])).
% 96.17/12.59 fof(f88,plain,(
% 96.17/12.59 ![X0,X1]: (least_upper_bound(least_upper_bound(X0,X1),X1)=least_upper_bound(X0,X1))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f75,f56])).
% 96.17/12.59 fof(f92,plain,(
% 96.17/12.59 ![X0,X1]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X0))=greatest_lower_bound(X1,X0))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f23,f82])).
% 96.17/12.59 fof(f94,plain,(
% 96.17/12.59 ![X0,X1]: (least_upper_bound(X0,least_upper_bound(X1,X0))=least_upper_bound(X1,X0))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f24,f88])).
% 96.17/12.59 fof(f96,plain,(
% 96.17/12.59 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f21,f22])).
% 96.17/12.59 fof(f98,plain,(
% 96.17/12.59 ![X0]: (multiply(sF0_fnc,X0)=multiply(sF1_fnc,multiply(sF2_fnc,X0)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f41,f22])).
% 96.17/12.59 fof(f101,plain,(
% 96.17/12.59 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f20,f96])).
% 96.17/12.59 fof(f104,plain,(
% 96.17/12.59 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(X2,greatest_lower_bound(X0,X1)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f23,f25])).
% 96.17/12.59 fof(f108,plain,(
% 96.17/12.59 ![X0]: (greatest_lower_bound(a,greatest_lower_bound(sF1_fnc,X0))=greatest_lower_bound(a,X0))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f47,f25])).
% 96.17/12.59 fof(f128,plain,(
% 96.17/12.59 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f36,f21])).
% 96.17/12.59 fof(f147,plain,(
% 96.17/12.59 ![X0,X1]: (multiply(identity,X0)=multiply(X1,multiply(inverse(X1),X0)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f128,f22])).
% 96.17/12.59 fof(f148,plain,(
% 96.17/12.59 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f20,f147])).
% 96.17/12.59 fof(f153,plain,(
% 96.17/12.59 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f21,f101])).
% 96.17/12.59 fof(f159,plain,(
% 96.17/12.59 ![X0]: (X0=multiply(X0,identity))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f36,f153])).
% 96.17/12.59 fof(f225,plain,(
% 96.17/12.59 ![X0,X1]: (greatest_lower_bound(X0,greatest_lower_bound(X0,X1))=greatest_lower_bound(X1,X0))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f23,f92])).
% 96.17/12.59 fof(f253,plain,(
% 96.17/12.59 ![X0,X1]: (least_upper_bound(X0,least_upper_bound(X0,X1))=least_upper_bound(X1,X0))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f24,f94])).
% 96.17/12.59 fof(f522,plain,(
% 96.17/12.59 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,X2))=least_upper_bound(X2,least_upper_bound(X0,X1)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f24,f26])).
% 96.17/12.59 fof(f529,plain,(
% 96.17/12.59 ![X0]: (least_upper_bound(a,least_upper_bound(sF2_fnc,X0))=least_upper_bound(a,X0))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f44,f26])).
% 96.17/12.59 fof(f588,plain,(
% 96.17/12.59 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X2),multiply(X0,X1)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f24,f31])).
% 96.17/12.59 fof(f598,plain,(
% 96.17/12.59 ![X0,X1]: (multiply(X0,least_upper_bound(identity,X1))=least_upper_bound(X0,multiply(X0,X1)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f159,f31])).
% 96.17/12.59 fof(f648,plain,(
% 96.17/12.59 ![X0,X1]: (multiply(inverse(X0),greatest_lower_bound(X0,X1))=greatest_lower_bound(identity,multiply(inverse(X0),X1)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f21,f32])).
% 96.17/12.59 fof(f650,plain,(
% 96.17/12.59 ![X0]: (multiply(sF1_fnc,greatest_lower_bound(sF2_fnc,X0))=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,X0)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f41,f32])).
% 96.17/12.59 fof(f765,plain,(
% 96.17/12.59 ![X0]: (greatest_lower_bound(a,greatest_lower_bound(a,X0))=greatest_lower_bound(greatest_lower_bound(sF1_fnc,X0),a))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f108,f225])).
