%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:50:09 PM UTC 2026
% Result : Theorem 2.97s 0.84s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.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 08:35:52 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 2.97/0.84 % Refutation found
% 2.97/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.97/0.84 % SZS output start CNFRefutation for theBenchmark
% 2.97/0.84 fof(f9,axiom,(
% 2.97/0.84 (! [X,Y] :( ( leq(X,Y)& X != Y )=> gt(Y,X) ) )),
% 2.97/0.84 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.97/0.84 fof(f10,axiom,(
% 2.97/0.84 (! [X,Y] :( leq(X,pred(Y))<=> gt(Y,X) ) )),
% 2.97/0.84 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.97/0.84 fof(f53,conjecture,(
% 2.97/0.84 ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))& leq(n0,pv10)& leq(n0,pv47)& leq(pv10,n135299)& leq(pv47,n4)& (! [A] :( ( leq(n0,A)& leq(A,pred(pv47)) )=> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ))& (! [B] :( ( leq(n0,B)& leq(B,pred(pv10)) )=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ))=> (! [C] :( ( leq(n0,C)& leq(C,pv47) )=> ( pv47 != C=> a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ) )) ),
% 2.97/0.84 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.97/0.84 fof(f54,negated_conjecture,(
% 2.97/0.84 ~(( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))& leq(n0,pv10)& leq(n0,pv47)& leq(pv10,n135299)& leq(pv47,n4)& (! [A] :( ( leq(n0,A)& leq(A,pred(pv47)) )=> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ))& (! [B] :( ( leq(n0,B)& leq(B,pred(pv10)) )=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ))=> (! [C] :( ( leq(n0,C)& leq(C,pv47) )=> ( pv47 != C=> a_select3(q,pv10,C) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ) )) )),
% 2.97/0.84 inference(negated_conjecture,[status(cth)],[f53])).
% 2.97/0.84 fof(f121,plain,(
% 2.97/0.84 ![X,Y]: ((~leq(X,Y)|X=Y)|gt(Y,X))),
% 2.97/0.84 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 2.97/0.84 fof(f122,plain,(
% 2.97/0.84 ![X0,X1]: (~leq(X0,X1)|X0=X1|gt(X1,X0))),
% 2.97/0.84 inference(cnf_transformation,[status(thm)],[f121])).
% 2.97/0.84 fof(f123,plain,(
% 2.97/0.84 ![X,Y]: ((~leq(X,pred(Y))|gt(Y,X))&(leq(X,pred(Y))|~gt(Y,X)))),
% 2.97/0.84 inference(NNF_transformation,[status(thm)],[f10])).
% 2.97/0.84 fof(f124,plain,(
% 2.97/0.84 (![X,Y]: (~leq(X,pred(Y))|gt(Y,X)))&(![X,Y]: (leq(X,pred(Y))|~gt(Y,X)))),
% 2.97/0.84 inference(miniscoping,[status(thm)],[f123])).
% 2.97/0.84 fof(f126,plain,(
% 2.97/0.84 ![X0,X1]: (leq(X0,pred(X1))|~gt(X1,X0))),
% 2.97/0.84 inference(cnf_transformation,[status(thm)],[f124])).
% 2.97/0.84 fof(f259,plain,(
% 2.97/0.84 (((((((pv84=sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))&leq(n0,pv10))&leq(n0,pv47))&leq(pv10,n135299))&leq(pv47,n4))&(![A]: ((~leq(n0,A)|~leq(A,pred(pv47)))|a_select3(q,pv10,A)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))))))&(![B]: ((~leq(n0,B)|~leq(B,pred(pv10)))|sum(n0,n4,a_select3(q,B,tptp_sum_index))=n1)))&(?[C]: ((leq(n0,C)&leq(C,pv47))&(~pv47=C&~a_select3(q,pv10,C)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,C)),minus(a_select2(x,pv10),a_select2(mu,C))),tptp_minus_2),times(a_select2(sigma,C),a_select2(sigma,C)))),a_select2(rho,C)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,C))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))))))),
% 2.97/0.84 inference(pre_NNF_transformation,[status(thm)],[f54])).
% 2.97/0.84 fof(f260,plain,(
% 2.97/0.84 ((((((pv84=sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))&leq(n0,pv10))&leq(n0,pv47))&leq(pv10,n135299))&leq(pv47,n4))&(![A]: ((~leq(n0,A)|~leq(A,pred(pv47)))|a_select3(q,pv10,A)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))))))&(![B]: ((~leq(n0,B)|~leq(B,pred(pv10)))|sum(n0,n4,a_select3(q,B,tptp_sum_index))=n1)))&((leq(n0,sK23_skl)&leq(sK23_skl,pv47))&(~pv47=sK23_skl&~a_select3(q,pv10,sK23_skl)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK23_skl)),minus(a_select2(x,pv10),a_select2(mu,sK23_skl))),tptp_minus_2),times(a_select2(sigma,sK23_skl),a_select2(sigma,sK23_skl)))),a_select2(rho,sK23_skl)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK23_skl))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))))),
% 2.97/0.84 inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(C,sK23_skl)],[f259])).
