%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP179-2 : 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 : n014.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 20.93s 3.18s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP179-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n014.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 20:04:37 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 20.93/3.18 % Refutation found
% 20.93/3.18 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 20.93/3.18 % SZS output start CNFRefutation for theBenchmark
% 20.93/3.18 fof(f1,axiom,(
% 20.93/3.18 (![X]: (multiply(identity,X) = X ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f2,axiom,(
% 20.93/3.18 (![X]: (multiply(inverse(X),X) = identity ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f3,axiom,(
% 20.93/3.18 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f4,axiom,(
% 20.93/3.18 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f5,axiom,(
% 20.93/3.18 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f6,axiom,(
% 20.93/3.18 (![X,Y,Z]: (greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f7,axiom,(
% 20.93/3.18 (![X,Y,Z]: (least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f10,axiom,(
% 20.93/3.18 (![X,Y]: (least_upper_bound(X,greatest_lower_bound(X,Y)) = X ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f11,axiom,(
% 20.93/3.18 (![X,Y]: (greatest_lower_bound(X,least_upper_bound(X,Y)) = X ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f12,axiom,(
% 20.93/3.18 (![X,Y,Z]: (multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f13,axiom,(
% 20.93/3.18 (![X,Y,Z]: (multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f14,axiom,(
% 20.93/3.18 (![Y,Z,X]: (multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ))),
% 20.93/3.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.18 fof(f15,axiom,(
% 20.93/3.19 (![Y,Z,X]: (multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ))),
% 20.93/3.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.19 fof(f16,negated_conjecture,(
% 20.93/3.19 least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)) ),
% 20.93/3.19 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 20.93/3.19 fof(f17,plain,(
% 20.93/3.19 ![X0]: (multiply(identity,X0)=X0)),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f1])).
% 20.93/3.19 fof(f18,plain,(
% 20.93/3.19 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f2])).
% 20.93/3.19 fof(f19,plain,(
% 20.93/3.19 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f3])).
% 20.93/3.19 fof(f20,plain,(
% 20.93/3.19 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f4])).
% 20.93/3.19 fof(f21,plain,(
% 20.93/3.19 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f5])).
% 20.93/3.19 fof(f22,plain,(
% 20.93/3.19 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(greatest_lower_bound(X0,X1),X2))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f6])).
% 20.93/3.19 fof(f23,plain,(
% 20.93/3.19 ![X0,X1,X2]: (least_upper_bound(X0,least_upper_bound(X1,X2))=least_upper_bound(least_upper_bound(X0,X1),X2))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f7])).
% 20.93/3.19 fof(f26,plain,(
% 20.93/3.19 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X0,X1))=X0)),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f10])).
% 20.93/3.19 fof(f27,plain,(
% 20.93/3.19 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X0,X1))=X0)),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f11])).
% 20.93/3.19 fof(f28,plain,(
% 20.93/3.19 ![X0,X1,X2]: (multiply(X0,least_upper_bound(X1,X2))=least_upper_bound(multiply(X0,X1),multiply(X0,X2)))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f12])).
% 20.93/3.19 fof(f29,plain,(
% 20.93/3.19 ![X0,X1,X2]: (multiply(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f13])).
% 20.93/3.19 fof(f30,plain,(
% 20.93/3.19 ![X0,X1,X2]: (multiply(least_upper_bound(X0,X1),X2)=least_upper_bound(multiply(X0,X2),multiply(X1,X2)))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f14])).
% 20.93/3.19 fof(f31,plain,(
% 20.93/3.19 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,X1),X2)=greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f15])).
% 20.93/3.19 fof(f32,plain,(
% 20.93/3.19 ~least_upper_bound(inverse(a),identity)=inverse(greatest_lower_bound(a,identity))),
% 20.93/3.19 inference(cnf_transformation,[status(thm)],[f16])).
