%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP186-2 : 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 : n005.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 12:36:13 PM UTC 2026
% Result : Unsatisfiable 163.83s 21.12s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP186-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:05:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 163.83/21.12 % Refutation found
% 163.83/21.12 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 163.83/21.12 % SZS output start CNFRefutation for theBenchmark
% 163.83/21.12 fof(f1,axiom,(
% 163.83/21.12 (![X]: (multiply(identity,X) = X ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f2,axiom,(
% 163.83/21.12 (![X]: (multiply(inverse(X),X) = identity ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f3,axiom,(
% 163.83/21.12 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f4,axiom,(
% 163.83/21.12 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f5,axiom,(
% 163.83/21.12 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f6,axiom,(
% 163.83/21.12 (![X,Y,Z]: (greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f7,axiom,(
% 163.83/21.12 (![X,Y,Z]: (least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f10,axiom,(
% 163.83/21.12 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f11,axiom,(
% 163.83/21.12 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f12,axiom,(
% 163.83/21.12 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f13,axiom,(
% 163.83/21.12 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f14,axiom,(
% 163.83/21.12 (![Y,Z,X]: (multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f15,axiom,(
% 163.83/21.12 (![Y,Z,X]: (multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f16,hypothesis,(
% 163.83/21.12 inverse(identity) = identity ),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f17,hypothesis,(
% 163.83/21.12 (![X]: (inverse(inverse(X)) = X ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f18,hypothesis,(
% 163.83/21.12 (![X,Y]: (inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ))),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f19,negated_conjecture,(
% 163.83/21.12 least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) ),
% 163.83/21.12 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 163.83/21.12 fof(f20,plain,(
% 163.83/21.12 ![X0]: (multiply(identity,X0)=X0)),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f1])).
% 163.83/21.12 fof(f21,plain,(
% 163.83/21.12 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f2])).
% 163.83/21.12 fof(f22,plain,(
% 163.83/21.12 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f3])).
% 163.83/21.12 fof(f23,plain,(
% 163.83/21.12 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f4])).
% 163.83/21.12 fof(f24,plain,(
% 163.83/21.12 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f5])).
% 163.83/21.12 fof(f25,plain,(
% 163.83/21.12 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(greatest_lower_bound(X0,X1),X2))),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f6])).
% 163.83/21.12 fof(f26,plain,(
% 163.83/21.12 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,X2))=least_upper_bound(least_upper_bound(X0,X1),X2))),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f7])).
% 163.83/21.12 fof(f29,plain,(
% 163.83/21.12 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f10])).
% 163.83/21.12 fof(f30,plain,(
% 163.83/21.12 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 163.83/21.12 inference(cnf_transformation,[status(thm)],[f11])).
% 163.83/21.13 fof(f31,plain,(
% 163.83/21.13 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 163.83/21.13 inference(cnf_transformation,[status(thm)],[f12])).
% 163.83/21.13 fof(f32,plain,(
% 163.83/21.13 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 163.83/21.13 inference(cnf_transformation,[status(thm)],[f13])).
% 163.83/21.13 fof(f33,plain,(
% 163.83/21.13 ![X0,X1,X2]: (multiply(least_upper_bound(X0,X1),X2)=least_upper_bound(multiply(X0,X2),multiply(X1,X2)))),
% 163.83/21.13 inference(cnf_transformation,[status(thm)],[f14])).
% 163.83/21.13 fof(f34,plain,(
% 163.83/21.13 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,X1),X2)=greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)))),
% 163.83/21.13 inference(cnf_transformation,[status(thm)],[f15])).
% 163.83/21.13 fof(f35,plain,(
% 163.83/21.13 inverse(identity)=identity),
% 163.83/21.13 inference(cnf_transformation,[status(thm)],[f16])).
% 163.83/21.13 fof(f36,plain,(
% 163.83/21.13 ![X0]: (inverse(inverse(X0))=X0)),
% 163.83/21.13 inference(cnf_transformation,[status(thm)],[f17])).
