%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:06:45 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.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 13:50:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f1,axiom,(
% 0.13/0.39 (![X,Y]: (add(X,Y) = add(Y,X) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f2,axiom,(
% 0.13/0.39 (![X,Y]: (multiply(X,Y) = multiply(Y,X) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f3,axiom,(
% 0.13/0.39 (![X,Y,Z]: (add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f4,axiom,(
% 0.13/0.39 (![X,Y,Z]: (multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f5,axiom,(
% 0.13/0.39 (![X]: (add(X,additive_identity) = X ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f6,axiom,(
% 0.13/0.39 (![X]: (multiply(X,multiplicative_identity) = X ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f7,axiom,(
% 0.13/0.39 (![X]: (add(X,inverse(X)) = multiplicative_identity ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f8,axiom,(
% 0.13/0.39 (![X]: (multiply(X,inverse(X)) = additive_identity ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f9,hypothesis,(
% 0.13/0.39 add(a,b) = multiplicative_identity ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f10,hypothesis,(
% 0.13/0.39 multiply(a,b) = additive_identity ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f11,negated_conjecture,(
% 0.13/0.39 b != inverse(a) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f12,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,X1)=add(X1,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.39 fof(f13,plain,(
% 0.13/0.39 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.39 fof(f14,plain,(
% 0.13/0.39 ![X0,X1,X2]: (add(X0,multiply(X1,X2))=multiply(add(X0,X1),add(X0,X2)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f15,plain,(
% 0.13/0.39 ![X0,X1,X2]: (multiply(X0,add(X1,X2))=add(multiply(X0,X1),multiply(X0,X2)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.39 fof(f16,plain,(
% 0.13/0.39 ![X0]: (add(X0,additive_identity)=X0)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f17,plain,(
% 0.13/0.39 ![X0]: (multiply(X0,multiplicative_identity)=X0)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.39 fof(f18,plain,(
% 0.13/0.39 ![X0]: (add(X0,inverse(X0))=multiplicative_identity)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.39 fof(f19,plain,(
% 0.13/0.39 ![X0]: (multiply(X0,inverse(X0))=additive_identity)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.39 fof(f20,plain,(
% 0.13/0.39 add(a,b)=multiplicative_identity),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.13/0.39 fof(f21,plain,(
% 0.13/0.39 multiply(a,b)=additive_identity),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/0.39 fof(f22,plain,(
% 0.13/0.39 ~b=inverse(a)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.13/0.39 fof(f26,plain,(
% 0.13/0.39 ![X0]: (X0=add(additive_identity,X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f16,f12])).
% 0.13/0.39 fof(f48,plain,(
% 0.13/0.39 ![X0]: (X0=multiply(multiplicative_identity,X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f17,f13])).
% 0.13/0.39 fof(f59,plain,(
% 0.13/0.39 ![X0,X1,X2]: (add(X0,multiply(X1,X2))=multiply(add(X0,X2),add(X0,X1)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f13,f14])).
% 0.13/0.39 fof(f63,plain,(
% 0.13/0.39 ![X0]: (add(a,multiply(b,X0))=multiply(multiplicative_identity,add(a,X0)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f20,f14])).
% 0.13/0.39 fof(f65,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,multiply(inverse(X0),X1))=multiply(multiplicative_identity,add(X0,X1)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f18,f14])).
% 0.13/0.39 fof(f66,plain,(
% 0.13/0.39 ![X0,X1,X2]: (add(X0,multiply(X1,X2))=multiply(add(X1,X0),add(X0,X2)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f12,f14])).
% 0.13/0.39 fof(f72,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,multiply(X1,inverse(X0)))=multiply(add(X0,X1),multiplicative_identity))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f18,f14])).
% 0.13/0.39 fof(f79,plain,(
% 0.13/0.39 ![X0]: (add(a,multiply(b,X0))=add(a,X0))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f48,f63])).
% 0.13/0.39 fof(f80,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,multiply(inverse(X0),X1))=add(X0,X1))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f48,f65])).
% 0.13/0.39 fof(f84,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,multiply(X1,inverse(X0)))=add(X0,X1))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f17,f72])).
% 0.13/0.39 fof(f87,plain,(
% 0.13/0.39 add(a,additive_identity)=add(a,inverse(b))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f19,f79])).
% 0.13/0.39 fof(f94,plain,(
% 0.13/0.39 a=add(a,inverse(b))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f16,f87])).
% 0.13/0.39 fof(f116,plain,(
% 0.13/0.39 ![X0]: (add(X0,inverse(X0))=add(X0,multiplicative_identity))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f17,f80])).
% 0.13/0.39 fof(f117,plain,(
% 0.13/0.39 ![X0]: (add(X0,additive_identity)=add(X0,inverse(inverse(X0))))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f19,f80])).
% 0.13/0.39 fof(f128,plain,(
% 0.13/0.39 ![X0]: (multiplicative_identity=add(X0,multiplicative_identity))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f18,f116])).