% 20.93/3.19 fof(f33,definition,(
% 20.93/3.19 sF1_fnc=inverse(a)),
% 20.93/3.19 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 20.93/3.19 fof(f34,definition,(
% 20.93/3.19 sF0_fnc=least_upper_bound(sF1_fnc,identity)),
% 20.93/3.19 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 20.93/3.19 fof(f35,definition,(
% 20.93/3.19 sF3_fnc=greatest_lower_bound(a,identity)),
% 20.93/3.19 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 20.93/3.19 fof(f36,definition,(
% 20.93/3.19 sF2_fnc=inverse(sF3_fnc)),
% 20.93/3.19 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 20.93/3.19 fof(f37,plain,(
% 20.93/3.19 ~sF0_fnc=sF2_fnc),
% 20.93/3.19 inference(definition_folding,[],[f32,f36,f35,f34,f33])).
% 20.93/3.19 fof(f38,plain,(
% 20.93/3.19 multiply(sF2_fnc,sF3_fnc)=identity),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f36,f18])).
% 20.93/3.19 fof(f39,plain,(
% 20.93/3.19 multiply(sF1_fnc,a)=identity),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f33,f18])).
% 20.93/3.19 fof(f40,plain,(
% 20.93/3.19 sF3_fnc=greatest_lower_bound(identity,a)),
% 20.93/3.19 inference(backward_demodulation,[status(thm)],[f20,f35])).
% 20.93/3.19 fof(f45,plain,(
% 20.93/3.19 sF0_fnc=least_upper_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(backward_demodulation,[status(thm)],[f21,f34])).
% 20.93/3.19 fof(f50,plain,(
% 20.93/3.19 ![X0,X1]: (least_upper_bound(X0,greatest_lower_bound(X1,X0))=X0)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f20,f26])).
% 20.93/3.19 fof(f54,plain,(
% 20.93/3.19 ![X0,X1]: (greatest_lower_bound(X0,least_upper_bound(X1,X0))=X0)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f21,f27])).
% 20.93/3.19 fof(f58,plain,(
% 20.93/3.19 least_upper_bound(identity,sF3_fnc)=identity),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f40,f26])).
% 20.93/3.19 fof(f59,plain,(
% 20.93/3.19 greatest_lower_bound(identity,sF0_fnc)=identity),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f45,f27])).
% 20.93/3.19 fof(f61,plain,(
% 20.93/3.19 least_upper_bound(a,sF3_fnc)=a),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f40,f50])).
% 20.93/3.19 fof(f70,plain,(
% 20.93/3.19 ![X0,X1,X2]: (greatest_lower_bound(X0,greatest_lower_bound(X1,X2))=greatest_lower_bound(X2,greatest_lower_bound(X0,X1)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f20,f22])).
% 20.93/3.19 fof(f80,plain,(
% 20.93/3.19 ![X0,X1,X2]: (least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0)))=X0)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f22,f50])).
% 20.93/3.19 fof(f93,plain,(
% 20.93/3.19 ![X0]: (least_upper_bound(identity,least_upper_bound(sF1_fnc,X0))=least_upper_bound(sF0_fnc,X0))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f45,f23])).
% 20.93/3.19 fof(f125,plain,(
% 20.93/3.19 greatest_lower_bound(sF3_fnc,identity)=sF3_fnc),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f58,f54])).
% 20.93/3.19 fof(f128,plain,(
% 20.93/3.19 greatest_lower_bound(identity,sF3_fnc)=sF3_fnc),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f20,f125])).
% 20.93/3.19 fof(f130,plain,(
% 20.93/3.19 least_upper_bound(sF0_fnc,identity)=sF0_fnc),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f59,f50])).
% 20.93/3.19 fof(f132,plain,(
% 20.93/3.19 least_upper_bound(identity,sF0_fnc)=sF0_fnc),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f130])).
% 20.93/3.19 fof(f144,plain,(
% 20.93/3.19 ![X0]: (least_upper_bound(identity,least_upper_bound(sF0_fnc,X0))=least_upper_bound(sF0_fnc,X0))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f132,f23])).
% 20.93/3.19 fof(f224,plain,(
% 20.93/3.19 ![X0]: (least_upper_bound(sF0_fnc,greatest_lower_bound(X0,identity))=sF0_fnc)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f59,f80])).
% 20.93/3.19 fof(f371,plain,(
% 20.93/3.19 ![X0]: (multiply(identity,X0)=multiply(sF1_fnc,multiply(a,X0)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f39,f19])).
% 20.93/3.19 fof(f372,plain,(
% 20.93/3.19 ![X0]: (multiply(identity,X0)=multiply(sF2_fnc,multiply(sF3_fnc,X0)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f38,f19])).
