%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO450+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 : n011.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 12:26:30 PM UTC 2026
% Result : Theorem 2.42s 28.13s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO450+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
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/25.44 % CPULimit : 300
% 0.09/25.44 % WCLimit : 300
% 0.09/25.44 % DateTime : Sun Sep 20 16:18:10 UTC 2026
% 0.09/25.44 % CPUTime :
% 2.30/27.40 % Drodi V4.1.1
% 2.42/28.13 % Refutation found
% 2.42/28.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.42/28.13 % SZS output start CNFRefutation for theBenchmark
% 2.42/28.13 fof(f200,axiom,(
% 2.42/28.13 (! [N0] : s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0) )),
% 2.42/28.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.42/28.13 fof(f3104,axiom,(
% 2.42/28.13 (! [Q114603,Q114604,A5] : s(cart(cart(real,Q114603),Q114604),i(s(fun(cart(cart(real,Q114603),Q114604),cart(cart(real,Q114603),Q114604)),i(s(fun(cart(cart(real,Q114603),Q114604),fun(cart(cart(real,Q114603),Q114604),cart(cart(real,Q114603),Q114604))),matrixu_add),s(cart(cart(real,Q114603),Q114604),i(s(fun(num,cart(cart(real,Q114603),Q114604)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,Q114603),Q114604),A5))) = s(cart(cart(real,Q114603),Q114604),A5) )),
% 2.42/28.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.42/28.13 fof(f3108,axiom,(
% 2.42/28.13 (! [N,M,A5,B0] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),B0))))) )),
% 2.42/28.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.42/28.13 fof(f3135,conjecture,(
% 2.42/28.13 (! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))) )),
% 2.42/28.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.42/28.13 fof(f3136,negated_conjecture,(
% 2.42/28.13 ~((! [N,M,A5] : s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))) ))),
% 2.42/28.13 inference(negated_conjecture,[status(cth)],[f3135])).
% 2.42/28.13 fof(f4153,plain,(
% 2.42/28.13 ![X0]: (s(num,i(s(fun(num,num),numeral),s(num,X0)))=s(num,X0))),
% 2.42/28.13 inference(cnf_transformation,[status(thm)],[f200])).
% 2.42/28.13 fof(f13815,plain,(
% 2.42/28.13 ![X0,X1,X2]: (s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_add),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,X0),X1),X2)))=s(cart(cart(real,X0),X1),X2))),
% 2.42/28.13 inference(cnf_transformation,[status(thm)],[f3104])).
% 2.42/28.13 fof(f13819,plain,(
% 2.42/28.13 ![X0,X1,X2,X3]: (s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_sub),s(cart(cart(real,X0),X1),X2))),s(cart(cart(real,X0),X1),X3)))=s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_add),s(cart(cart(real,X0),X1),X2))),s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),matrixu_neg),s(cart(cart(real,X0),X1),X3))))))),
% 2.42/28.13 inference(cnf_transformation,[status(thm)],[f3108])).
% 2.42/28.13 fof(f13846,plain,(
% 2.42/28.13 (?[N,M,A5]: ~s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,N),M),A5)))=s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))))),
% 2.42/28.14 inference(pre_NNF_transformation,[status(thm)],[f3136])).
% 2.42/28.14 fof(f13847,plain,(
% 2.42/28.14 ~s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl))),matrixu_sub),s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(num,cart(cart(real,sK3338_skl),sK3339_skl)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl)))=s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl)))),
% 2.42/28.14 inference(skolemize,[status(esa),new_symbols(skolem,[sK3338_skl,sK3339_skl,sK3340_skl]),skolemize(N,sK3338_skl),skolemize(M,sK3339_skl),skolemize(A5,sK3340_skl)],[f13846])).
% 2.42/28.14 fof(f13848,plain,(
% 2.42/28.14 ~s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl))),matrixu_sub),s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(num,cart(cart(real,sK3338_skl),sK3339_skl)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl)))=s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl)))),
% 2.42/28.14 inference(cnf_transformation,[status(thm)],[f13847])).
% 2.42/28.14 fof(f17268,plain,(
% 2.42/28.14 ~s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl))),matrixu_sub),s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(num,cart(cart(real,sK3338_skl),sK3339_skl)),mat),s(num,u_0))))),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl)))=s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl)))),
% 2.42/28.14 inference(backward_demodulation,[status(thm)],[f4153,f13848])).
% 2.42/28.14 fof(f17286,plain,(
% 2.42/28.14 ![X0,X1,X2]: (s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_add),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,u_0))))),s(cart(cart(real,X0),X1),X2)))=s(cart(cart(real,X0),X1),X2))),
% 2.42/28.14 inference(forward_demodulation,[status(thm)],[f4153,f13815])).
% 2.42/28.14 fof(f17817,plain,(
% 2.42/28.14 ![X0,X1,X2]: (s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),i(s(fun(cart(cart(real,X0),X1),fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1))),matrixu_sub),s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,u_0))))),s(cart(cart(real,X0),X1),X2)))=s(cart(cart(real,X0),X1),i(s(fun(cart(cart(real,X0),X1),cart(cart(real,X0),X1)),matrixu_neg),s(cart(cart(real,X0),X1),X2))))),
% 2.42/28.14 inference(paramodulation,[status(thm)],[f17286,f13819])).
% 2.42/28.14 fof(f17984,plain,(
% 2.42/28.14 ~s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl)))=s(cart(cart(real,sK3338_skl),sK3339_skl),i(s(fun(cart(cart(real,sK3338_skl),sK3339_skl),cart(cart(real,sK3338_skl),sK3339_skl)),matrixu_neg),s(cart(cart(real,sK3338_skl),sK3339_skl),sK3340_skl)))),
% 2.42/28.14 inference(backward_demodulation,[status(thm)],[f17817,f17268])).
% 2.42/28.14 fof(f18025,plain,(
% 2.42/28.14 $false),
% 2.42/28.14 inference(trivial_equality_resolution,[status(thm)],[f17984])).
% 2.42/28.14 % SZS output end CNFRefutation for theBenchmark.p
% 2.47/28.32 % Elapsed time: 2.856700 seconds
% 2.47/28.32 % CPU time: 7.868862 seconds
% 2.47/28.32 % Total memory used: 1.442 GB
% 2.47/28.32 % Net memory used: 1.438 GB
%------------------------------------------------------------------------------