%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP167-5 : 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 : n009.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 0.16s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 20 20:03:13 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.62 % Refutation found
% 0.16/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.62 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.62 fof(f1,axiom,(
% 0.16/0.62 (![X]: (multiply(identity,X) = X ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f2,axiom,(
% 0.16/0.62 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f3,axiom,(
% 0.16/0.62 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f4,axiom,(
% 0.16/0.62 (![X,Y]: (greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f5,axiom,(
% 0.16/0.62 (![X,Y]: (least_upper_bound(X,Y) = least_upper_bound(Y,X) ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f15,axiom,(
% 0.16/0.62 (![Y,Z,X]: (multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f16,axiom,(
% 0.16/0.62 (![A,B]: (inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)) ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f17,axiom,(
% 0.16/0.62 (![X]: (positive_part(X) = least_upper_bound(X,identity) ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f18,axiom,(
% 0.16/0.62 (![X]: (negative_part(X) = greatest_lower_bound(X,identity) ))),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f21,negated_conjecture,(
% 0.16/0.62 a != multiply(positive_part(a),negative_part(a)) ),
% 0.16/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.62 fof(f22,plain,(
% 0.16/0.62 ![X0]: (multiply(identity,X0)=X0)),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f1])).
% 0.16/0.62 fof(f23,plain,(
% 0.16/0.62 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f2])).
% 0.16/0.62 fof(f24,plain,(
% 0.16/0.62 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f3])).
% 0.16/0.62 fof(f25,plain,(
% 0.16/0.62 ![X0,X1]: (greatest_lower_bound(X0,X1)=greatest_lower_bound(X1,X0))),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f4])).
% 0.16/0.62 fof(f26,plain,(
% 0.16/0.62 ![X0,X1]: (least_upper_bound(X0,X1)=least_upper_bound(X1,X0))),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f5])).
% 0.16/0.62 fof(f36,plain,(
% 0.16/0.62 ![X0,X1,X2]: (multiply(greatest_lower_bound(X0,X1),X2)=greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)))),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f15])).
% 0.16/0.62 fof(f37,plain,(
% 0.16/0.62 ![X0,X1]: (inverse(least_upper_bound(X0,X1))=greatest_lower_bound(inverse(X0),inverse(X1)))),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f16])).
% 0.16/0.62 fof(f38,plain,(
% 0.16/0.62 ![X0]: (positive_part(X0)=least_upper_bound(X0,identity))),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f17])).
% 0.16/0.62 fof(f39,plain,(
% 0.16/0.62 ![X0]: (negative_part(X0)=greatest_lower_bound(X0,identity))),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f18])).
% 0.16/0.62 fof(f42,plain,(
% 0.16/0.62 ~a=multiply(positive_part(a),negative_part(a))),
% 0.16/0.62 inference(cnf_transformation,[status(thm)],[f21])).
% 0.16/0.62 fof(f87,plain,(
% 0.16/0.62 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.16/0.62 inference(paramodulation,[status(thm)],[f23,f24])).
% 0.16/0.62 fof(f90,plain,(
% 0.16/0.62 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.16/0.62 inference(forward_demodulation,[status(thm)],[f22,f87])).
% 0.16/0.62 fof(f92,plain,(
% 0.16/0.62 ![X0]: (negative_part(X0)=greatest_lower_bound(identity,X0))),
% 0.16/0.62 inference(paramodulation,[status(thm)],[f39,f25])).
% 0.16/0.62 fof(f105,plain,(
% 0.16/0.62 ![X0]: (positive_part(X0)=least_upper_bound(identity,X0))),
% 0.16/0.62 inference(paramodulation,[status(thm)],[f38,f26])).
% 0.16/0.62 fof(f149,plain,(
% 0.16/0.62 ![X0,X1]: (multiply(greatest_lower_bound(inverse(X0),X1),X0)=greatest_lower_bound(identity,multiply(X1,X0)))),
% 0.16/0.62 inference(paramodulation,[status(thm)],[f23,f36])).