% 163.83/21.13 fof(f37,plain,(
% 163.83/21.13 ![X0,X1]: (inverse(multiply(X0,X1))=multiply(inverse(X1),inverse(X0)))),
% 163.83/21.13 inference(cnf_transformation,[status(thm)],[f18])).
% 163.83/21.13 fof(f38,plain,(
% 163.83/21.13 ~least_upper_bound(multiply(a,b),identity)=multiply(a,inverse(greatest_lower_bound(a,inverse(b))))),
% 163.83/21.13 inference(cnf_transformation,[status(thm)],[f19])).
% 163.83/21.13 fof(f39,definition,(
% 163.83/21.13 sF1_fnc=multiply(a,b)),
% 163.83/21.13 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 163.83/21.13 fof(f40,definition,(
% 163.83/21.13 sF0_fnc=least_upper_bound(sF1_fnc,identity)),
% 163.83/21.13 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 163.83/21.13 fof(f41,definition,(
% 163.83/21.13 sF5_fnc=inverse(b)),
% 163.83/21.13 introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition])).
% 163.83/21.13 fof(f42,definition,(
% 163.83/21.13 sF4_fnc=greatest_lower_bound(a,sF5_fnc)),
% 163.83/21.13 introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition])).
% 163.83/21.13 fof(f43,definition,(
% 163.83/21.13 sF3_fnc=inverse(sF4_fnc)),
% 163.83/21.13 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 163.83/21.13 fof(f44,definition,(
% 163.83/21.13 sF2_fnc=multiply(a,sF3_fnc)),
% 163.83/21.13 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 163.83/21.13 fof(f45,plain,(
% 163.83/21.13 ~sF0_fnc=sF2_fnc),
% 163.83/21.13 inference(definition_folding,[],[f38,f44,f43,f42,f41,f40,f39])).
% 163.83/21.13 fof(f46,plain,(
% 163.83/21.13 sF0_fnc=least_upper_bound(identity,sF1_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f24,f40])).
% 163.83/21.13 fof(f48,plain,(
% 163.83/21.13 multiply(sF5_fnc,b)=identity),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f41,f21])).
% 163.83/21.13 fof(f49,plain,(
% 163.83/21.13 multiply(sF3_fnc,sF4_fnc)=identity),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f43,f21])).
% 163.83/21.13 fof(f51,plain,(
% 163.83/21.13 inverse(sF3_fnc)=sF4_fnc),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f43,f36])).
% 163.83/21.13 fof(f52,plain,(
% 163.83/21.13 inverse(sF5_fnc)=b),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f41,f36])).
% 163.83/21.13 fof(f54,plain,(
% 163.83/21.13 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f36,f21])).
% 163.83/21.13 fof(f56,plain,(
% 163.83/21.13 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f21,f22])).
% 163.83/21.13 fof(f60,plain,(
% 163.83/21.13 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f20,f56])).
% 163.83/21.13 fof(f62,plain,(
% 163.83/21.13 multiply(sF4_fnc,sF3_fnc)=identity),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f51,f21])).
% 163.83/21.13 fof(f64,plain,(
% 163.83/21.13 multiply(b,sF5_fnc)=identity),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f52,f21])).
% 163.83/21.13 fof(f70,plain,(
% 163.83/21.13 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X1,X0))=X0)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f23,f29])).
% 163.83/21.13 fof(f72,plain,(
% 163.83/21.13 ![X0]: (multiply(sF1_fnc,X0)=multiply(a,multiply(b,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f39,f22])).
% 163.83/21.13 fof(f73,plain,(
% 163.83/21.13 ![X0]: (multiply(sF2_fnc,X0)=multiply(a,multiply(sF3_fnc,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f44,f22])).
% 163.83/21.13 fof(f76,plain,(
% 163.83/21.13 ![X0]: (multiply(identity,X0)=multiply(sF3_fnc,multiply(sF4_fnc,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f49,f22])).
% 163.83/21.13 fof(f77,plain,(
% 163.83/21.13 ![X0]: (X0=multiply(sF3_fnc,multiply(sF4_fnc,X0)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f20,f76])).
% 163.83/21.13 fof(f86,plain,(
% 163.83/21.13 least_upper_bound(a,sF4_fnc)=a),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f42,f29])).
