%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM845+2 : 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 : n019.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 01:43:56 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:13:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f1,conjecture,(
% 0.10/0.40 (! [Vd416] :( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f2,negated_conjecture,(
% 0.10/0.40 ~((! [Vd416] :( vmul(vsucc(vd411),Vd416) = vplus(vmul(vd411,Vd416),Vd416)=> vmul(vsucc(vd411),vsucc(Vd416)) = vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416)) ) ))),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f1])).
% 0.10/0.40 fof(f9,axiom,(
% 0.10/0.40 (! [Vd413] :( vmul(vsucc(vd411),Vd413) = vplus(vmul(vd411,Vd413),Vd413)=> vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411)) = vplus(vplus(vmul(vd411,Vd413),Vd413),vsucc(vd411)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f12,axiom,(
% 0.10/0.40 (! [Vd396,Vd397] :( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)& vmul(Vd396,v1) = Vd396 ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f13,axiom,(
% 0.10/0.40 (! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f14,axiom,(
% 0.10/0.40 (! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f15,axiom,(
% 0.10/0.40 (! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f16,axiom,(
% 0.10/0.40 (! [Vd42,Vd43] :( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))& vplus(Vd42,v1) = vsucc(Vd42) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f17,plain,(
% 0.10/0.40 (?[Vd416]: (vmul(vsucc(vd411),Vd416)=vplus(vmul(vd411,Vd416),Vd416)&~vmul(vsucc(vd411),vsucc(Vd416))=vplus(vmul(vd411,vsucc(Vd416)),vsucc(Vd416))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.10/0.40 fof(f18,plain,(
% 0.10/0.40 (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)))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd416,sK0_skl)],[f17])).
% 0.10/0.40 fof(f19,plain,(
% 0.10/0.40 vmul(vsucc(vd411),sK0_skl)=vplus(vmul(vd411,sK0_skl),sK0_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f18])).
% 0.10/0.40 fof(f20,plain,(
% 0.10/0.40 ~vmul(vsucc(vd411),vsucc(sK0_skl))=vplus(vmul(vd411,vsucc(sK0_skl)),vsucc(sK0_skl))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f18])).
% 0.10/0.40 fof(f33,plain,(
% 0.10/0.40 ![Vd413]: (~vmul(vsucc(vd411),Vd413)=vplus(vmul(vd411,Vd413),Vd413)|vplus(vmul(vsucc(vd411),Vd413),vsucc(vd411))=vplus(vplus(vmul(vd411,Vd413),Vd413),vsucc(vd411)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.10/0.40 fof(f34,plain,(
% 0.10/0.40 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vplus(vmul(vsucc(vd411),X0),vsucc(vd411))=vplus(vplus(vmul(vd411,X0),X0),vsucc(vd411)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.10/0.40 fof(f38,plain,(
% 0.10/0.40 (![Vd396,Vd397]: vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396))&(![Vd396]: vmul(Vd396,v1)=Vd396)),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f12])).
% 0.10/0.40 fof(f39,plain,(
% 0.10/0.40 ![X0,X1]: (vmul(X0,vsucc(X1))=vplus(vmul(X0,X1),X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f38])).
% 0.10/0.40 fof(f41,plain,(
% 0.10/0.40 ![X0,X1]: (vplus(X0,X1)=vplus(X1,X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f13])).
% 0.10/0.40 fof(f42,plain,(
% 0.10/0.40 ![X0]: (vplus(v1,X0)=vsucc(X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.10/0.40 fof(f43,plain,(
% 0.10/0.40 ![X0,X1,X2]: (vplus(vplus(X0,X1),X2)=vplus(X0,vplus(X1,X2)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f15])).
% 0.10/0.40 fof(f44,plain,(
% 0.10/0.40 (![Vd42,Vd43]: vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)))&(![Vd42]: vplus(Vd42,v1)=vsucc(Vd42))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f16])).
% 0.10/0.40 fof(f45,plain,(
% 0.10/0.40 ![X0,X1]: (vplus(X0,vsucc(X1))=vsucc(vplus(X0,X1)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f44])).
% 0.10/0.40 fof(f48,plain,(
% 0.10/0.40 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(vmul(vd411,X0),X0)|vmul(vsucc(vd411),vsucc(X0))=vplus(vplus(vmul(vd411,X0),X0),vsucc(vd411)))),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f39,f34])).
