%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWV167+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 : n020.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 02:50:10 PM UTC 2026
% Result : Theorem 7.22s 1.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV167+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
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 08:34:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 7.22/1.36 % Refutation found
% 7.22/1.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.22/1.36 % SZS output start CNFRefutation for theBenchmark
% 7.22/1.36 fof(f4,axiom,(
% 7.22/1.36 (! [X] : leq(X,X) )),
% 7.22/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.22/1.36 fof(f8,axiom,(
% 7.22/1.36 (! [X,Y] :( gt(Y,X)=> leq(X,Y) ) )),
% 7.22/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.22/1.36 fof(f9,axiom,(
% 7.22/1.36 (! [X,Y] :( ( leq(X,Y)& X != Y )=> gt(Y,X) ) )),
% 7.22/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.22/1.36 fof(f10,axiom,(
% 7.22/1.36 (! [X,Y] :( leq(X,pred(Y))<=> gt(Y,X) ) )),
% 7.22/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.22/1.36 fof(f41,axiom,(
% 7.22/1.36 (! [X] : succ(pred(X)) = X )),
% 7.22/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.22/1.36 fof(f42,axiom,(
% 7.22/1.36 (! [X,Y] :( leq(succ(X),succ(Y))<=> leq(X,Y) ) )),
% 7.22/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.22/1.36 fof(f53,conjecture,(
% 7.22/1.36 ( ( a_select2(mu_init,pv40) = init& a_select2(sigma_init,pv40) = init& leq(n0,pv40)& leq(pv40,n4)& (! [A] :( ( leq(n0,A)& leq(A,n135299) )=> (! [B] :( ( leq(n0,B)& leq(B,n4) )=> a_select3(q_init,A,B) = init ) )))& (! [C] :( ( leq(n0,C)& leq(C,n4) )=> a_select2(rho_init,C) = init ))& (! [D] :( ( leq(n0,D)& leq(D,pred(pv40)) )=> a_select2(mu_init,D) = init ))& (! [E] :( ( leq(n0,E)& leq(E,pred(pv40)) )=> a_select2(sigma_init,E) = init ))& (! [F] :( ( leq(n0,F)& leq(F,n4) )=> a_select3(center_init,F,n0) = init ))& ( gt(loopcounter,n1)=> (! [G] :( ( leq(n0,G)& leq(G,n4) )=> a_select2(muold_init,G) = init ) ))& ( gt(loopcounter,n1)=> (! [H] :( ( leq(n0,H)& leq(H,n4) )=> a_select2(rhoold_init,H) = init ) ))& ( gt(loopcounter,n1)=> (! [I] :( ( leq(n0,I)& leq(I,n4) )=> a_select2(sigmaold_init,I) = init ) )) )=> (! [J] :( ( leq(n0,J)& leq(J,pv40) )=> a_select2(mu_init,J) = init ) )) ),
% 7.22/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.22/1.36 fof(f54,negated_conjecture,(
% 7.22/1.36 ~(( ( a_select2(mu_init,pv40) = init& a_select2(sigma_init,pv40) = init& leq(n0,pv40)& leq(pv40,n4)& (! [A] :( ( leq(n0,A)& leq(A,n135299) )=> (! [B] :( ( leq(n0,B)& leq(B,n4) )=> a_select3(q_init,A,B) = init ) )))& (! [C] :( ( leq(n0,C)& leq(C,n4) )=> a_select2(rho_init,C) = init ))& (! [D] :( ( leq(n0,D)& leq(D,pred(pv40)) )=> a_select2(mu_init,D) = init ))& (! [E] :( ( leq(n0,E)& leq(E,pred(pv40)) )=> a_select2(sigma_init,E) = init ))& (! [F] :( ( leq(n0,F)& leq(F,n4) )=> a_select3(center_init,F,n0) = init ))& ( gt(loopcounter,n1)=> (! [G] :( ( leq(n0,G)& leq(G,n4) )=> a_select2(muold_init,G) = init ) ))& ( gt(loopcounter,n1)=> (! [H] :( ( leq(n0,H)& leq(H,n4) )=> a_select2(rhoold_init,H) = init ) ))& ( gt(loopcounter,n1)=> (! [I] :( ( leq(n0,I)& leq(I,n4) )=> a_select2(sigmaold_init,I) = init ) )) )=> (! [J] :( ( leq(n0,J)& leq(J,pv40) )=> a_select2(mu_init,J) = init ) )) )),
% 7.22/1.36 inference(negated_conjecture,[status(cth)],[f53])).
