%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:06:44 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:45:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.37 fof(f2,axiom,(
% 0.08/0.37 (![X,Y]: (multiply(X,Y) = multiply(Y,X) ))),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f4,axiom,(
% 0.08/0.37 (![X,Y,Z]: (add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ))),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f6,axiom,(
% 0.08/0.37 (![X,Y,Z]: (multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ))),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f9,axiom,(
% 0.08/0.37 (![X]: (multiply(X,inverse(X)) = additive_identity ))),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f13,axiom,(
% 0.08/0.37 (![X]: (add(X,additive_identity) = X ))),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f14,axiom,(
% 0.08/0.37 (![X]: (add(additive_identity,X) = X ))),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f15,negated_conjecture,(
% 0.08/0.37 multiply(a,add(a,b)) != a ),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f17,plain,(
% 0.08/0.37 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/0.37 fof(f19,plain,(
% 0.08/0.37 ![X0,X1,X2]: (add(X0,multiply(X1,X2))=multiply(add(X0,X1),add(X0,X2)))),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/0.37 fof(f21,plain,(
% 0.08/0.37 ![X0,X1,X2]: (multiply(X0,add(X1,X2))=add(multiply(X0,X1),multiply(X0,X2)))),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.37 fof(f24,plain,(
% 0.08/0.37 ![X0]: (multiply(X0,inverse(X0))=additive_identity)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.08/0.37 fof(f28,plain,(
% 0.08/0.37 ![X0]: (add(X0,additive_identity)=X0)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f13])).
% 0.08/0.37 fof(f29,plain,(
% 0.08/0.37 ![X0]: (add(additive_identity,X0)=X0)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f14])).
% 0.08/0.37 fof(f30,plain,(
% 0.08/0.37 ~multiply(a,add(a,b))=a),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f15])).
% 0.08/0.37 fof(f143,plain,(
% 0.08/0.37 ![X0,X1]: (add(X0,multiply(additive_identity,X1))=multiply(X0,add(X0,X1)))),
% 0.08/0.37 inference(paramodulation,[status(thm)],[f28,f19])).
% 0.08/0.37 fof(f152,plain,(
% 0.08/0.37 ~add(a,multiply(additive_identity,b))=a),
% 0.08/0.37 inference(backward_demodulation,[status(thm)],[f143,f30])).
% 0.08/0.37 fof(f187,plain,(
% 0.08/0.37 ![X0,X1]: (multiply(X0,add(X1,inverse(X0)))=add(multiply(X0,X1),additive_identity))),
% 0.08/0.37 inference(paramodulation,[status(thm)],[f24,f21])).
% 0.08/0.37 fof(f191,plain,(
% 0.08/0.37 ![X0,X1]: (multiply(X0,add(X1,inverse(X0)))=multiply(X0,X1))),
% 0.08/0.37 inference(forward_demodulation,[status(thm)],[f28,f187])).
% 0.08/0.37 fof(f226,plain,(
% 0.08/0.37 ~add(a,multiply(b,additive_identity))=a),
% 0.08/0.37 inference(paramodulation,[status(thm)],[f17,f152])).
% 0.08/0.37 fof(f270,plain,(
% 0.08/0.37 ![X0]: (multiply(X0,inverse(X0))=multiply(X0,additive_identity))),
% 0.08/0.37 inference(paramodulation,[status(thm)],[f29,f191])).
% 0.08/0.37 fof(f284,plain,(
% 0.08/0.37 ~add(a,additive_identity)=a),
% 0.08/0.37 inference(backward_demodulation,[status(thm)],[f291,f226])).
% 0.08/0.37 fof(f291,plain,(
% 0.08/0.37 ![X0]: (additive_identity=multiply(X0,additive_identity))),
% 0.08/0.37 inference(forward_demodulation,[status(thm)],[f24,f270])).
% 0.08/0.37 fof(f302,plain,(
% 0.08/0.37 ~a=a),
% 0.08/0.37 inference(forward_demodulation,[status(thm)],[f28,f284])).
% 0.08/0.37 fof(f303,plain,(
% 0.08/0.37 $false),
% 0.08/0.37 inference(trivial_equality_resolution,[status(thm)],[f302])).
% 0.08/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.39 % Elapsed time: 0.036100 seconds
% 0.08/0.39 % CPU time: 0.076056 seconds
% 0.08/0.39 % Total memory used: 3.098 MB
% 0.08/0.39 % Net memory used: 3.087 MB
%------------------------------------------------------------------------------