% 0.10/0.40 fof(f53,plain,(
% 0.10/0.40 ~vmul(vsucc(vd411),vsucc(sK0_skl))=vplus(vsucc(sK0_skl),vmul(vd411,vsucc(sK0_skl)))),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f41,f20])).
% 0.10/0.40 fof(f54,plain,(
% 0.10/0.40 vmul(vsucc(vd411),sK0_skl)=vplus(sK0_skl,vmul(vd411,sK0_skl))),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f41,f19])).
% 0.10/0.40 fof(f58,plain,(
% 0.10/0.40 ![X0,X1]: (vmul(X0,vsucc(X1))=vplus(X0,vmul(X0,X1)))),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f41,f39])).
% 0.10/0.40 fof(f59,plain,(
% 0.10/0.40 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(X0,vmul(vd411,X0))|vmul(vsucc(vd411),vsucc(X0))=vplus(vplus(vmul(vd411,X0),X0),vsucc(vd411)))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f41,f48])).
% 0.10/0.40 fof(f60,plain,(
% 0.10/0.40 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(X0,vmul(vd411,X0))|vmul(vsucc(vd411),vsucc(X0))=vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f43,f59])).
% 0.10/0.40 fof(f61,plain,(
% 0.10/0.40 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(X0,vmul(vd411,X0))|vmul(vsucc(vd411),vsucc(X0))=vplus(vmul(vd411,X0),vsucc(vplus(X0,vd411))))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f45,f60])).
% 0.10/0.40 fof(f62,plain,(
% 0.10/0.40 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(X0,vmul(vd411,X0))|vmul(vsucc(vd411),vsucc(X0))=vsucc(vplus(vmul(vd411,X0),vplus(X0,vd411))))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f45,f61])).
% 0.10/0.40 fof(f86,plain,(
% 0.10/0.40 ![X0,X1,X2]: (vplus(X0,vplus(X1,X2))=vplus(X1,vplus(X2,X0)))),
% 0.10/0.40 inference(paramodulation,[status(thm)],[f41,f43])).
% 0.10/0.40 fof(f89,plain,(
% 0.10/0.40 ![X0,X1]: (vplus(vsucc(X0),X1)=vplus(v1,vplus(X0,X1)))),
% 0.10/0.40 inference(paramodulation,[status(thm)],[f42,f43])).
% 0.10/0.40 fof(f98,plain,(
% 0.10/0.40 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(X0,vmul(vd411,X0))|vmul(vsucc(vd411),vsucc(X0))=vsucc(vplus(X0,vplus(vd411,vmul(vd411,X0)))))),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f86,f62])).
% 0.10/0.40 fof(f101,plain,(
% 0.10/0.40 ~vmul(vsucc(vd411),vsucc(sK0_skl))=vsucc(vplus(sK0_skl,vmul(vd411,vsucc(sK0_skl))))),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f102,f53])).
% 0.10/0.40 fof(f102,plain,(
% 0.10/0.40 ![X0,X1]: (vplus(vsucc(X0),X1)=vsucc(vplus(X0,X1)))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f42,f89])).
% 0.10/0.40 fof(f111,plain,(
% 0.10/0.40 ![X0]: (~vmul(vsucc(vd411),X0)=vplus(X0,vmul(vd411,X0))|vmul(vsucc(vd411),vsucc(X0))=vsucc(vplus(X0,vmul(vd411,vsucc(X0)))))),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f58,f98])).
% 0.10/0.40 fof(f326,plain,(
% 0.10/0.40 vmul(vsucc(vd411),vsucc(sK0_skl))=vsucc(vplus(sK0_skl,vmul(vd411,vsucc(sK0_skl))))),
% 0.10/0.40 inference(resolution,[status(thm)],[f111,f54])).
% 0.10/0.40 fof(f335,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f326,f101])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.42 % Elapsed time: 0.055212 seconds
% 0.10/0.42 % CPU time: 0.199242 seconds
% 0.10/0.42 % Total memory used: 68.356 MB
% 0.10/0.42 % Net memory used: 68.009 MB
%------------------------------------------------------------------------------