% 20.93/3.19 fof(f373,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f18,f19])).
% 20.93/3.19 fof(f377,plain,(
% 20.93/3.19 ![X0]: (X0=multiply(sF1_fnc,multiply(a,X0)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f17,f371])).
% 20.93/3.19 fof(f378,plain,(
% 20.93/3.19 ![X0]: (X0=multiply(sF2_fnc,multiply(sF3_fnc,X0)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f17,f372])).
% 20.93/3.19 fof(f379,plain,(
% 20.93/3.19 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f17,f373])).
% 20.93/3.19 fof(f384,plain,(
% 20.93/3.19 ![X0]: (multiply(sF1_fnc,least_upper_bound(a,X0))=least_upper_bound(identity,multiply(sF1_fnc,X0)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f39,f28])).
% 20.93/3.19 fof(f385,plain,(
% 20.93/3.19 ![X0]: (multiply(sF2_fnc,least_upper_bound(sF3_fnc,X0))=least_upper_bound(identity,multiply(sF2_fnc,X0)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f38,f28])).
% 20.93/3.19 fof(f389,plain,(
% 20.93/3.19 ![X0]: (multiply(sF1_fnc,least_upper_bound(X0,a))=least_upper_bound(multiply(sF1_fnc,X0),identity))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f39,f28])).
% 20.93/3.19 fof(f390,plain,(
% 20.93/3.19 ![X0]: (multiply(sF2_fnc,least_upper_bound(X0,sF3_fnc))=least_upper_bound(multiply(sF2_fnc,X0),identity))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f38,f28])).
% 20.93/3.19 fof(f391,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(multiply(inverse(X0),X1),identity))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f18,f28])).
% 20.93/3.19 fof(f409,plain,(
% 20.93/3.19 ![X0]: (multiply(sF1_fnc,least_upper_bound(X0,a))=least_upper_bound(identity,multiply(sF1_fnc,X0)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f389])).
% 20.93/3.19 fof(f410,plain,(
% 20.93/3.19 ![X0]: (multiply(sF2_fnc,least_upper_bound(X0,sF3_fnc))=least_upper_bound(identity,multiply(sF2_fnc,X0)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f390])).
% 20.93/3.19 fof(f411,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(inverse(X0),least_upper_bound(X1,X0))=least_upper_bound(identity,multiply(inverse(X0),X1)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f391])).
% 20.93/3.19 fof(f421,plain,(
% 20.93/3.19 ![X0]: (multiply(sF1_fnc,greatest_lower_bound(a,X0))=greatest_lower_bound(identity,multiply(sF1_fnc,X0)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f39,f29])).
% 20.93/3.19 fof(f428,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(inverse(X0),greatest_lower_bound(X1,X0))=greatest_lower_bound(multiply(inverse(X0),X1),identity))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f18,f29])).
% 20.93/3.19 fof(f448,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(inverse(X0),greatest_lower_bound(X1,X0))=greatest_lower_bound(identity,multiply(inverse(X0),X1)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f20,f428])).
% 20.93/3.19 fof(f470,plain,(
% 20.93/3.19 ![X0]: (least_upper_bound(sF0_fnc,greatest_lower_bound(identity,X0))=sF0_fnc)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f20,f224])).
% 20.93/3.19 fof(f575,plain,(
% 20.93/3.19 ![X0]: (multiply(a,X0)=multiply(inverse(sF1_fnc),X0))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f377,f379])).
% 20.93/3.19 fof(f579,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f379,f379])).
% 20.93/3.19 fof(f580,plain,(
% 20.93/3.19 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f18,f379])).
% 20.93/3.19 fof(f581,plain,(
% 20.93/3.19 ![X0]: (X0=multiply(inverse(identity),X0))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f17,f379])).
% 20.93/3.19 fof(f592,plain,(
% 20.93/3.19 ![X0]: (X0=multiply(inverse(inverse(identity)),X0))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f581,f379])).
% 20.93/3.19 fof(f633,plain,(
% 20.93/3.19 inverse(identity)=identity),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f18,f592])).
% 20.93/3.19 fof(f706,plain,(
% 20.93/3.19 ![X0]: (multiply(least_upper_bound(sF2_fnc,X0),sF3_fnc)=least_upper_bound(identity,multiply(X0,sF3_fnc)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f38,f30])).