% 163.83/21.13 fof(f87,plain,(
% 163.83/21.13 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(X2,greatest_lower_bound(X0,X1)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f23,f25])).
% 163.83/21.13 fof(f111,plain,(
% 163.83/21.13 ![X0,X1]: (multiply(identity,X0)=multiply(X1,multiply(inverse(X1),X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f54,f22])).
% 163.83/21.13 fof(f112,plain,(
% 163.83/21.13 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f20,f111])).
% 163.83/21.13 fof(f115,plain,(
% 163.83/21.13 least_upper_bound(sF5_fnc,sF4_fnc)=sF5_fnc),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f42,f70])).
% 163.83/21.13 fof(f120,plain,(
% 163.83/21.13 least_upper_bound(sF4_fnc,sF5_fnc)=sF5_fnc),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f24,f115])).
% 163.83/21.13 fof(f124,plain,(
% 163.83/21.13 greatest_lower_bound(identity,sF0_fnc)=identity),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f46,f30])).
% 163.83/21.13 fof(f127,plain,(
% 163.83/21.13 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X1,X0))=X0)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f24,f30])).
% 163.83/21.13 fof(f132,plain,(
% 163.83/21.13 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2))=greatest_lower_bound(X0,X2))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f30,f25])).
% 163.83/21.13 fof(f143,plain,(
% 163.83/21.13 ![X0]: (least_upper_bound(identity,least_upper_bound(sF1_fnc,X0))=least_upper_bound(sF0_fnc,X0))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f46,f26])).
% 163.83/21.13 fof(f173,plain,(
% 163.83/21.13 greatest_lower_bound(sF1_fnc,sF0_fnc)=sF1_fnc),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f46,f127])).
% 163.83/21.13 fof(f185,plain,(
% 163.83/21.13 greatest_lower_bound(sF0_fnc,sF1_fnc)=sF1_fnc),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f23,f173])).
% 163.83/21.13 fof(f197,plain,(
% 163.83/21.13 ![X0]: (multiply(a,least_upper_bound(sF3_fnc,X0))=least_upper_bound(sF2_fnc,multiply(a,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f44,f31])).
% 163.83/21.13 fof(f210,plain,(
% 163.83/21.13 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(multiply(inverse(X0),X1),identity))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f21,f31])).
% 163.83/21.13 fof(f232,plain,(
% 163.83/21.13 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(identity,multiply(inverse(X0),X1)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f24,f210])).
% 163.83/21.13 fof(f262,plain,(
% 163.83/21.13 ![X0]: (multiply(a,greatest_lower_bound(sF3_fnc,X0))=greatest_lower_bound(sF2_fnc,multiply(a,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f44,f32])).
% 163.83/21.13 fof(f265,plain,(
% 163.83/21.13 ![X0,X1]: (multiply(inverse(X0),greatest_lower_bound(X0,X1))=greatest_lower_bound(identity,multiply(inverse(X0),X1)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f21,f32])).
% 163.83/21.13 fof(f351,plain,(
% 163.83/21.13 ![X0]: (multiply(least_upper_bound(a,X0),sF3_fnc)=least_upper_bound(sF2_fnc,multiply(X0,sF3_fnc)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f44,f33])).
% 163.83/21.13 fof(f355,plain,(
% 163.83/21.13 ![X0,X1]: (multiply(least_upper_bound(identity,X0),X1)=least_upper_bound(X1,multiply(X0,X1)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f20,f33])).
% 163.83/21.13 fof(f436,plain,(
% 163.83/21.13 ![X0]: (X0=multiply(X0,identity))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f21,f112])).
% 163.83/21.13 fof(f492,plain,(
% 163.83/21.13 ![X0]: (multiply(greatest_lower_bound(a,X0),sF3_fnc)=greatest_lower_bound(sF2_fnc,multiply(X0,sF3_fnc)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f44,f34])).
% 163.83/21.13 fof(f493,plain,(
% 163.83/21.13 ![X0]: (multiply(greatest_lower_bound(a,X0),b)=greatest_lower_bound(sF1_fnc,multiply(X0,b)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f39,f34])).