% 96.17/12.59 fof(f787,plain,(
% 96.17/12.59 ![X0]: (greatest_lower_bound(X0,a)=greatest_lower_bound(greatest_lower_bound(sF1_fnc,X0),a))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f225,f765])).
% 96.17/12.59 fof(f788,plain,(
% 96.17/12.59 ![X0]: (greatest_lower_bound(X0,a)=greatest_lower_bound(sF1_fnc,greatest_lower_bound(X0,a)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f25,f787])).
% 96.17/12.59 fof(f789,plain,(
% 96.17/12.59 ![X0]: (greatest_lower_bound(X0,a)=greatest_lower_bound(a,greatest_lower_bound(sF1_fnc,X0)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f104,f788])).
% 96.17/12.59 fof(f1177,plain,(
% 96.17/12.59 ![X0,X1]: (multiply(least_upper_bound(X0,identity),X1)=least_upper_bound(multiply(X0,X1),X1))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f20,f33])).
% 96.17/12.59 fof(f1204,plain,(
% 96.17/12.59 ![X0,X1]: (multiply(least_upper_bound(X0,identity),X1)=least_upper_bound(X1,multiply(X0,X1)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f24,f1177])).
% 96.17/12.59 fof(f1246,plain,(
% 96.17/12.59 ![X0,X1]: (multiply(greatest_lower_bound(X0,identity),X1)=greatest_lower_bound(multiply(X0,X1),X1))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f20,f34])).
% 96.17/12.59 fof(f1272,plain,(
% 96.17/12.59 ![X0,X1]: (multiply(greatest_lower_bound(X0,identity),X1)=greatest_lower_bound(X1,multiply(X0,X1)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f23,f1246])).
% 96.17/12.59 fof(f1404,plain,(
% 96.17/12.59 ![X0,X1]: (inverse(multiply(inverse(X0),X1))=multiply(inverse(X1),X0))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f36,f37])).
% 96.17/12.59 fof(f1406,plain,(
% 96.17/12.59 ![X0,X1]: (inverse(X0)=multiply(X1,inverse(multiply(X0,X1))))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f37,f148])).
% 96.17/12.59 fof(f1444,plain,(
% 96.17/12.59 ![X0,X1]: (inverse(X0)=multiply(inverse(multiply(X1,X0)),inverse(inverse(X1))))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f1406,f1406])).
% 96.17/12.59 fof(f1446,plain,(
% 96.17/12.59 ![X0]: (multiply(sF0_fnc,inverse(multiply(X0,sF2_fnc)))=multiply(sF1_fnc,inverse(X0)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f1406,f98])).
% 96.17/12.59 fof(f1483,plain,(
% 96.17/12.59 ![X0,X1]: (inverse(X0)=inverse(multiply(inverse(X1),multiply(X1,X0))))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f37,f1444])).
% 96.17/12.59 fof(f1484,plain,(
% 96.17/12.59 ![X0,X1]: (inverse(X0)=multiply(inverse(multiply(X1,X0)),X1))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f1404,f1483])).
% 96.17/12.59 fof(f2860,plain,(
% 96.17/12.59 ![X0]: (least_upper_bound(a,least_upper_bound(a,X0))=least_upper_bound(least_upper_bound(sF2_fnc,X0),a))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f529,f253])).
% 96.17/12.59 fof(f2880,plain,(
% 96.17/12.59 ![X0]: (least_upper_bound(X0,a)=least_upper_bound(least_upper_bound(sF2_fnc,X0),a))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f253,f2860])).
% 96.17/12.59 fof(f2881,plain,(
% 96.17/12.59 ![X0]: (least_upper_bound(X0,a)=least_upper_bound(sF2_fnc,least_upper_bound(X0,a)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f26,f2880])).
% 96.17/12.59 fof(f2882,plain,(
% 96.17/12.59 ![X0]: (least_upper_bound(X0,a)=least_upper_bound(a,least_upper_bound(sF2_fnc,X0)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f522,f2881])).
% 96.17/12.59 fof(f9001,plain,(
% 96.17/12.59 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=multiply(X0,least_upper_bound(X2,X1)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f31,f588])).
