%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO440+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:26:29 PM UTC 2026
% Result : Theorem 14.14s 3.76s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO440+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 16:11:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 1.77/2.12 % Drodi V4.1.1
% 14.14/3.76 % Refutation found
% 14.14/3.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.14/3.76 % SZS output start CNFRefutation for theBenchmark
% 14.14/3.76 fof(f200,axiom,(
% 14.14/3.76 (! [N0] : s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0) )),
% 14.14/3.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.14/3.76 fof(f1028,axiom,(
% 14.14/3.76 (! [X,Y] :( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))<=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))| s(real,X) = s(real,Y) ) ) )),
% 14.14/3.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.14/3.76 fof(f1032,axiom,(
% 14.14/3.76 (! [X,Y] :( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))<=> ( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))& s(real,X) != s(real,Y) ) ) )),
% 14.14/3.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.14/3.76 fof(f2845,axiom,(
% 14.14/3.76 (! [Q102146] : s(real,i(s(fun(cart(real,Q102146),real),vectoru_norm),s(cart(real,Q102146),i(s(fun(num,cart(real,Q102146)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )),
% 14.14/3.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.14/3.77 fof(f2846,axiom,(
% 14.14/3.77 (! [Q102162,X] : p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102162),real),vectoru_norm),s(cart(real,Q102162),X)))))) )),
% 14.14/3.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.14/3.77 fof(f2851,axiom,(
% 14.14/3.77 (! [Q102285,X] :( s(real,i(s(fun(cart(real,Q102285),real),vectoru_norm),s(cart(real,Q102285),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))<=> s(cart(real,Q102285),X) = s(cart(real,Q102285),i(s(fun(num,cart(real,Q102285)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )),
% 14.14/3.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.14/3.77 fof(f2852,conjecture,(
% 14.14/3.77 (! [Q102307,X] :( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102307),real),vectoru_norm),s(cart(real,Q102307),X))))))<=> s(cart(real,Q102307),X) != s(cart(real,Q102307),i(s(fun(num,cart(real,Q102307)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) )),
% 14.14/3.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.14/3.77 fof(f2853,negated_conjecture,(
% 14.14/3.77 ~((! [Q102307,X] :( p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102307),real),vectoru_norm),s(cart(real,Q102307),X))))))<=> s(cart(real,Q102307),X) != s(cart(real,Q102307),i(s(fun(num,cart(real,Q102307)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ) ))),
% 14.14/3.77 inference(negated_conjecture,[status(cth)],[f2852])).
% 14.14/3.77 fof(f3870,plain,(
% 14.14/3.77 ![X0]: (s(num,i(s(fun(num,num),numeral),s(num,X0)))=s(num,X0))),
% 14.14/3.77 inference(cnf_transformation,[status(thm)],[f200])).
% 14.14/3.77 fof(f6030,plain,(
% 14.14/3.77 ![X,Y]: ((~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))|(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))|s(real,X)=s(real,Y)))&(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))|(~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))&~s(real,X)=s(real,Y))))),
% 14.14/3.77 inference(NNF_transformation,[status(thm)],[f1028])).
% 14.14/3.77 fof(f6031,plain,(
% 14.14/3.77 (![X,Y]: (~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))|(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))|s(real,X)=s(real,Y))))&(![X,Y]: (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))|(~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))&~s(real,X)=s(real,Y))))),
% 14.14/3.77 inference(miniscoping,[status(thm)],[f6030])).
% 14.14/3.77 fof(f6032,plain,(
% 14.14/3.77 ![X0,X1]: (~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X0))),s(real,X1))))|p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X0))),s(real,X1))))|s(real,X0)=s(real,X1))),
% 14.14/3.77 inference(cnf_transformation,[status(thm)],[f6031])).
% 14.14/3.77 fof(f6044,plain,(
% 14.14/3.77 ![X,Y]: ((~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))|(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))&~s(real,X)=s(real,Y)))&(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))|(~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))|s(real,X)=s(real,Y))))),
% 14.14/3.77 inference(NNF_transformation,[status(thm)],[f1032])).
% 14.14/3.77 fof(f6045,plain,(
% 14.14/3.77 (![X,Y]: (~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))|(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))&~s(real,X)=s(real,Y))))&(![X,Y]: (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))|(~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))|s(real,X)=s(real,Y))))),
% 14.14/3.77 inference(miniscoping,[status(thm)],[f6044])).
