%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 01:43:55 PM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 03:12:20 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.38 fof(f1,conjecture,(
% 0.11/0.38 (! [Vd416] :( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f2,negated_conjecture,(
% 0.11/0.38 ~((! [Vd416] :( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ) ))),
% 0.11/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.11/0.38 fof(f3,axiom,(
% 0.11/0.38 (! [Vd413] :( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)=> vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) = vplus(vmul(vd411,vsucc(Vd413)),vsucc(Vd413)) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f4,axiom,(
% 0.11/0.38 (! [Vd413] :( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)=> vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413))) = vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f5,axiom,(
% 0.11/0.38 (! [Vd413] :( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)=> vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413))) = vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413))) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f6,axiom,(
% 0.11/0.38 (! [Vd413] :( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)=> vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413)) = vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413))) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f7,axiom,(
% 0.11/0.38 (! [Vd413] :( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)=> vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411))) = vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413)) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f8,axiom,(
% 0.11/0.38 (! [Vd413] :( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)=> vplus(vplus(vmul(vd411,Vd413),Vd413),vsucc(vd411)) = vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411))) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f10,axiom,(
% 0.11/0.38 (! [Vd413] :( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)=> vmul(vsucc(vd411),vsucc(Vd413)) = vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f60,plain,(
% 0.11/0.38 (?[Vd416]: (vmul(vsucc(vd411),Vd416)=vplus(vmul(vd411,Vd416),Vd416)&~vmul(vsucc(vd411),vsucc(Vd416))=vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416))))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.11/0.38 fof(f61,plain,(
% 0.11/0.38 (vmul(vsucc(vd411),sK0_skl)=vplus(vmul(vd411,sK0_skl),sK0_skl)&~vmul(vsucc(vd411),vsucc(sK0_skl))=vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl)))),
% 0.11/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd416,sK0_skl)],[f60])).
% 0.11/0.38 fof(f62,plain,(
% 0.11/0.38 vmul(vsucc(vd411),sK0_skl)=vplus(vmul(vd411,sK0_skl),sK0_skl)),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f61])).
% 0.11/0.38 fof(f63,plain,(
% 0.11/0.38 ~vmul(vsucc(vd411),vsucc(sK0_skl))=vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f61])).
% 0.11/0.38 fof(f64,plain,(
% 0.11/0.38 ![Vd413]: (~vmul(vsucc(vd411),Vd413)=vplus(vmul(vd411,Vd413),Vd413)|vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413))=vplus(vmul(vd411,vsucc(Vd413)),vsucc(Vd413)))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.11/0.38 fof(f65,plain,(
% 0.11/0.38 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0))=vplus(vmul(vd411,vsucc(X0)),vsucc(X0)))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f64])).
% 0.11/0.38 fof(f66,plain,(
% 0.11/0.38 ![Vd413]: (~vmul(vsucc(vd411),Vd413)=vplus(vmul(vd411,Vd413),Vd413)|vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413)))=vplus(vplus(vmul(vd411,Vd413),vd411),vsucc(Vd413)))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.11/0.38 fof(f67,plain,(
% 0.11/0.38 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0)))=vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0)))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f66])).
% 0.11/0.38 fof(f68,plain,(
% 0.11/0.38 ![Vd413]: (~vmul(vsucc(vd411),Vd413)=vplus(vmul(vd411,Vd413),Vd413)|vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413)))=vplus(vmul(vd411,Vd413),vplus(vd411,vsucc(Vd413))))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.11/0.38 fof(f69,plain,(
% 0.11/0.38 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0)))=vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0))))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f68])).
% 0.11/0.38 fof(f70,plain,(
% 0.11/0.38 ![Vd413]: (~vmul(vsucc(vd411),Vd413)=vplus(vmul(vd411,Vd413),Vd413)|vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413))=vplus(vmul(vd411,Vd413),vsucc(vplus(vd411,Vd413))))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.11/0.38 fof(f71,plain,(
% 0.11/0.38 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0))=vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f70])).
% 0.11/0.38 fof(f72,plain,(
% 0.11/0.38 ![Vd413]: (~vmul(vsucc(vd411),Vd413)=vplus(vmul(vd411,Vd413),Vd413)|vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411)))=vplus(vmul(vd411,Vd413),vplus(vsucc(vd411),Vd413)))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.11/0.38 fof(f73,plain,(
% 0.11/0.38 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411)))=vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f72])).
% 0.11/0.38 fof(f74,plain,(
% 0.11/0.38 ![Vd413]: (~vmul(vsucc(vd411),Vd413)=vplus(vmul(vd411,Vd413),Vd413)|vplus(vplus(vmul(vd411,Vd413),Vd413),vsucc(vd411))=vplus(vmul(vd411,Vd413),vplus(Vd413,vsucc(vd411))))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.11/0.38 fof(f75,plain,(
% 0.11/0.38 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vplus(vplus(vmul(vd411,X0),X0),vsucc(vd411))=vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f74])).
