%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:06:42 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 13:49:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f1,axiom,(
% 0.09/0.39 (![X,Y]: (add(X,Y) = add(Y,X) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f2,axiom,(
% 0.09/0.39 (![X,Y]: (multiply(X,Y) = multiply(Y,X) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f3,axiom,(
% 0.09/0.39 (![X,Y,Z]: (add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f4,axiom,(
% 0.09/0.39 (![X,Y,Z]: (add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f5,axiom,(
% 0.09/0.39 (![X,Y,Z]: (multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f7,axiom,(
% 0.09/0.39 (![X]: (add(X,inverse(X)) = multiplicative_identity ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f8,axiom,(
% 0.09/0.39 (![X]: (add(inverse(X),X) = multiplicative_identity ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f9,axiom,(
% 0.09/0.39 (![X]: (multiply(X,inverse(X)) = additive_identity ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f12,axiom,(
% 0.09/0.39 (![X]: (multiply(multiplicative_identity,X) = X ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f13,axiom,(
% 0.09/0.39 (![X]: (add(X,additive_identity) = X ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f14,axiom,(
% 0.09/0.39 (![X]: (add(additive_identity,X) = X ))),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f15,negated_conjecture,(
% 0.09/0.39 multiply(a,a) != a ),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f16,plain,(
% 0.09/0.39 ![X0,X1]: (add(X0,X1)=add(X1,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.39 fof(f17,plain,(
% 0.09/0.39 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/0.39 fof(f18,plain,(
% 0.09/0.39 ![X0,X1,X2]: (add(multiply(X0,X1),X2)=multiply(add(X0,X2),add(X1,X2)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.39 fof(f19,plain,(
% 0.09/0.39 ![X0,X1,X2]: (add(X0,multiply(X1,X2))=multiply(add(X0,X1),add(X0,X2)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.09/0.39 fof(f20,plain,(
% 0.09/0.39 ![X0,X1,X2]: (multiply(add(X0,X1),X2)=add(multiply(X0,X2),multiply(X1,X2)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.09/0.39 fof(f22,plain,(
% 0.09/0.39 ![X0]: (add(X0,inverse(X0))=multiplicative_identity)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.39 fof(f23,plain,(
% 0.09/0.39 ![X0]: (add(inverse(X0),X0)=multiplicative_identity)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.09/0.39 fof(f24,plain,(
% 0.09/0.39 ![X0]: (multiply(X0,inverse(X0))=additive_identity)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/0.39 fof(f27,plain,(
% 0.09/0.39 ![X0]: (multiply(multiplicative_identity,X0)=X0)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.39 fof(f28,plain,(
% 0.09/0.39 ![X0]: (add(X0,additive_identity)=X0)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.09/0.39 fof(f29,plain,(
% 0.09/0.39 ![X0]: (add(additive_identity,X0)=X0)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.39 fof(f30,plain,(
% 0.09/0.39 ~multiply(a,a)=a),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f15])).
% 0.09/0.39 fof(f49,plain,(
% 0.09/0.39 ![X0,X1,X2]: (add(multiply(X0,X1),X2)=multiply(add(X1,X2),add(X0,X2)))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f17,f18])).
% 0.09/0.39 fof(f65,plain,(
% 0.09/0.39 ![X0,X1,X2]: (add(multiply(X0,X1),X2)=multiply(add(X2,X1),add(X0,X2)))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f16,f49])).
% 0.09/0.39 fof(f178,plain,(
% 0.09/0.39 ![X0,X1,X2]: (add(X0,multiply(X1,X2))=multiply(add(X0,X2),add(X0,X1)))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f17,f19])).
% 0.09/0.39 fof(f207,plain,(
% 0.09/0.39 ![X0,X1]: (multiply(add(multiplicative_identity,X0),X1)=add(X1,multiply(X0,X1)))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f27,f20])).
% 0.09/0.39 fof(f223,plain,(
% 0.09/0.39 ![X0,X1,X2]: (multiply(add(X0,X1),X2)=add(multiply(X0,X2),multiply(X2,X1)))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f17,f20])).
% 0.09/0.39 fof(f290,plain,(
% 0.09/0.39 ![X0,X1]: (add(multiply(X0,inverse(X1)),X1)=multiply(multiplicative_identity,add(X0,X1)))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f22,f65])).
% 0.09/0.39 fof(f298,plain,(
% 0.09/0.39 ![X0,X1]: (add(multiply(X0,inverse(X1)),X1)=add(X0,X1))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f27,f290])).
% 0.09/0.39 fof(f354,plain,(
% 0.09/0.39 ![X0]: (add(inverse(X0),X0)=add(multiplicative_identity,X0))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f27,f298])).
% 0.09/0.39 fof(f355,plain,(
% 0.09/0.39 ![X0]: (add(additive_identity,X0)=add(X0,X0))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f24,f298])).
% 0.09/0.39 fof(f376,plain,(
% 0.09/0.39 ![X0,X1]: (multiply(multiplicative_identity,X0)=add(X0,multiply(X1,X0)))),
% 0.09/0.39 inference(backward_demodulation,[status(thm)],[f377,f207])).
% 0.09/0.39 fof(f377,plain,(
% 0.09/0.39 ![X0]: (multiplicative_identity=add(multiplicative_identity,X0))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f23,f354])).
% 0.09/0.39 fof(f379,plain,(
% 0.09/0.39 ![X0]: (X0=add(X0,X0))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f29,f355])).
% 0.09/0.39 fof(f389,plain,(
% 0.09/0.39 ![X0,X1]: (X0=add(X0,multiply(X1,X0)))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f27,f376])).
% 0.09/0.39 fof(f415,plain,(
% 0.09/0.39 ![X0,X1]: (add(X0,multiply(additive_identity,X1))=multiply(add(X0,X1),X0))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f28,f178])).
% 0.09/0.39 fof(f501,plain,(
% 0.09/0.39 ![X0]: (multiply(X0,X0)=multiply(add(X0,X0),X0))),
% 0.09/0.39 inference(paramodulation,[status(thm)],[f223,f379])).
% 0.09/0.39 fof(f524,plain,(
% 0.09/0.39 ![X0]: (multiply(X0,X0)=add(X0,multiply(additive_identity,X0)))),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f415,f501])).
% 0.09/0.39 fof(f525,plain,(
% 0.09/0.39 ~a=a),
% 0.09/0.39 inference(backward_demodulation,[status(thm)],[f527,f30])).
% 0.09/0.39 fof(f527,plain,(
% 0.09/0.39 ![X0]: (multiply(X0,X0)=X0)),
% 0.09/0.39 inference(forward_demodulation,[status(thm)],[f389,f524])).
% 0.09/0.39 fof(f557,plain,(
% 0.09/0.39 $false),
% 0.09/0.39 inference(trivial_equality_resolution,[status(thm)],[f525])).
% 0.09/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.41 % Elapsed time: 0.031979 seconds
% 0.09/0.41 % CPU time: 0.092034 seconds
% 0.09/0.41 % Total memory used: 3.435 MB
% 0.09/0.41 % Net memory used: 3.406 MB
%------------------------------------------------------------------------------