% 163.83/21.13 fof(f498,plain,(
% 163.83/21.13 ![X0,X1]: (multiply(greatest_lower_bound(X0,X1),inverse(X0))=greatest_lower_bound(identity,multiply(X1,inverse(X0))))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f54,f34])).
% 163.83/21.13 fof(f555,plain,(
% 163.83/21.13 ![X0,X1]: (multiply(X0,greatest_lower_bound(identity,X1))=greatest_lower_bound(X0,multiply(X0,X1)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f436,f32])).
% 163.83/21.13 fof(f605,plain,(
% 163.83/21.13 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,inverse(X1)),multiply(X1,X2))=greatest_lower_bound(multiply(X0,multiply(X1,X2)),X2))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f60,f34])).
% 163.83/21.13 fof(f609,plain,(
% 163.83/21.13 ![X0,X1,X2]: (multiply(inverse(X0),greatest_lower_bound(X1,multiply(X0,X2)))=greatest_lower_bound(multiply(inverse(X0),X1),X2))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f60,f32])).
% 163.83/21.13 fof(f621,plain,(
% 163.83/21.13 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,inverse(X1)),multiply(X1,X2))=greatest_lower_bound(X2,multiply(X0,multiply(X1,X2))))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f23,f605])).
% 163.83/21.13 fof(f658,plain,(
% 163.83/21.13 ![X0]: (inverse(multiply(X0,sF5_fnc))=multiply(b,inverse(X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f52,f37])).
% 163.83/21.13 fof(f661,plain,(
% 163.83/21.13 ![X0]: (inverse(multiply(X0,sF4_fnc))=multiply(sF3_fnc,inverse(X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f43,f37])).
% 163.83/21.13 fof(f662,plain,(
% 163.83/21.13 ![X0]: (inverse(multiply(X0,b))=multiply(sF5_fnc,inverse(X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f41,f37])).
% 163.83/21.13 fof(f665,plain,(
% 163.83/21.13 ![X0]: (inverse(multiply(sF3_fnc,X0))=multiply(inverse(X0),sF4_fnc))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f51,f37])).
% 163.83/21.13 fof(f668,plain,(
% 163.83/21.13 ![X0]: (inverse(multiply(b,X0))=multiply(inverse(X0),sF5_fnc))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f41,f37])).
% 163.83/21.13 fof(f974,plain,(
% 163.83/21.13 ![X0]: (multiply(sF2_fnc,multiply(sF4_fnc,X0))=multiply(a,X0))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f77,f73])).
% 163.83/21.13 fof(f1096,plain,(
% 163.83/21.13 ![X0,X1,X2]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(least_upper_bound(X1,X2),greatest_lower_bound(X0,X1)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f30,f87])).
% 163.83/21.13 fof(f1169,plain,(
% 163.83/21.13 ![X0,X1,X2]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X0)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f87,f1096])).
% 163.83/21.13 fof(f4360,plain,(
% 163.83/21.13 inverse(multiply(sF3_fnc,sF5_fnc))=multiply(b,sF4_fnc)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f51,f658])).
% 163.83/21.13 fof(f4686,plain,(
% 163.83/21.13 inverse(multiply(sF4_fnc,b))=multiply(sF5_fnc,sF3_fnc)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f43,f662])).
% 163.83/21.13 fof(f9871,plain,(
% 163.83/21.13 multiply(inverse(sF5_fnc),sF5_fnc)=least_upper_bound(identity,multiply(inverse(sF5_fnc),sF4_fnc))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f120,f232])).
% 163.83/21.13 fof(f9945,plain,(
% 163.83/21.13 inverse(multiply(b,sF5_fnc))=least_upper_bound(identity,multiply(inverse(sF5_fnc),sF4_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f668,f9871])).
% 163.83/21.13 fof(f9946,plain,(
% 163.83/21.13 inverse(identity)=least_upper_bound(identity,multiply(inverse(sF5_fnc),sF4_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f64,f9945])).
% 163.83/21.13 fof(f9947,plain,(
% 163.83/21.13 identity=least_upper_bound(identity,multiply(inverse(sF5_fnc),sF4_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f35,f9946])).