% 14.14/3.77 fof(f6047,plain,(
% 14.14/3.77 ![X0,X1]: (~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X0))),s(real,X1))))|~s(real,X0)=s(real,X1))),
% 14.14/3.77 inference(cnf_transformation,[status(thm)],[f6045])).
% 14.14/3.77 fof(f12650,plain,(
% 14.14/3.77 ![X0]: (s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
% 14.14/3.77 inference(cnf_transformation,[status(thm)],[f2845])).
% 14.14/3.77 fof(f12651,plain,(
% 14.14/3.77 ![X0,X1]: (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),X1)))))))),
% 14.14/3.77 inference(cnf_transformation,[status(thm)],[f2846])).
% 14.14/3.77 fof(f12659,plain,(
% 14.14/3.77 ![Q102285,X]: ((~s(real,i(s(fun(cart(real,Q102285),real),vectoru_norm),s(cart(real,Q102285),X)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))|s(cart(real,Q102285),X)=s(cart(real,Q102285),i(s(fun(num,cart(real,Q102285)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))&(s(real,i(s(fun(cart(real,Q102285),real),vectoru_norm),s(cart(real,Q102285),X)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))|~s(cart(real,Q102285),X)=s(cart(real,Q102285),i(s(fun(num,cart(real,Q102285)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))),
% 14.14/3.77 inference(NNF_transformation,[status(thm)],[f2851])).
% 14.14/3.77 fof(f12660,plain,(
% 14.14/3.77 (![Q102285,X]: (~s(real,i(s(fun(cart(real,Q102285),real),vectoru_norm),s(cart(real,Q102285),X)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))|s(cart(real,Q102285),X)=s(cart(real,Q102285),i(s(fun(num,cart(real,Q102285)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))&(![Q102285,X]: (s(real,i(s(fun(cart(real,Q102285),real),vectoru_norm),s(cart(real,Q102285),X)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))|~s(cart(real,Q102285),X)=s(cart(real,Q102285),i(s(fun(num,cart(real,Q102285)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))),
% 14.14/3.77 inference(miniscoping,[status(thm)],[f12659])).
% 14.14/3.77 fof(f12661,plain,(
% 14.14/3.77 ![X0,X1]: (~s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),X1)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))|s(cart(real,X0),X1)=s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
% 14.14/3.77 inference(cnf_transformation,[status(thm)],[f12660])).
% 14.14/3.77 fof(f12663,plain,(
% 14.14/3.77 (?[Q102307,X]: (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102307),real),vectoru_norm),s(cart(real,Q102307),X))))))<~>~s(cart(real,Q102307),X)=s(cart(real,Q102307),i(s(fun(num,cart(real,Q102307)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))),
% 14.14/3.77 inference(pre_NNF_transformation,[status(thm)],[f2853])).
% 14.14/3.77 fof(f12664,plain,(
% 14.14/3.77 ?[Q102307,X]: ((p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102307),real),vectoru_norm),s(cart(real,Q102307),X))))))|~s(cart(real,Q102307),X)=s(cart(real,Q102307),i(s(fun(num,cart(real,Q102307)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))&(~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102307),real),vectoru_norm),s(cart(real,Q102307),X))))))|s(cart(real,Q102307),X)=s(cart(real,Q102307),i(s(fun(num,cart(real,Q102307)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))),
% 14.14/3.77 inference(NNF_transformation,[status(thm)],[f12663])).
% 14.14/3.77 fof(f12665,plain,(
% 14.14/3.77 ((p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|~s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))&(~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))),
% 14.14/3.77 inference(skolemize,[status(esa),new_symbols(skolem,[sK2954_skl,sK2955_skl]),skolemize(Q102307,sK2954_skl),skolemize(X,sK2955_skl)],[f12664])).
% 14.14/3.77 fof(f12666,plain,(
% 14.14/3.77 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|~s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))),
% 14.14/3.77 inference(cnf_transformation,[status(thm)],[f12665])).
% 14.14/3.77 fof(f12667,plain,(
% 14.14/3.77 ~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))),
% 14.14/3.77 inference(cnf_transformation,[status(thm)],[f12665])).
% 14.14/3.77 fof(f15145,plain,(
% 14.14/3.77 ~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,u_0)))),
% 14.14/3.77 inference(backward_demodulation,[status(thm)],[f3870,f12667])).
% 14.14/3.77 fof(f15146,plain,(
% 14.14/3.77 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|~s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,u_0)))),
% 14.14/3.77 inference(backward_demodulation,[status(thm)],[f3870,f12666])).