% 7.22/1.36 fof(f99,plain,(
% 7.22/1.36 ![X0]: (leq(X0,X0))),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f4])).
% 7.22/1.36 fof(f111,plain,(
% 7.22/1.36 ![X,Y]: (~gt(Y,X)|leq(X,Y))),
% 7.22/1.36 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 7.22/1.36 fof(f112,plain,(
% 7.22/1.36 ![X0,X1]: (~gt(X0,X1)|leq(X1,X0))),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f111])).
% 7.22/1.36 fof(f113,plain,(
% 7.22/1.36 ![X,Y]: ((~leq(X,Y)|X=Y)|gt(Y,X))),
% 7.22/1.36 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 7.22/1.36 fof(f114,plain,(
% 7.22/1.36 ![X0,X1]: (~leq(X0,X1)|X0=X1|gt(X1,X0))),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f113])).
% 7.22/1.36 fof(f115,plain,(
% 7.22/1.36 ![X,Y]: ((~leq(X,pred(Y))|gt(Y,X))&(leq(X,pred(Y))|~gt(Y,X)))),
% 7.22/1.36 inference(NNF_transformation,[status(thm)],[f10])).
% 7.22/1.36 fof(f116,plain,(
% 7.22/1.36 (![X,Y]: (~leq(X,pred(Y))|gt(Y,X)))&(![X,Y]: (leq(X,pred(Y))|~gt(Y,X)))),
% 7.22/1.36 inference(miniscoping,[status(thm)],[f115])).
% 7.22/1.36 fof(f118,plain,(
% 7.22/1.36 ![X0,X1]: (leq(X0,pred(X1))|~gt(X1,X0))),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f116])).
% 7.22/1.36 fof(f219,plain,(
% 7.22/1.36 ![X0]: (succ(pred(X0))=X0)),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f41])).
% 7.22/1.36 fof(f220,plain,(
% 7.22/1.36 ![X,Y]: ((~leq(succ(X),succ(Y))|leq(X,Y))&(leq(succ(X),succ(Y))|~leq(X,Y)))),
% 7.22/1.36 inference(NNF_transformation,[status(thm)],[f42])).
% 7.22/1.36 fof(f221,plain,(
% 7.22/1.36 (![X,Y]: (~leq(succ(X),succ(Y))|leq(X,Y)))&(![X,Y]: (leq(succ(X),succ(Y))|~leq(X,Y)))),
% 7.22/1.36 inference(miniscoping,[status(thm)],[f220])).
% 7.22/1.36 fof(f222,plain,(
% 7.22/1.36 ![X0,X1]: (~leq(succ(X0),succ(X1))|leq(X0,X1))),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f221])).
% 7.22/1.36 fof(f223,plain,(
% 7.22/1.36 ![X0,X1]: (leq(succ(X0),succ(X1))|~leq(X0,X1))),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f221])).
% 7.22/1.36 fof(f251,plain,(
% 7.22/1.36 ((((((((((((a_select2(mu_init,pv40)=init&a_select2(sigma_init,pv40)=init)&leq(n0,pv40))&leq(pv40,n4))&(![A]: ((~leq(n0,A)|~leq(A,n135299))|(![B]: ((~leq(n0,B)|~leq(B,n4))|a_select3(q_init,A,B)=init)))))&(![C]: ((~leq(n0,C)|~leq(C,n4))|a_select2(rho_init,C)=init)))&(![D]: ((~leq(n0,D)|~leq(D,pred(pv40)))|a_select2(mu_init,D)=init)))&(![E]: ((~leq(n0,E)|~leq(E,pred(pv40)))|a_select2(sigma_init,E)=init)))&(![F]: ((~leq(n0,F)|~leq(F,n4))|a_select3(center_init,F,n0)=init)))&(~gt(loopcounter,n1)|(![G]: ((~leq(n0,G)|~leq(G,n4))|a_select2(muold_init,G)=init))))&(~gt(loopcounter,n1)|(![H]: ((~leq(n0,H)|~leq(H,n4))|a_select2(rhoold_init,H)=init))))&(~gt(loopcounter,n1)|(![I]: ((~leq(n0,I)|~leq(I,n4))|a_select2(sigmaold_init,I)=init))))&(?[J]: ((leq(n0,J)&leq(J,pv40))&~a_select2(mu_init,J)=init)))),
% 7.22/1.36 inference(pre_NNF_transformation,[status(thm)],[f54])).