% 0.16/0.62 fof(f160,plain,(
% 0.16/0.62 ![X0,X1]: (multiply(greatest_lower_bound(inverse(X0),X1),X0)=negative_part(multiply(X1,X0)))),
% 0.16/0.62 inference(forward_demodulation,[status(thm)],[f92,f149])).
% 0.16/0.62 fof(f339,plain,(
% 0.16/0.62 ![X0,X1]: (multiply(X0,X1)=multiply(inverse(inverse(X0)),X1))),
% 0.16/0.62 inference(paramodulation,[status(thm)],[f90,f90])).
% 0.16/0.62 fof(f342,plain,(
% 0.16/0.62 ![X0]: (X0=multiply(inverse(inverse(X0)),identity))),
% 0.16/0.64 inference(paramodulation,[status(thm)],[f23,f90])).
% 0.16/0.64 fof(f358,plain,(
% 0.16/0.64 ![X0]: (X0=multiply(X0,identity))),
% 0.16/0.64 inference(forward_demodulation,[status(thm)],[f339,f342])).
% 0.16/0.64 fof(f409,plain,(
% 0.16/0.64 inverse(identity)=identity),
% 0.16/0.64 inference(paramodulation,[status(thm)],[f23,f358])).
% 0.16/0.64 fof(f481,plain,(
% 0.16/0.64 ![X0]: (inverse(least_upper_bound(identity,X0))=greatest_lower_bound(identity,inverse(X0)))),
% 0.16/0.64 inference(paramodulation,[status(thm)],[f409,f37])).
% 0.16/0.64 fof(f490,plain,(
% 0.16/0.64 ![X0]: (inverse(positive_part(X0))=greatest_lower_bound(identity,inverse(X0)))),
% 0.16/0.64 inference(forward_demodulation,[status(thm)],[f105,f481])).
% 0.16/0.64 fof(f492,plain,(
% 0.16/0.64 ![X0]: (inverse(positive_part(X0))=negative_part(inverse(X0)))),
% 0.16/0.64 inference(forward_demodulation,[status(thm)],[f92,f490])).
% 0.16/0.64 fof(f1744,plain,(
% 0.16/0.64 ![X0]: (multiply(negative_part(inverse(X0)),X0)=negative_part(multiply(identity,X0)))),
% 0.16/0.64 inference(paramodulation,[status(thm)],[f39,f160])).
% 0.16/0.64 fof(f1788,plain,(
% 0.16/0.64 ![X0]: (multiply(negative_part(inverse(X0)),X0)=negative_part(X0))),
% 0.16/0.64 inference(forward_demodulation,[status(thm)],[f22,f1744])).
% 0.16/0.64 fof(f1844,plain,(
% 0.16/0.64 ![X0]: (X0=multiply(inverse(negative_part(inverse(X0))),negative_part(X0)))),
% 0.16/0.64 inference(paramodulation,[status(thm)],[f1788,f90])).
% 0.16/0.64 fof(f2015,plain,(
% 0.16/0.64 ![X0,X1]: (multiply(positive_part(X0),X1)=multiply(inverse(negative_part(inverse(X0))),X1))),
% 0.16/0.64 inference(paramodulation,[status(thm)],[f492,f339])).
% 0.16/0.64 fof(f2058,plain,(
% 0.16/0.64 ![X0]: (X0=multiply(positive_part(X0),negative_part(X0)))),
% 0.16/0.64 inference(backward_demodulation,[status(thm)],[f2015,f1844])).
% 0.16/0.64 fof(f2101,plain,(
% 0.16/0.64 ~a=a),
% 0.16/0.64 inference(backward_demodulation,[status(thm)],[f2058,f42])).
% 0.16/0.64 fof(f2102,plain,(
% 0.16/0.64 $false),
% 0.16/0.64 inference(trivial_equality_resolution,[status(thm)],[f2101])).
% 0.16/0.64 % SZS output end CNFRefutation for theBenchmark.p
% 1.63/0.65 % Elapsed time: 0.207700 seconds
% 1.63/0.65 % CPU time: 1.447905 seconds
% 1.63/0.65 % Total memory used: 33.600 MB
% 1.63/0.65 % Net memory used: 33.231 MB
%------------------------------------------------------------------------------