% 163.83/21.13 fof(f9948,plain,(
% 163.83/21.13 identity=least_upper_bound(identity,inverse(multiply(sF3_fnc,sF5_fnc)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f665,f9947])).
% 163.83/21.13 fof(f9949,plain,(
% 163.83/21.13 identity=least_upper_bound(identity,multiply(b,sF4_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f4360,f9948])).
% 163.83/21.13 fof(f19133,plain,(
% 163.83/21.13 multiply(a,sF3_fnc)=least_upper_bound(sF2_fnc,multiply(sF4_fnc,sF3_fnc))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f86,f351])).
% 163.83/21.13 fof(f19190,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(sF2_fnc,multiply(sF4_fnc,sF3_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f44,f19133])).
% 163.83/21.13 fof(f19191,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(sF2_fnc,identity)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f62,f19190])).
% 163.83/21.13 fof(f19192,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(identity,sF2_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f24,f19191])).
% 163.83/21.13 fof(f20978,plain,(
% 163.83/21.13 ![X0]: (multiply(identity,X0)=least_upper_bound(X0,multiply(multiply(b,sF4_fnc),X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f9949,f355])).
% 163.83/21.13 fof(f21120,plain,(
% 163.83/21.13 ![X0]: (X0=least_upper_bound(X0,multiply(multiply(b,sF4_fnc),X0)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f20,f20978])).
% 163.83/21.13 fof(f21121,plain,(
% 163.83/21.13 ![X0]: (X0=least_upper_bound(X0,multiply(b,multiply(sF4_fnc,X0))))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f22,f21120])).
% 163.83/21.13 fof(f22343,plain,(
% 163.83/21.13 multiply(a,sF3_fnc)=least_upper_bound(sF2_fnc,multiply(a,multiply(b,multiply(sF4_fnc,sF3_fnc))))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f21121,f197])).
% 163.83/21.13 fof(f22424,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(sF2_fnc,multiply(a,multiply(b,multiply(sF4_fnc,sF3_fnc))))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f44,f22343])).
% 163.83/21.13 fof(f22425,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(sF2_fnc,multiply(sF1_fnc,multiply(sF4_fnc,sF3_fnc)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f72,f22424])).
% 163.83/21.13 fof(f22426,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(sF2_fnc,multiply(sF1_fnc,identity))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f62,f22425])).
% 163.83/21.13 fof(f22427,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(sF2_fnc,sF1_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f436,f22426])).
% 163.83/21.13 fof(f22428,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(sF1_fnc,sF2_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f24,f22427])).
% 163.83/21.13 fof(f23010,plain,(
% 163.83/21.13 least_upper_bound(identity,sF2_fnc)=least_upper_bound(sF0_fnc,sF2_fnc)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f22428,f143])).
% 163.83/21.13 fof(f23042,plain,(
% 163.83/21.13 sF2_fnc=least_upper_bound(sF0_fnc,sF2_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f19192,f23010])).
% 163.83/21.13 fof(f23076,plain,(
% 163.83/21.13 ![X0]: (greatest_lower_bound(X0,sF0_fnc)=greatest_lower_bound(sF0_fnc,greatest_lower_bound(sF2_fnc,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f23042,f1169])).
% 163.83/21.13 fof(f23091,plain,(
% 163.83/21.13 ![X0]: (greatest_lower_bound(sF0_fnc,greatest_lower_bound(sF2_fnc,X0))=greatest_lower_bound(sF0_fnc,X0))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f23042,f132])).
% 163.83/21.13 fof(f26152,plain,(
% 163.83/21.13 multiply(sF4_fnc,sF3_fnc)=greatest_lower_bound(sF2_fnc,multiply(sF5_fnc,sF3_fnc))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f42,f492])).
% 163.83/21.13 fof(f26222,plain,(
% 163.83/21.13 identity=greatest_lower_bound(sF2_fnc,multiply(sF5_fnc,sF3_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f62,f26152])).
% 163.83/21.13 fof(f26518,plain,(
% 163.83/21.13 multiply(sF4_fnc,b)=greatest_lower_bound(sF1_fnc,multiply(sF5_fnc,b))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f42,f493])).