% 7.22/1.36 fof(f252,plain,(
% 7.22/1.36 (((((((((((a_select2(mu_init,pv40)=init&a_select2(sigma_init,pv40)=init)&leq(n0,pv40))&leq(pv40,n4))&(![A]: ((~leq(n0,A)|~leq(A,n135299))|(![B]: ((~leq(n0,B)|~leq(B,n4))|a_select3(q_init,A,B)=init)))))&(![C]: ((~leq(n0,C)|~leq(C,n4))|a_select2(rho_init,C)=init)))&(![D]: ((~leq(n0,D)|~leq(D,pred(pv40)))|a_select2(mu_init,D)=init)))&(![E]: ((~leq(n0,E)|~leq(E,pred(pv40)))|a_select2(sigma_init,E)=init)))&(![F]: ((~leq(n0,F)|~leq(F,n4))|a_select3(center_init,F,n0)=init)))&(~gt(loopcounter,n1)|(![G]: ((~leq(n0,G)|~leq(G,n4))|a_select2(muold_init,G)=init))))&(~gt(loopcounter,n1)|(![H]: ((~leq(n0,H)|~leq(H,n4))|a_select2(rhoold_init,H)=init))))&(~gt(loopcounter,n1)|(![I]: ((~leq(n0,I)|~leq(I,n4))|a_select2(sigmaold_init,I)=init))))&((leq(n0,sK23_skl)&leq(sK23_skl,pv40))&~a_select2(mu_init,sK23_skl)=init)),
% 7.22/1.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(J,sK23_skl)],[f251])).
% 7.22/1.36 fof(f253,plain,(
% 7.22/1.36 a_select2(mu_init,pv40)=init),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f252])).
% 7.22/1.36 fof(f259,plain,(
% 7.22/1.36 ![X0]: (~leq(n0,X0)|~leq(X0,pred(pv40))|a_select2(mu_init,X0)=init)),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f252])).
% 7.22/1.36 fof(f265,plain,(
% 7.22/1.36 leq(n0,sK23_skl)),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f252])).
% 7.22/1.36 fof(f266,plain,(
% 7.22/1.36 leq(sK23_skl,pv40)),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f252])).
% 7.22/1.36 fof(f267,plain,(
% 7.22/1.36 ~a_select2(mu_init,sK23_skl)=init),
% 7.22/1.36 inference(cnf_transformation,[status(thm)],[f252])).
% 7.22/1.36 fof(f479,plain,(
% 7.22/1.36 sK23_skl=pv40|gt(pv40,sK23_skl)),
% 7.22/1.36 inference(resolution,[status(thm)],[f266,f114])).
% 7.22/1.36 fof(f482,definition,(
% 7.22/1.36 sQ16_spl <=> (sK23_skl=pv40)),
% 7.22/1.36 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 7.22/1.36 fof(f483,plain,(
% 7.22/1.36 sK23_skl=pv40|~sQ16_spl),
% 7.22/1.36 inference(component_clause,[status(thm)],[f482])).
% 7.22/1.36 fof(f485,definition,(
% 7.22/1.36 sQ17_spl <=> (gt(pv40,sK23_skl))),
% 7.22/1.36 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 7.22/1.36 fof(f486,plain,(
% 7.22/1.36 gt(pv40,sK23_skl)|~sQ17_spl),
% 7.22/1.36 inference(component_clause,[status(thm)],[f485])).
% 7.22/1.36 fof(f488,plain,(
% 7.22/1.36 sQ16_spl|sQ17_spl),
% 7.22/1.36 inference(split_clause,[status(thm)],[f479,f482,f485])).
% 7.22/1.36 fof(f548,plain,(
% 7.22/1.36 ![X0,X1]: (~leq(succ(X0),X1)|leq(X0,pred(X1)))),
% 7.22/1.36 inference(paramodulation,[status(thm)],[f219,f222])).