% 2.97/0.84 fof(f261,plain,(
% 2.97/0.84 pv84=sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))),
% 2.97/0.84 inference(cnf_transformation,[status(thm)],[f260])).
% 2.97/0.84 fof(f266,plain,(
% 2.97/0.84 ![X0]: (~leq(n0,X0)|~leq(X0,pred(pv47))|a_select3(q,pv10,X0)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))))),
% 2.97/0.84 inference(cnf_transformation,[status(thm)],[f260])).
% 2.97/0.84 fof(f268,plain,(
% 2.97/0.84 leq(n0,sK23_skl)),
% 2.97/0.84 inference(cnf_transformation,[status(thm)],[f260])).
% 2.97/0.84 fof(f269,plain,(
% 2.97/0.84 leq(sK23_skl,pv47)),
% 2.97/0.84 inference(cnf_transformation,[status(thm)],[f260])).
% 2.97/0.84 fof(f270,plain,(
% 2.97/0.84 ~pv47=sK23_skl),
% 2.97/0.84 inference(cnf_transformation,[status(thm)],[f260])).
% 2.97/0.84 fof(f271,plain,(
% 2.97/0.84 ~a_select3(q,pv10,sK23_skl)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK23_skl)),minus(a_select2(x,pv10),a_select2(mu,sK23_skl))),tptp_minus_2),times(a_select2(sigma,sK23_skl),a_select2(sigma,sK23_skl)))),a_select2(rho,sK23_skl)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK23_skl))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))),
% 2.97/0.84 inference(cnf_transformation,[status(thm)],[f260])).
% 2.97/0.84 fof(f370,plain,(
% 2.97/0.84 ![X0]: (~leq(n0,X0)|~leq(X0,pred(pv47))|a_select3(q,pv10,X0)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),pv84))),
% 2.97/0.84 inference(forward_demodulation,[status(thm)],[f261,f266])).
% 2.97/0.84 fof(f371,plain,(
% 2.97/0.84 ~a_select3(q,pv10,sK23_skl)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK23_skl)),minus(a_select2(x,pv10),a_select2(mu,sK23_skl))),tptp_minus_2),times(a_select2(sigma,sK23_skl),a_select2(sigma,sK23_skl)))),a_select2(rho,sK23_skl)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK23_skl))),pv84)),
% 2.97/0.84 inference(forward_demodulation,[status(thm)],[f261,f271])).
% 2.97/0.84 fof(f394,plain,(
% 2.97/0.84 ![X0]: (~gt(pv47,X0)|~leq(n0,X0)|a_select3(q,pv10,X0)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),pv84))),
% 2.97/0.84 inference(resolution,[status(thm)],[f126,f370])).
% 2.97/0.84 fof(f414,plain,(
% 2.97/0.84 sK23_skl=pv47|gt(pv47,sK23_skl)),
% 2.97/0.84 inference(resolution,[status(thm)],[f122,f269])).
% 2.91/0.85 fof(f424,plain,(
% 2.91/0.85 gt(pv47,sK23_skl)),
% 2.91/0.85 inference(forward_subsumption_resolution,[status(thm)],[f414,f270])).
% 2.91/0.85 fof(f560,plain,(
% 2.91/0.85 ~leq(n0,sK23_skl)|a_select3(q,pv10,sK23_skl)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK23_skl)),minus(a_select2(x,pv10),a_select2(mu,sK23_skl))),tptp_minus_2),times(a_select2(sigma,sK23_skl),a_select2(sigma,sK23_skl)))),a_select2(rho,sK23_skl)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK23_skl))),pv84)),
% 2.91/0.85 inference(resolution,[status(thm)],[f394,f424])).
% 2.91/0.85 fof(f568,plain,(
% 2.91/0.85 ~a_select3(q,pv10,sK23_skl)=a_select3(q,pv10,sK23_skl)),
% 2.91/0.85 inference(backward_demodulation,[status(thm)],[f569,f371])).
% 2.91/0.85 fof(f569,plain,(
% 2.91/0.85 a_select3(q,pv10,sK23_skl)=divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK23_skl)),minus(a_select2(x,pv10),a_select2(mu,sK23_skl))),tptp_minus_2),times(a_select2(sigma,sK23_skl),a_select2(sigma,sK23_skl)))),a_select2(rho,sK23_skl)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK23_skl))),pv84)),
% 2.91/0.85 inference(forward_subsumption_resolution,[status(thm)],[f560,f268])).
% 2.91/0.85 fof(f570,plain,(
% 2.91/0.85 $false),
% 2.91/0.85 inference(trivial_equality_resolution,[status(thm)],[f568])).
% 2.91/0.85 % SZS output end CNFRefutation for theBenchmark.p
% 2.91/0.87 % Elapsed time: 0.488685 seconds
% 2.91/0.87 % CPU time: 3.502295 seconds
% 2.91/0.87 % Total memory used: 143.389 MB
% 2.91/0.87 % Net memory used: 138.441 MB
%------------------------------------------------------------------------------