% 20.93/3.19 fof(f712,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(least_upper_bound(identity,X0),X1)=least_upper_bound(X1,multiply(X0,X1)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f17,f30])).
% 20.93/3.19 fof(f723,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(least_upper_bound(X0,identity),X1)=least_upper_bound(multiply(X0,X1),X1))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f17,f30])).
% 20.93/3.19 fof(f743,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(least_upper_bound(X0,identity),X1)=least_upper_bound(X1,multiply(X0,X1)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f723])).
% 20.93/3.19 fof(f757,plain,(
% 20.93/3.19 ![X0]: (multiply(greatest_lower_bound(sF2_fnc,X0),sF3_fnc)=greatest_lower_bound(identity,multiply(X0,sF3_fnc)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f38,f31])).
% 20.93/3.19 fof(f763,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(greatest_lower_bound(identity,X0),X1)=greatest_lower_bound(X1,multiply(X0,X1)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f17,f31])).
% 20.93/3.19 fof(f872,plain,(
% 20.93/3.19 least_upper_bound(sF0_fnc,sF3_fnc)=sF0_fnc),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f128,f470])).
% 20.93/3.19 fof(f1173,plain,(
% 20.93/3.19 ![X0]: (greatest_lower_bound(X0,sF3_fnc)=greatest_lower_bound(a,greatest_lower_bound(X0,identity)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f40,f70])).
% 20.93/3.19 fof(f1278,plain,(
% 20.93/3.19 ![X0]: (greatest_lower_bound(X0,sF3_fnc)=greatest_lower_bound(identity,greatest_lower_bound(a,X0)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f70,f1173])).
% 20.93/3.19 fof(f2188,plain,(
% 20.93/3.19 ![X0]: (multiply(a,multiply(sF1_fnc,X0))=X0)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f379,f575])).
% 20.93/3.19 fof(f2189,plain,(
% 20.93/3.19 multiply(a,sF1_fnc)=identity),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f18,f575])).
% 20.93/3.19 fof(f2571,plain,(
% 20.93/3.19 ![X0]: (X0=multiply(X0,identity))),
% 20.93/3.19 inference(backward_demodulation,[status(thm)],[f579,f580])).
% 20.93/3.19 fof(f2573,plain,(
% 20.93/3.19 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f18,f579])).
% 20.93/3.19 fof(f2786,plain,(
% 20.93/3.19 ![X0]: (inverse(inverse(X0))=multiply(X0,identity))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f579,f2571])).
% 20.93/3.19 fof(f2811,plain,(
% 20.93/3.19 ![X0]: (inverse(inverse(X0))=X0)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f2571,f2786])).
% 20.93/3.19 fof(f2838,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(X0,multiply(X1,inverse(multiply(X0,X1))))=identity)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f19,f2573])).
% 20.93/3.19 fof(f3409,plain,(
% 20.93/3.19 multiply(sF1_fnc,least_upper_bound(a,identity))=least_upper_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f2571,f384])).
% 20.93/3.19 fof(f3426,plain,(
% 20.93/3.19 multiply(sF1_fnc,least_upper_bound(identity,a))=least_upper_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f3409])).
% 20.93/3.19 fof(f3427,plain,(
% 20.93/3.19 multiply(sF1_fnc,least_upper_bound(identity,a))=sF0_fnc),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f45,f3426])).
% 20.93/3.19 fof(f3439,plain,(
% 20.93/3.19 multiply(a,sF0_fnc)=least_upper_bound(identity,a)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f3427,f2188])).
% 20.93/3.19 fof(f5956,plain,(
% 20.93/3.19 multiply(sF2_fnc,least_upper_bound(sF3_fnc,identity))=least_upper_bound(identity,sF2_fnc)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f2571,f385])).
% 20.93/3.19 fof(f5981,plain,(
% 20.93/3.19 multiply(sF2_fnc,least_upper_bound(identity,sF3_fnc))=least_upper_bound(identity,sF2_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f5956])).
% 20.93/3.19 fof(f5982,plain,(
% 20.93/3.19 multiply(sF2_fnc,identity)=least_upper_bound(identity,sF2_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f58,f5981])).