% 14.14/3.77 fof(f15152,plain,(
% 14.14/3.77 ~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,u_0)))),
% 14.14/3.77 inference(forward_demodulation,[status(thm)],[f3870,f15145])).
% 14.14/3.77 fof(f15153,plain,(
% 14.14/3.77 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|~s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,u_0)))),
% 14.14/3.77 inference(forward_demodulation,[status(thm)],[f3870,f15146])).
% 14.14/3.77 fof(f15365,plain,(
% 14.14/3.77 ~p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))=s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl)))|s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,u_0)))),
% 14.14/3.77 inference(resolution,[status(thm)],[f6032,f15152])).
% 14.14/3.77 fof(f16541,plain,(
% 14.14/3.77 ![X0]: (s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,u_0)))))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
% 14.14/3.77 inference(forward_demodulation,[status(thm)],[f3870,f12650])).
% 14.14/3.77 fof(f16542,plain,(
% 14.14/3.77 ![X0]: (s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,u_0)))))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))),
% 14.14/3.77 inference(forward_demodulation,[status(thm)],[f3870,f16541])).
% 14.14/3.77 fof(f16651,plain,(
% 14.14/3.77 s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))=s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl)))|s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,u_0)))),
% 14.14/3.77 inference(backward_subsumption_resolution,[status(thm)],[f15365,f16652])).
% 14.14/3.77 fof(f16652,plain,(
% 14.14/3.77 ![X0,X1]: (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))),s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),X1)))))))),
% 14.14/3.77 inference(forward_demodulation,[status(thm)],[f3870,f12651])).
% 14.14/3.77 fof(f17063,plain,(
% 14.14/3.77 s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))|s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))=s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl)))),
% 14.14/3.77 inference(paramodulation,[status(thm)],[f16651,f16542])).
% 14.14/3.77 fof(f17089,plain,(
% 14.14/3.77 s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))),
% 14.14/3.77 inference(duplicate_literals_removal,[status(thm)],[f17063])).
% 14.14/3.77 fof(f17540,plain,(
% 14.14/3.77 ![X0,X1]: (~s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),X1)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))|s(cart(real,X0),X1)=s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
% 14.14/3.77 inference(forward_demodulation,[status(thm)],[f3870,f12661])).
% 14.14/3.77 fof(f17541,plain,(
% 14.14/3.77 s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),i(s(fun(num,cart(real,sK2954_skl)),vec),s(num,u_0)))),
% 14.14/3.77 inference(backward_subsumption_resolution,[status(thm)],[f16651,f17543])).
% 14.14/3.77 fof(f17543,plain,(
% 14.14/3.77 ![X0,X1]: (~s(real,i(s(fun(cart(real,X0),real),vectoru_norm),s(cart(real,X0),X1)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))|s(cart(real,X0),X1)=s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,u_0))))),
% 14.14/3.77 inference(forward_demodulation,[status(thm)],[f3870,f17540])).
% 14.14/3.77 fof(f17804,plain,(
% 14.14/3.77 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))|~s(cart(real,sK2954_skl),sK2955_skl)=s(cart(real,sK2954_skl),sK2955_skl)),
% 14.94/3.86 inference(backward_demodulation,[status(thm)],[f17541,f15153])).
% 14.94/3.86 fof(f17851,plain,(
% 14.94/3.86 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0))))),s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl))))))),
% 14.94/3.86 inference(trivial_equality_resolution,[status(thm)],[f17804])).
% 14.94/3.86 fof(f17886,plain,(
% 14.94/3.86 ~s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))=s(real,i(s(fun(cart(real,sK2954_skl),real),vectoru_norm),s(cart(real,sK2954_skl),sK2955_skl)))),
% 14.94/3.86 inference(resolution,[status(thm)],[f17851,f6047])).
% 14.94/3.86 fof(f22938,plain,(
% 14.94/3.86 ~s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))=s(real,i(s(fun(num,real),realu_ofu_num),s(num,u_0)))),
% 14.94/3.86 inference(forward_demodulation,[status(thm)],[f17089,f17886])).
% 14.94/3.86 fof(f22939,plain,(
% 14.94/3.86 $false),
% 14.94/3.86 inference(trivial_equality_resolution,[status(thm)],[f22938])).
% 14.94/3.86 % SZS output end CNFRefutation for theBenchmark.p
% 6.53/3.95 % Elapsed time: 3.564969 seconds
% 6.53/3.95 % CPU time: 15.105948 seconds
% 6.53/3.95 % Total memory used: 1.435 GB
% 6.53/3.95 % Net memory used: 1.428 GB
%------------------------------------------------------------------------------