% 163.83/21.13 fof(f26582,plain,(
% 163.83/21.13 multiply(sF4_fnc,b)=greatest_lower_bound(sF1_fnc,identity)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f48,f26518])).
% 163.83/21.13 fof(f26616,plain,(
% 163.83/21.13 inverse(greatest_lower_bound(identity,sF1_fnc))=multiply(sF5_fnc,sF3_fnc)),
% 163.83/21.13 inference(backward_demodulation,[status(thm)],[f26618,f4686])).
% 163.83/21.13 fof(f26618,plain,(
% 163.83/21.13 multiply(sF4_fnc,b)=greatest_lower_bound(identity,sF1_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f23,f26582])).
% 163.83/21.13 fof(f26932,plain,(
% 163.83/21.13 multiply(sF2_fnc,greatest_lower_bound(identity,sF1_fnc))=multiply(a,b)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f26618,f974])).
% 163.83/21.13 fof(f26963,plain,(
% 163.83/21.13 ![X0]: (multiply(greatest_lower_bound(identity,sF1_fnc),X0)=multiply(sF4_fnc,multiply(b,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f26618,f22])).
% 163.83/21.13 fof(f26965,plain,(
% 163.83/21.13 greatest_lower_bound(sF2_fnc,multiply(sF2_fnc,sF1_fnc))=multiply(a,b)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f555,f26932])).
% 163.83/21.13 fof(f26966,plain,(
% 163.83/21.13 greatest_lower_bound(sF2_fnc,multiply(sF2_fnc,sF1_fnc))=sF1_fnc),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f39,f26965])).
% 163.83/21.13 fof(f27376,plain,(
% 163.83/21.13 multiply(inverse(sF2_fnc),sF1_fnc)=greatest_lower_bound(identity,multiply(inverse(sF2_fnc),multiply(sF2_fnc,sF1_fnc)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f26966,f265])).
% 163.83/21.13 fof(f27403,plain,(
% 163.83/21.13 multiply(inverse(sF2_fnc),sF1_fnc)=greatest_lower_bound(identity,sF1_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f60,f27376])).
% 163.83/21.13 fof(f85469,plain,(
% 163.83/21.13 greatest_lower_bound(multiply(sF5_fnc,sF3_fnc),sF0_fnc)=greatest_lower_bound(sF0_fnc,identity)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f26222,f23076])).
% 163.83/21.13 fof(f85625,plain,(
% 163.83/21.13 greatest_lower_bound(sF0_fnc,multiply(sF5_fnc,sF3_fnc))=greatest_lower_bound(sF0_fnc,identity)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f23,f85469])).
% 163.83/21.13 fof(f85626,plain,(
% 163.83/21.13 greatest_lower_bound(sF0_fnc,multiply(sF5_fnc,sF3_fnc))=greatest_lower_bound(identity,sF0_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f23,f85625])).
% 163.83/21.13 fof(f85627,plain,(
% 163.83/21.13 greatest_lower_bound(sF0_fnc,multiply(sF5_fnc,sF3_fnc))=identity),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f124,f85626])).
% 163.83/21.13 fof(f86304,plain,(
% 163.83/21.13 multiply(inverse(sF0_fnc),identity)=greatest_lower_bound(identity,multiply(inverse(sF0_fnc),multiply(sF5_fnc,sF3_fnc)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f85627,f265])).
% 163.83/21.13 fof(f86368,plain,(
% 163.83/21.13 inverse(sF0_fnc)=greatest_lower_bound(identity,multiply(inverse(sF0_fnc),multiply(sF5_fnc,sF3_fnc)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f436,f86304])).
% 163.83/21.13 fof(f87390,plain,(
% 163.83/21.13 multiply(identity,inverse(sF2_fnc))=greatest_lower_bound(identity,multiply(multiply(sF5_fnc,sF3_fnc),inverse(sF2_fnc)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f26222,f498])).
% 163.83/21.13 fof(f87715,plain,(
% 163.83/21.13 inverse(sF2_fnc)=greatest_lower_bound(identity,multiply(multiply(sF5_fnc,sF3_fnc),inverse(sF2_fnc)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f20,f87390])).