% 0.13/0.39 fof(f129,plain,(
% 0.13/0.39 ![X0]: (X0=add(X0,inverse(inverse(X0))))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f16,f117])).
% 0.13/0.39 fof(f137,plain,(
% 0.13/0.39 ![X0]: (multiplicative_identity=add(multiplicative_identity,X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f12,f128])).
% 0.13/0.39 fof(f181,plain,(
% 0.13/0.39 ![X0]: (add(X0,additive_identity)=add(X0,X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f19,f84])).
% 0.13/0.39 fof(f197,plain,(
% 0.13/0.39 ![X0]: (X0=add(X0,X0))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f16,f181])).
% 0.13/0.39 fof(f215,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,multiply(X0,X1))=multiply(X0,add(X0,X1)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f197,f14])).
% 0.13/0.39 fof(f241,plain,(
% 0.13/0.39 ![X0]: (multiply(a,add(b,X0))=add(additive_identity,multiply(a,X0)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f21,f15])).
% 0.13/0.39 fof(f242,plain,(
% 0.13/0.39 ![X0,X1]: (multiply(X0,add(multiplicative_identity,X1))=add(X0,multiply(X0,X1)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f17,f15])).
% 0.13/0.39 fof(f243,plain,(
% 0.13/0.39 ![X0,X1]: (multiply(X0,add(inverse(X0),X1))=add(additive_identity,multiply(X0,X1)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f19,f15])).
% 0.13/0.39 fof(f262,plain,(
% 0.13/0.39 ![X0]: (multiply(a,add(b,X0))=multiply(a,X0))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f26,f241])).
% 0.13/0.39 fof(f263,plain,(
% 0.13/0.39 ![X0,X1]: (multiply(X0,multiplicative_identity)=add(X0,multiply(X0,X1)))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f137,f242])).
% 0.13/0.39 fof(f264,plain,(
% 0.13/0.39 ![X0,X1]: (X0=multiply(X0,add(X0,X1)))),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f265,f215])).
% 0.13/0.39 fof(f265,plain,(
% 0.13/0.39 ![X0,X1]: (X0=add(X0,multiply(X0,X1)))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f17,f263])).
% 0.13/0.39 fof(f266,plain,(
% 0.13/0.39 ![X0,X1]: (multiply(X0,add(inverse(X0),X1))=multiply(X0,X1))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f26,f243])).
% 0.13/0.39 fof(f292,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,multiply(X1,additive_identity))=multiply(X0,add(X0,X1)))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f16,f59])).
% 0.13/0.39 fof(f334,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,multiply(X1,additive_identity))=X0)),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f264,f292])).
% 0.13/0.39 fof(f389,plain,(
% 0.13/0.39 ![X0,X1]: (add(X0,multiply(X1,additive_identity))=multiply(add(X1,X0),X0))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f16,f66])).
% 0.13/0.39 fof(f426,plain,(
% 0.13/0.39 ![X0,X1]: (X0=multiply(add(X1,X0),X0))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f334,f389])).
% 0.13/0.39 fof(f714,plain,(
% 0.13/0.39 inverse(b)=multiply(a,inverse(b))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f94,f426])).
% 0.13/0.39 fof(f724,plain,(
% 0.13/0.39 ![X0]: (inverse(inverse(X0))=multiply(X0,inverse(inverse(X0))))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f129,f426])).
% 0.13/0.39 fof(f872,plain,(
% 0.13/0.39 multiply(a,multiplicative_identity)=multiply(a,inverse(b))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f18,f262])).
% 0.13/0.39 fof(f893,plain,(
% 0.13/0.39 inverse(b)=a),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f894,f714])).
% 0.13/0.39 fof(f894,plain,(
% 0.13/0.39 a=multiply(a,inverse(b))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f17,f872])).
% 0.13/0.39 fof(f921,plain,(
% 0.13/0.39 ![X0]: (multiply(X0,multiplicative_identity)=multiply(X0,inverse(inverse(X0))))),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f18,f266])).
% 0.13/0.39 fof(f947,plain,(
% 0.13/0.39 ![X0]: (inverse(inverse(X0))=X0)),
% 0.13/0.39 inference(backward_demodulation,[status(thm)],[f948,f724])).
% 0.13/0.39 fof(f948,plain,(
% 0.13/0.39 ![X0]: (X0=multiply(X0,inverse(inverse(X0))))),
% 0.13/0.39 inference(forward_demodulation,[status(thm)],[f17,f921])).
% 0.13/0.39 fof(f979,plain,(
% 0.13/0.39 inverse(a)=b),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f893,f947])).
% 0.13/0.39 fof(f987,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f979,f22])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.41 % Elapsed time: 0.044790 seconds
% 0.13/0.41 % CPU time: 0.185188 seconds
% 0.13/0.41 % Total memory used: 6.751 MB
% 0.13/0.41 % Net memory used: 6.653 MB
%------------------------------------------------------------------------------