% 96.17/12.59 fof(f31336,plain,(
% 96.17/12.59 ![X0]: (multiply(sF1_fnc,X0)=least_upper_bound(X0,multiply(a,X0)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f39,f1204])).
% 96.17/12.59 fof(f33953,plain,(
% 96.17/12.59 ![X0]: (multiply(sF1_fnc,multiply(a,X0))=multiply(a,least_upper_bound(multiply(a,X0),X0)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f588,f31336])).
% 96.17/12.59 fof(f33970,plain,(
% 96.17/12.59 least_upper_bound(multiply(a,sF2_fnc),a)=least_upper_bound(a,multiply(sF1_fnc,sF2_fnc))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f31336,f2882])).
% 96.17/12.59 fof(f34047,plain,(
% 96.17/12.59 ![X0]: (multiply(sF1_fnc,multiply(a,X0))=multiply(a,least_upper_bound(X0,multiply(a,X0))))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f9001,f33953])).
% 96.17/12.59 fof(f34048,plain,(
% 96.17/12.59 ![X0]: (multiply(sF1_fnc,multiply(a,X0))=multiply(a,multiply(sF1_fnc,X0)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f31336,f34047])).
% 96.17/12.59 fof(f34072,plain,(
% 96.17/12.59 least_upper_bound(a,multiply(a,sF2_fnc))=least_upper_bound(a,multiply(sF1_fnc,sF2_fnc))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f24,f33970])).
% 96.17/12.59 fof(f34073,plain,(
% 96.17/12.59 least_upper_bound(a,multiply(a,sF2_fnc))=least_upper_bound(a,sF0_fnc)),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f41,f34072])).
% 96.17/12.59 fof(f55087,plain,(
% 96.17/12.59 ![X0]: (multiply(sF2_fnc,X0)=greatest_lower_bound(X0,multiply(a,X0)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f40,f1272])).
% 96.17/12.59 fof(f56570,plain,(
% 96.17/12.59 multiply(sF1_fnc,multiply(sF2_fnc,sF2_fnc))=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f55087,f650])).
% 96.17/12.59 fof(f56584,plain,(
% 96.17/12.59 greatest_lower_bound(multiply(a,sF1_fnc),a)=greatest_lower_bound(a,multiply(sF2_fnc,sF1_fnc))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f55087,f789])).
% 96.17/12.59 fof(f56695,plain,(
% 96.17/12.59 multiply(sF0_fnc,sF2_fnc)=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f98,f56570])).
% 96.17/12.59 fof(f56696,plain,(
% 96.17/12.59 multiply(sF0_fnc,sF2_fnc)=greatest_lower_bound(sF0_fnc,multiply(a,multiply(sF1_fnc,sF2_fnc)))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f34048,f56695])).
% 96.17/12.59 fof(f56697,plain,(
% 96.17/12.59 multiply(sF0_fnc,sF2_fnc)=greatest_lower_bound(sF0_fnc,multiply(a,sF0_fnc))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f41,f56696])).
% 96.17/12.59 fof(f56717,plain,(
% 96.17/12.59 multiply(sF0_fnc,sF2_fnc)=multiply(sF2_fnc,sF0_fnc)),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f55087,f56697])).
% 96.17/12.59 fof(f56733,plain,(
% 96.17/12.59 greatest_lower_bound(a,multiply(a,sF1_fnc))=greatest_lower_bound(a,multiply(sF2_fnc,sF1_fnc))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f23,f56584])).
% 96.17/12.59 fof(f56875,plain,(
% 96.17/12.59 inverse(sF2_fnc)=multiply(sF0_fnc,inverse(multiply(sF0_fnc,sF2_fnc)))),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f56717,f1406])).
% 96.17/12.59 fof(f56901,plain,(
% 96.17/12.59 inverse(sF2_fnc)=multiply(sF1_fnc,inverse(sF0_fnc))),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f1446,f56875])).
% 96.17/12.59 fof(f56943,plain,(
% 96.17/12.59 inverse(inverse(sF0_fnc))=multiply(inverse(inverse(sF2_fnc)),sF1_fnc)),
% 96.17/12.59 inference(paramodulation,[status(thm)],[f56901,f1484])).