% 20.93/3.19 fof(f5983,plain,(
% 20.93/3.19 sF2_fnc=least_upper_bound(identity,sF2_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f2571,f5982])).
% 20.93/3.19 fof(f9215,plain,(
% 20.93/3.19 ![X0]: (multiply(inverse(least_upper_bound(sF0_fnc,X0)),least_upper_bound(sF0_fnc,X0))=least_upper_bound(identity,multiply(inverse(least_upper_bound(sF0_fnc,X0)),identity)))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f144,f411])).
% 20.93/3.19 fof(f9297,plain,(
% 20.93/3.19 ![X0]: (identity=least_upper_bound(identity,multiply(inverse(least_upper_bound(sF0_fnc,X0)),identity)))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f18,f9215])).
% 20.93/3.19 fof(f9298,plain,(
% 20.93/3.19 ![X0]: (identity=least_upper_bound(identity,inverse(least_upper_bound(sF0_fnc,X0))))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f2571,f9297])).
% 20.93/3.19 fof(f9613,plain,(
% 20.93/3.19 identity=least_upper_bound(identity,inverse(sF0_fnc))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f872,f9298])).
% 20.93/3.19 fof(f9706,plain,(
% 20.93/3.19 greatest_lower_bound(inverse(sF0_fnc),identity)=inverse(sF0_fnc)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f9613,f54])).
% 20.93/3.19 fof(f9730,plain,(
% 20.93/3.19 greatest_lower_bound(identity,inverse(sF0_fnc))=inverse(sF0_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f20,f9706])).
% 20.93/3.19 fof(f17083,plain,(
% 20.93/3.19 multiply(sF1_fnc,greatest_lower_bound(a,identity))=greatest_lower_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f2571,f421])).
% 20.93/3.19 fof(f17121,plain,(
% 20.93/3.19 multiply(sF1_fnc,greatest_lower_bound(identity,a))=greatest_lower_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f20,f17083])).
% 20.93/3.19 fof(f17122,plain,(
% 20.93/3.19 multiply(sF1_fnc,sF3_fnc)=greatest_lower_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f40,f17121])).
% 20.93/3.19 fof(f18908,plain,(
% 20.93/3.19 ![X0,X1]: (greatest_lower_bound(X0,multiply(least_upper_bound(identity,X1),X0))=X0)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f712,f27])).
% 20.93/3.19 fof(f19396,plain,(
% 20.93/3.19 ![X0]: (greatest_lower_bound(X0,multiply(multiply(a,sF0_fnc),X0))=X0)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f3439,f18908])).
% 20.93/3.19 fof(f19512,plain,(
% 20.93/3.19 ![X0]: (greatest_lower_bound(X0,multiply(a,multiply(sF0_fnc,X0)))=X0)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f19,f19396])).
% 20.93/3.19 fof(f22824,plain,(
% 20.93/3.19 greatest_lower_bound(inverse(sF0_fnc),multiply(a,identity))=inverse(sF0_fnc)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f2573,f19512])).
% 20.93/3.19 fof(f22899,plain,(
% 20.93/3.19 greatest_lower_bound(inverse(sF0_fnc),a)=inverse(sF0_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f2571,f22824])).
% 20.93/3.19 fof(f22900,plain,(
% 20.93/3.19 greatest_lower_bound(a,inverse(sF0_fnc))=inverse(sF0_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f20,f22899])).
% 20.93/3.19 fof(f22954,plain,(
% 20.93/3.19 greatest_lower_bound(inverse(sF0_fnc),sF3_fnc)=greatest_lower_bound(identity,inverse(sF0_fnc))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f22900,f1278])).
% 20.93/3.19 fof(f22987,plain,(
% 20.93/3.19 greatest_lower_bound(sF3_fnc,inverse(sF0_fnc))=greatest_lower_bound(identity,inverse(sF0_fnc))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f20,f22954])).
% 20.93/3.19 fof(f22988,plain,(
% 20.93/3.19 greatest_lower_bound(sF3_fnc,inverse(sF0_fnc))=inverse(sF0_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f9730,f22987])).
% 20.93/3.19 fof(f23087,plain,(
% 20.93/3.19 multiply(inverse(inverse(sF0_fnc)),inverse(sF0_fnc))=greatest_lower_bound(identity,multiply(inverse(inverse(sF0_fnc)),sF3_fnc))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f22988,f448])).