% 163.83/21.13 fof(f87716,plain,(
% 163.83/21.13 inverse(sF2_fnc)=greatest_lower_bound(identity,multiply(sF5_fnc,multiply(sF3_fnc,inverse(sF2_fnc))))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f22,f87715])).
% 163.83/21.13 fof(f87717,plain,(
% 163.83/21.13 inverse(sF2_fnc)=greatest_lower_bound(identity,multiply(sF5_fnc,inverse(multiply(sF2_fnc,sF4_fnc))))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f661,f87716])).
% 163.83/21.13 fof(f87718,plain,(
% 163.83/21.13 inverse(sF2_fnc)=greatest_lower_bound(identity,inverse(multiply(multiply(sF2_fnc,sF4_fnc),b)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f662,f87717])).
% 163.83/21.13 fof(f87719,plain,(
% 163.83/21.13 inverse(sF2_fnc)=greatest_lower_bound(identity,inverse(multiply(sF2_fnc,multiply(sF4_fnc,b))))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f22,f87718])).
% 163.83/21.13 fof(f87720,plain,(
% 163.83/21.13 inverse(sF2_fnc)=greatest_lower_bound(identity,inverse(multiply(a,b)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f974,f87719])).
% 163.83/21.13 fof(f87724,plain,(
% 163.83/21.13 inverse(sF2_fnc)=greatest_lower_bound(identity,inverse(sF1_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f39,f87720])).
% 163.83/21.13 fof(f90988,plain,(
% 163.83/21.13 ![X0]: (inverse(multiply(greatest_lower_bound(identity,sF1_fnc),X0))=multiply(inverse(X0),multiply(sF5_fnc,sF3_fnc)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f26616,f37])).
% 163.83/21.13 fof(f91093,plain,(
% 163.83/21.13 inverse(sF0_fnc)=greatest_lower_bound(identity,inverse(multiply(sF4_fnc,multiply(b,sF0_fnc))))),
% 163.83/21.13 inference(backward_demodulation,[status(thm)],[f91095,f86368])).
% 163.83/21.13 fof(f91095,plain,(
% 163.83/21.13 ![X0]: (inverse(multiply(sF4_fnc,multiply(b,X0)))=multiply(inverse(X0),multiply(sF5_fnc,sF3_fnc)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f26963,f90988])).
% 163.83/21.13 fof(f91367,plain,(
% 163.83/21.13 ![X0]: (multiply(greatest_lower_bound(identity,sF1_fnc),X0)=multiply(inverse(sF2_fnc),multiply(sF1_fnc,X0)))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f27403,f22])).
% 163.83/21.13 fof(f91473,plain,(
% 163.83/21.13 ![X0]: (multiply(sF4_fnc,multiply(b,X0))=multiply(inverse(sF2_fnc),multiply(sF1_fnc,X0)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f26963,f91367])).
% 163.83/21.13 fof(f93014,plain,(
% 163.83/21.13 ![X0]: (multiply(inverse(sF2_fnc),multiply(sF1_fnc,X0))=greatest_lower_bound(X0,multiply(identity,multiply(sF1_fnc,X0))))),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f87724,f621])).
% 163.83/21.13 fof(f93370,plain,(
% 163.83/21.13 ![X0]: (multiply(sF4_fnc,multiply(b,X0))=greatest_lower_bound(X0,multiply(identity,multiply(sF1_fnc,X0))))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f91473,f93014])).
% 163.83/21.13 fof(f93371,plain,(
% 163.83/21.13 inverse(sF0_fnc)=greatest_lower_bound(identity,inverse(greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,sF0_fnc))))),
% 163.83/21.13 inference(backward_demodulation,[status(thm)],[f93379,f91093])).
% 163.83/21.13 fof(f93379,plain,(
% 163.83/21.13 ![X0]: (multiply(sF4_fnc,multiply(b,X0))=greatest_lower_bound(X0,multiply(sF1_fnc,X0)))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f20,f93370])).