% 7.22/1.36 fof(f901,plain,(
% 7.22/1.36 ![X0,X1]: (~leq(X0,X1)|leq(pred(X0),pred(X1)))),
% 7.22/1.36 inference(paramodulation,[status(thm)],[f219,f548])).
% 7.22/1.36 fof(f965,plain,(
% 7.22/1.36 leq(sK23_skl,pred(pv40))|~sQ17_spl),
% 7.22/1.36 inference(resolution,[status(thm)],[f486,f118])).
% 7.22/1.36 fof(f1171,plain,(
% 7.22/1.36 leq(pred(n0),pred(sK23_skl))),
% 7.22/1.36 inference(resolution,[status(thm)],[f901,f265])).
% 7.22/1.36 fof(f1250,plain,(
% 7.22/1.36 sK23_skl=pred(pv40)|gt(pred(pv40),sK23_skl)|~sQ17_spl),
% 7.22/1.36 inference(resolution,[status(thm)],[f965,f114])).
% 7.22/1.36 fof(f1257,definition,(
% 7.22/1.36 sQ62_spl <=> (sK23_skl=pred(pv40))),
% 7.22/1.36 introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition])).
% 7.22/1.36 fof(f1258,plain,(
% 7.22/1.36 sK23_skl=pred(pv40)|~sQ62_spl),
% 7.22/1.36 inference(component_clause,[status(thm)],[f1257])).
% 7.22/1.36 fof(f1260,definition,(
% 7.22/1.36 sQ63_spl <=> (gt(pred(pv40),sK23_skl))),
% 7.22/1.36 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 7.22/1.36 fof(f1261,plain,(
% 7.22/1.36 gt(pred(pv40),sK23_skl)|~sQ63_spl),
% 7.22/1.36 inference(component_clause,[status(thm)],[f1260])).
% 7.22/1.36 fof(f1263,plain,(
% 7.22/1.36 sQ62_spl|sQ63_spl|~sQ17_spl),
% 7.22/1.36 inference(split_clause,[status(thm)],[f1250,f1257,f1260,f485])).
% 7.22/1.36 fof(f1531,plain,(
% 7.22/1.36 leq(sK23_skl,pred(pv40))|~sQ63_spl),
% 7.22/1.36 inference(resolution,[status(thm)],[f1261,f112])).
% 7.22/1.36 fof(f1540,plain,(
% 7.22/1.36 ~a_select2(mu_init,pv40)=init|~sQ16_spl),
% 7.22/1.36 inference(backward_demodulation,[status(thm)],[f483,f267])).
% 7.22/1.36 fof(f1543,plain,(
% 7.22/1.36 ~init=init|~sQ16_spl),
% 7.22/1.36 inference(forward_demodulation,[status(thm)],[f253,f1540])).
% 7.22/1.36 fof(f1544,plain,(
% 7.22/1.36 $false|~sQ16_spl),
% 7.22/1.36 inference(trivial_equality_resolution,[status(thm)],[f1543])).
% 7.22/1.36 fof(f1545,plain,(
% 7.22/1.36 ~sQ16_spl),
% 7.22/1.36 inference(contradiction_clause,[status(thm)],[f1544])).
% 7.22/1.36 fof(f1705,plain,(
% 7.22/1.36 ![X0]: (~leq(n0,X0)|~leq(X0,sK23_skl)|a_select2(mu_init,X0)=init|~sQ62_spl)),
% 7.22/1.36 inference(backward_demodulation,[status(thm)],[f1258,f259])).
% 7.22/1.36 fof(f1740,plain,(
% 7.22/1.36 leq(succ(pred(n0)),succ(pred(sK23_skl)))),
% 7.22/1.36 inference(resolution,[status(thm)],[f1171,f223])).
% 7.22/1.36 fof(f1749,plain,(
% 7.22/1.36 leq(n0,succ(pred(sK23_skl)))),
% 7.22/1.36 inference(forward_demodulation,[status(thm)],[f219,f1740])).
% 7.22/1.36 fof(f1750,plain,(
% 7.22/1.36 leq(n0,sK23_skl)),
% 7.22/1.36 inference(forward_demodulation,[status(thm)],[f219,f1749])).