% 96.17/12.59 fof(f56984,plain,(
% 96.17/12.59 sF0_fnc=multiply(inverse(inverse(sF2_fnc)),sF1_fnc)),
% 96.17/12.59 inference(forward_demodulation,[status(thm)],[f36,f56943])).
% 96.17/12.59 fof(f56985,plain,(
% 96.17/12.59 greatest_lower_bound(a,multiply(a,sF1_fnc))=greatest_lower_bound(a,sF0_fnc)),
% 96.17/12.59 inference(backward_demodulation,[status(thm)],[f56988,f56733])).
% 96.17/12.59 fof(f56988,plain,(
% 96.17/12.59 sF0_fnc=multiply(sF2_fnc,sF1_fnc)),
% 76.97/12.75 inference(forward_demodulation,[status(thm)],[f36,f56984])).
% 76.97/12.75 fof(f71268,plain,(
% 76.97/12.75 ![X0]: (multiply(X0,identity)=least_upper_bound(X0,multiply(X0,sF2_fnc)))),
% 76.97/12.75 inference(paramodulation,[status(thm)],[f60,f598])).
% 76.97/12.75 fof(f71557,plain,(
% 76.97/12.75 a=least_upper_bound(a,sF0_fnc)),
% 76.97/12.75 inference(backward_demodulation,[status(thm)],[f71558,f34073])).
% 76.97/12.75 fof(f71558,plain,(
% 76.97/12.75 ![X0]: (X0=least_upper_bound(X0,multiply(X0,sF2_fnc)))),
% 76.97/12.75 inference(forward_demodulation,[status(thm)],[f159,f71268])).
% 76.97/12.75 fof(f71903,plain,(
% 76.97/12.75 greatest_lower_bound(sF0_fnc,a)=sF0_fnc),
% 76.97/12.75 inference(paramodulation,[status(thm)],[f71557,f75])).
% 76.97/12.75 fof(f71937,plain,(
% 76.97/12.75 greatest_lower_bound(a,multiply(a,sF1_fnc))=sF0_fnc),
% 76.97/12.75 inference(backward_demodulation,[status(thm)],[f71938,f56985])).
% 76.97/12.75 fof(f71938,plain,(
% 76.97/12.75 greatest_lower_bound(a,sF0_fnc)=sF0_fnc),
% 76.97/12.75 inference(forward_demodulation,[status(thm)],[f23,f71903])).
% 76.97/12.75 fof(f73853,plain,(
% 76.97/12.75 multiply(inverse(a),sF0_fnc)=greatest_lower_bound(identity,multiply(inverse(a),multiply(a,sF1_fnc)))),
% 76.97/12.75 inference(paramodulation,[status(thm)],[f71937,f648])).
% 76.97/12.75 fof(f73910,plain,(
% 76.97/12.75 multiply(inverse(a),sF0_fnc)=greatest_lower_bound(identity,sF1_fnc)),
% 76.97/12.75 inference(forward_demodulation,[status(thm)],[f101,f73853])).
% 76.97/12.75 fof(f73913,plain,(
% 76.97/12.75 multiply(inverse(a),sF0_fnc)=identity),
% 76.97/12.75 inference(forward_demodulation,[status(thm)],[f81,f73910])).
% 76.97/12.75 fof(f73948,plain,(
% 76.97/12.75 sF0_fnc=multiply(a,identity)),
% 76.97/12.75 inference(paramodulation,[status(thm)],[f73913,f148])).
% 76.97/12.75 fof(f73998,plain,(
% 76.97/12.75 sF0_fnc=a),
% 76.97/12.75 inference(forward_demodulation,[status(thm)],[f159,f73948])).
% 76.97/12.75 fof(f73999,plain,(
% 76.97/12.75 $false),
% 76.97/12.75 inference(forward_subsumption_resolution,[status(thm)],[f73998,f42])).
% 76.97/12.75 % SZS output end CNFRefutation for theBenchmark.p
% 76.97/12.79 % Elapsed time: 12.431527 seconds
% 76.97/12.79 % CPU time: 98.177036 seconds
% 76.97/12.79 % Total memory used: 775.819 MB
% 76.97/12.79 % Net memory used: 763.940 MB
%------------------------------------------------------------------------------