% 20.93/3.19 fof(f23123,plain,(
% 20.93/3.19 identity=greatest_lower_bound(identity,multiply(inverse(inverse(sF0_fnc)),sF3_fnc))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f18,f23087])).
% 20.93/3.19 fof(f23124,plain,(
% 20.93/3.19 identity=greatest_lower_bound(identity,multiply(sF0_fnc,sF3_fnc))),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f2811,f23123])).
% 20.93/3.19 fof(f27265,plain,(
% 20.93/3.19 multiply(greatest_lower_bound(identity,a),sF1_fnc)=greatest_lower_bound(sF1_fnc,identity)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f2189,f763])).
% 20.93/3.19 fof(f27407,plain,(
% 20.93/3.19 multiply(sF3_fnc,sF1_fnc)=greatest_lower_bound(sF1_fnc,identity)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f40,f27265])).
% 20.93/3.19 fof(f27408,plain,(
% 20.93/3.19 multiply(sF3_fnc,sF1_fnc)=greatest_lower_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f20,f27407])).
% 20.93/3.19 fof(f27409,plain,(
% 20.93/3.19 multiply(sF3_fnc,sF1_fnc)=multiply(sF1_fnc,sF3_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f17122,f27408])).
% 20.93/3.19 fof(f27714,plain,(
% 20.93/3.19 sF1_fnc=multiply(sF2_fnc,multiply(sF1_fnc,sF3_fnc))),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f27409,f378])).
% 20.93/3.19 fof(f27860,plain,(
% 20.93/3.19 multiply(sF2_fnc,least_upper_bound(multiply(sF1_fnc,sF3_fnc),sF3_fnc))=least_upper_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(paramodulation,[status(thm)],[f27714,f410])).
% 20.93/3.19 fof(f27911,plain,(
% 20.93/3.19 multiply(sF2_fnc,least_upper_bound(sF3_fnc,multiply(sF1_fnc,sF3_fnc)))=least_upper_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f27860])).
% 20.93/3.19 fof(f27912,plain,(
% 20.93/3.19 multiply(sF2_fnc,multiply(least_upper_bound(sF1_fnc,identity),sF3_fnc))=least_upper_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f743,f27911])).
% 20.93/3.19 fof(f27913,plain,(
% 20.93/3.19 multiply(sF2_fnc,multiply(least_upper_bound(identity,sF1_fnc),sF3_fnc))=least_upper_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f21,f27912])).
% 20.93/3.19 fof(f27914,plain,(
% 20.93/3.19 multiply(sF2_fnc,multiply(sF0_fnc,sF3_fnc))=least_upper_bound(identity,sF1_fnc)),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f45,f27913])).
% 20.93/3.19 fof(f27915,plain,(
% 20.93/3.19 multiply(sF2_fnc,multiply(sF0_fnc,sF3_fnc))=sF0_fnc),
% 20.93/3.19 inference(forward_demodulation,[status(thm)],[f45,f27914])).
% 20.93/3.19 fof(f32171,plain,(
% 20.93/3.19 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=multiply(inverse(X1),identity))),
% 14.99/3.22 inference(paramodulation,[status(thm)],[f2838,f379])).
% 14.99/3.22 fof(f32281,plain,(
% 14.99/3.22 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=inverse(X1))),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f2571,f32171])).
% 14.99/3.22 fof(f34324,plain,(
% 14.99/3.22 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),inverse(inverse(X0)))=inverse(X1))),
% 14.99/3.22 inference(paramodulation,[status(thm)],[f32281,f32281])).
% 14.99/3.22 fof(f34437,plain,(
% 14.99/3.22 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),X0)=inverse(X1))),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f2811,f34324])).
% 14.99/3.22 fof(f34761,plain,(
% 14.99/3.22 multiply(least_upper_bound(sF2_fnc,sF1_fnc),sF3_fnc)=multiply(sF1_fnc,least_upper_bound(sF3_fnc,a))),
% 14.99/3.22 inference(paramodulation,[status(thm)],[f409,f706])).