% 7.22/1.36 fof(f2414,definition,(
% 7.22/1.36 sQ119_spl <=> (leq(sK23_skl,sK23_skl))),
% 7.22/1.36 introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition])).
% 7.22/1.36 fof(f2416,plain,(
% 7.22/1.36 ~leq(sK23_skl,sK23_skl)|sQ119_spl),
% 7.22/1.36 inference(component_clause,[status(thm)],[f2414])).
% 7.22/1.36 fof(f2463,definition,(
% 7.22/1.36 sQ133_spl <=> (leq(n0,sK23_skl))),
% 7.22/1.36 introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition])).
% 7.22/1.36 fof(f2465,plain,(
% 7.22/1.36 ~leq(n0,sK23_skl)|sQ133_spl),
% 7.22/1.36 inference(component_clause,[status(thm)],[f2463])).
% 7.22/1.36 fof(f2470,plain,(
% 7.22/1.36 $false|sQ119_spl),
% 7.22/1.36 inference(forward_subsumption_resolution,[status(thm)],[f2416,f99])).
% 7.22/1.36 fof(f2471,plain,(
% 7.22/1.36 sQ119_spl),
% 7.22/1.36 inference(contradiction_clause,[status(thm)],[f2470])).
% 7.22/1.36 fof(f2474,plain,(
% 7.22/1.36 $false|sQ133_spl),
% 7.22/1.36 inference(forward_subsumption_resolution,[status(thm)],[f2465,f1750])).
% 7.22/1.36 fof(f2475,plain,(
% 7.22/1.36 sQ133_spl),
% 7.22/1.36 inference(contradiction_clause,[status(thm)],[f2474])).
% 7.22/1.36 fof(f2544,plain,(
% 7.22/1.36 ~leq(sK23_skl,sK23_skl)|a_select2(mu_init,sK23_skl)=init|~sQ62_spl),
% 7.22/1.36 inference(resolution,[status(thm)],[f1705,f1750])).
% 7.22/1.36 fof(f2552,definition,(
% 7.22/1.36 sQ135_spl <=> (a_select2(mu_init,sK23_skl)=init)),
% 7.22/1.36 introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition])).
% 7.22/1.36 fof(f2553,plain,(
% 7.22/1.36 a_select2(mu_init,sK23_skl)=init|~sQ135_spl),
% 7.22/1.36 inference(component_clause,[status(thm)],[f2552])).
% 7.22/1.36 fof(f2555,plain,(
% 7.22/1.36 ~sQ119_spl|sQ135_spl|~sQ62_spl),
% 7.22/1.36 inference(split_clause,[status(thm)],[f2544,f2414,f2552,f1257])).
% 7.22/1.36 fof(f2565,plain,(
% 7.22/1.36 $false|~sQ135_spl),
% 7.22/1.36 inference(forward_subsumption_resolution,[status(thm)],[f2553,f267])).
% 7.22/1.36 fof(f2566,plain,(
% 7.22/1.36 ~sQ135_spl),
% 7.22/1.36 inference(contradiction_clause,[status(thm)],[f2565])).
% 7.22/1.36 fof(f2706,plain,(
% 7.22/1.36 ~leq(n0,sK23_skl)|a_select2(mu_init,sK23_skl)=init|~sQ63_spl),
% 7.22/1.36 inference(resolution,[status(thm)],[f259,f1531])).
% 7.22/1.36 fof(f2710,plain,(
% 7.22/1.36 ~sQ133_spl|sQ135_spl|~sQ63_spl),
% 7.22/1.36 inference(split_clause,[status(thm)],[f2706,f2463,f2552,f1260])).
% 7.22/1.36 fof(f2714,plain,(
% 7.22/1.36 $false),
% 7.22/1.36 inference(sat_refutation,[status(thm)],[f488,f1263,f1545,f2471,f2475,f2555,f2566,f2710])).
% 7.22/1.36 % SZS output end CNFRefutation for theBenchmark.p
% 7.22/1.38 % Elapsed time: 1.007280 seconds
% 7.22/1.38 % CPU time: 7.659614 seconds
% 7.22/1.38 % Total memory used: 165.806 MB
% 7.22/1.38 % Net memory used: 154.748 MB
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