% 0.11/0.38 fof(f78,plain,(
% 0.11/0.38 ![Vd413]: (~vmul(vsucc(vd411),Vd413)=vplus(vmul(vd411,Vd413),Vd413)|vmul(vsucc(vd411),vsucc(Vd413))=vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.11/0.38 fof(f79,plain,(
% 0.11/0.38 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vmul(vsucc(vd411),vsucc(X0))=vplus(vmul(vsucc(vd411),X0),vsucc(vd411)))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f78])).
% 0.11/0.38 fof(f195,plain,(
% 0.11/0.38 vplus(vplus(vmul(vd411,sK0_skl),vd411),vsucc(sK0_skl))=vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl))),
% 0.11/0.38 inference(resolution,[status(thm)],[f65,f62])).
% 0.11/0.38 fof(f207,plain,(
% 0.11/0.38 vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl)))=vplus(vplus(vmul(vd411,sK0_skl),vd411),vsucc(sK0_skl))),
% 0.11/0.38 inference(resolution,[status(thm)],[f67,f62])).
% 0.11/0.38 fof(f213,plain,(
% 0.11/0.38 vplus(vmul(vd411,sK0_skl),vsucc(vplus(vd411,sK0_skl)))=vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl)))),
% 0.11/0.38 inference(resolution,[status(thm)],[f69,f62])).
% 0.11/0.38 fof(f219,plain,(
% 0.11/0.38 vplus(vmul(vd411,sK0_skl),vplus(vsucc(vd411),sK0_skl))=vplus(vmul(vd411,sK0_skl),vsucc(vplus(vd411,sK0_skl)))),
% 0.11/0.38 inference(resolution,[status(thm)],[f71,f62])).
% 0.11/0.38 fof(f225,plain,(
% 0.11/0.38 vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411)))=vplus(vmul(vd411,sK0_skl),vplus(vsucc(vd411),sK0_skl))),
% 0.11/0.38 inference(resolution,[status(thm)],[f73,f62])).
% 0.11/0.38 fof(f231,plain,(
% 0.11/0.38 vplus(vplus(vmul(vd411,sK0_skl),sK0_skl),vsucc(vd411))=vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411)))),
% 0.11/0.38 inference(resolution,[status(thm)],[f75,f62])).
% 0.11/0.38 fof(f233,plain,(
% 0.11/0.38 vplus(vmul(vsucc(vd411),sK0_skl),vsucc(vd411))=vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411)))),
% 0.11/0.38 inference(forward_demodulation,[status(thm)],[f62,f231])).
% 0.11/0.38 fof(f245,plain,(
% 0.11/0.38 vmul(vsucc(vd411),vsucc(sK0_skl))=vplus(vmul(vsucc(vd411),sK0_skl),vsucc(vd411))),
% 0.11/0.38 inference(resolution,[status(thm)],[f79,f62])).
% 0.11/0.38 fof(f304,plain,(
% 0.11/0.38 vplus(vmul(vd411,sK0_skl),vplus(vd411,vsucc(sK0_skl)))=vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl))),
% 0.11/0.38 inference(forward_demodulation,[status(thm)],[f195,f207])).
% 0.11/0.38 fof(f307,plain,(
% 0.11/0.38 vplus(vmul(vd411,sK0_skl),vsucc(vplus(vd411,sK0_skl)))=vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl))),
% 0.11/0.38 inference(forward_demodulation,[status(thm)],[f304,f213])).
% 0.11/0.38 fof(f311,plain,(
% 0.11/0.38 vmul(vsucc(vd411),vsucc(sK0_skl))=vplus(vmul(vd411,sK0_skl),vplus(sK0_skl,vsucc(vd411)))),
% 0.11/0.38 inference(forward_demodulation,[status(thm)],[f245,f233])).
% 0.11/0.38 fof(f313,plain,(
% 0.11/0.38 vplus(vmul(vd411,sK0_skl),vplus(vsucc(vd411),sK0_skl))=vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl))),
% 0.11/0.38 inference(forward_demodulation,[status(thm)],[f307,f219])).
% 0.11/0.38 fof(f316,plain,(
% 0.11/0.38 vmul(vsucc(vd411),vsucc(sK0_skl))=vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl))),
% 0.11/0.38 inference(backward_demodulation,[status(thm)],[f317,f313])).
% 0.11/0.38 fof(f317,plain,(
% 0.11/0.38 vmul(vsucc(vd411),vsucc(sK0_skl))=vplus(vmul(vd411,sK0_skl),vplus(vsucc(vd411),sK0_skl))),
% 0.11/0.38 inference(forward_demodulation,[status(thm)],[f311,f225])).
% 0.11/0.38 fof(f319,plain,(
% 0.11/0.38 $false),
% 0.11/0.38 inference(forward_subsumption_resolution,[status(thm)],[f316,f63])).
% 0.11/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.42 % Elapsed time: 0.067121 seconds
% 0.11/0.42 % CPU time: 0.181794 seconds
% 0.11/0.42 % Total memory used: 103.861 MB
% 0.11/0.42 % Net memory used: 103.806 MB
%------------------------------------------------------------------------------