% 163.83/21.13 fof(f102704,plain,(
% 163.83/21.13 multiply(inverse(sF5_fnc),identity)=greatest_lower_bound(multiply(inverse(sF5_fnc),sF0_fnc),sF3_fnc)),
% 163.83/21.13 inference(paramodulation,[status(thm)],[f85627,f609])).
% 163.83/21.13 fof(f103093,plain,(
% 163.83/21.13 inverse(sF5_fnc)=greatest_lower_bound(multiply(inverse(sF5_fnc),sF0_fnc),sF3_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f436,f102704])).
% 163.83/21.13 fof(f103094,plain,(
% 163.83/21.13 b=greatest_lower_bound(multiply(inverse(sF5_fnc),sF0_fnc),sF3_fnc)),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f52,f103093])).
% 163.83/21.13 fof(f103095,plain,(
% 163.83/21.13 b=greatest_lower_bound(sF3_fnc,multiply(inverse(sF5_fnc),sF0_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f23,f103094])).
% 163.83/21.13 fof(f103096,plain,(
% 163.83/21.13 b=greatest_lower_bound(sF3_fnc,multiply(b,sF0_fnc))),
% 163.83/21.13 inference(forward_demodulation,[status(thm)],[f52,f103095])).
% 163.83/21.13 fof(f103663,plain,(
% 21.08/21.41 multiply(a,b)=greatest_lower_bound(sF2_fnc,multiply(a,multiply(b,sF0_fnc)))),
% 21.08/21.41 inference(paramodulation,[status(thm)],[f103096,f262])).
% 21.08/21.41 fof(f103717,plain,(
% 21.08/21.41 sF1_fnc=greatest_lower_bound(sF2_fnc,multiply(a,multiply(b,sF0_fnc)))),
% 21.08/21.41 inference(forward_demodulation,[status(thm)],[f39,f103663])).
% 21.08/21.41 fof(f103718,plain,(
% 21.08/21.41 sF1_fnc=greatest_lower_bound(sF2_fnc,multiply(sF1_fnc,sF0_fnc))),
% 21.08/21.41 inference(forward_demodulation,[status(thm)],[f72,f103717])).
% 21.08/21.41 fof(f104857,plain,(
% 21.08/21.41 greatest_lower_bound(sF0_fnc,sF1_fnc)=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,sF0_fnc))),
% 21.08/21.41 inference(paramodulation,[status(thm)],[f103718,f23091])).
% 21.08/21.41 fof(f104912,plain,(
% 21.08/21.41 inverse(sF0_fnc)=greatest_lower_bound(identity,inverse(sF1_fnc))),
% 21.08/21.41 inference(backward_demodulation,[status(thm)],[f104913,f93371])).
% 21.08/21.41 fof(f104913,plain,(
% 21.08/21.41 sF1_fnc=greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,sF0_fnc))),
% 21.08/21.41 inference(forward_demodulation,[status(thm)],[f185,f104857])).
% 21.08/21.41 fof(f104999,plain,(
% 21.08/21.41 inverse(sF2_fnc)=inverse(sF0_fnc)),
% 21.08/21.41 inference(backward_demodulation,[status(thm)],[f104912,f87724])).
% 21.08/21.41 fof(f105883,plain,(
% 21.08/21.41 inverse(inverse(sF0_fnc))=sF2_fnc),
% 21.08/21.41 inference(paramodulation,[status(thm)],[f104999,f36])).
% 21.08/21.41 fof(f106222,plain,(
% 21.08/21.41 sF0_fnc=sF2_fnc),
% 21.08/21.41 inference(forward_demodulation,[status(thm)],[f36,f105883])).
% 21.08/21.41 fof(f106223,plain,(
% 21.08/21.41 $false),
% 21.08/21.41 inference(forward_subsumption_resolution,[status(thm)],[f106222,f45])).
% 21.08/21.41 % SZS output end CNFRefutation for theBenchmark.p
% 21.08/21.42 % Elapsed time: 21.030346 seconds
% 21.08/21.42 % CPU time: 166.571734 seconds
% 21.08/21.42 % Total memory used: 1.219 GB
% 21.08/21.42 % Net memory used: 1.200 GB
%------------------------------------------------------------------------------