% 14.99/3.22 fof(f34818,plain,(
% 14.99/3.22 multiply(least_upper_bound(sF1_fnc,sF2_fnc),sF3_fnc)=multiply(sF1_fnc,least_upper_bound(sF3_fnc,a))),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f21,f34761])).
% 14.99/3.22 fof(f34819,plain,(
% 14.99/3.22 multiply(least_upper_bound(sF1_fnc,sF2_fnc),sF3_fnc)=multiply(sF1_fnc,least_upper_bound(a,sF3_fnc))),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f21,f34818])).
% 14.99/3.22 fof(f34820,plain,(
% 14.99/3.22 multiply(least_upper_bound(sF1_fnc,sF2_fnc),sF3_fnc)=multiply(sF1_fnc,a)),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f61,f34819])).
% 14.99/3.22 fof(f34821,plain,(
% 14.99/3.22 multiply(least_upper_bound(sF1_fnc,sF2_fnc),sF3_fnc)=identity),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f39,f34820])).
% 14.99/3.22 fof(f34911,plain,(
% 14.99/3.22 multiply(inverse(identity),least_upper_bound(sF1_fnc,sF2_fnc))=inverse(sF3_fnc)),
% 14.99/3.22 inference(paramodulation,[status(thm)],[f34821,f34437])).
% 14.99/3.22 fof(f34953,plain,(
% 14.99/3.22 multiply(identity,least_upper_bound(sF1_fnc,sF2_fnc))=inverse(sF3_fnc)),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f633,f34911])).
% 14.99/3.22 fof(f34954,plain,(
% 14.99/3.22 least_upper_bound(sF1_fnc,sF2_fnc)=inverse(sF3_fnc)),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f17,f34953])).
% 14.99/3.22 fof(f34955,plain,(
% 14.99/3.22 least_upper_bound(sF1_fnc,sF2_fnc)=sF2_fnc),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f36,f34954])).
% 14.99/3.22 fof(f35010,plain,(
% 14.99/3.22 least_upper_bound(identity,sF2_fnc)=least_upper_bound(sF0_fnc,sF2_fnc)),
% 14.99/3.22 inference(paramodulation,[status(thm)],[f34955,f93])).
% 14.99/3.22 fof(f35043,plain,(
% 14.99/3.22 sF2_fnc=least_upper_bound(sF0_fnc,sF2_fnc)),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f5983,f35010])).
% 14.99/3.22 fof(f35102,plain,(
% 14.99/3.22 greatest_lower_bound(sF0_fnc,sF2_fnc)=sF0_fnc),
% 14.99/3.22 inference(paramodulation,[status(thm)],[f35043,f27])).
% 14.99/3.22 fof(f45655,plain,(
% 14.99/3.22 identity=multiply(greatest_lower_bound(sF2_fnc,sF0_fnc),sF3_fnc)),
% 14.99/3.22 inference(backward_demodulation,[status(thm)],[f757,f23124])).
% 14.99/3.22 fof(f45718,plain,(
% 14.99/3.22 identity=multiply(greatest_lower_bound(sF0_fnc,sF2_fnc),sF3_fnc)),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f20,f45655])).
% 14.99/3.22 fof(f45719,plain,(
% 14.99/3.22 identity=multiply(sF0_fnc,sF3_fnc)),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f35102,f45718])).
% 14.99/3.22 fof(f45816,plain,(
% 14.99/3.22 multiply(sF2_fnc,identity)=sF0_fnc),
% 14.99/3.22 inference(backward_demodulation,[status(thm)],[f45719,f27915])).
% 14.99/3.22 fof(f45872,plain,(
% 14.99/3.22 sF2_fnc=sF0_fnc),
% 14.99/3.22 inference(forward_demodulation,[status(thm)],[f2571,f45816])).
% 14.99/3.22 fof(f45873,plain,(
% 14.99/3.22 $false),
% 14.99/3.22 inference(forward_subsumption_resolution,[status(thm)],[f45872,f37])).
% 14.99/3.22 % SZS output end CNFRefutation for theBenchmark.p
% 14.99/3.25 % Elapsed time: 2.785615 seconds
% 14.99/3.25 % CPU time: 21.899900 seconds
% 14.99/3.25 % Total memory used: 267.951 MB
% 14.99/3.25 % Net memory used: 263.378 MB
%------------------------------------------------------------------------------