%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:42:49 PM UTC 2026
% Result : Theorem 0.24s 0.99s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n009.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 02:27:27 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.24/0.99 % Refutation found
% 0.24/0.99 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.99 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.99 fof(f1,axiom,(
% 0.24/0.99 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 0.24/0.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.99 fof(f6,axiom,(
% 0.24/0.99 (! [A] :( ( epsilon_transitive(A)& epsilon_connected(A) )=> ordinal(A) ) )),
% 0.24/0.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.99 fof(f8,axiom,(
% 0.24/0.99 (! [A] :( epsilon_transitive(A)<=> (! [B] :( in(B,A)=> subset(B,A) ) )) )),
% 0.24/0.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.99 fof(f9,axiom,(
% 0.24/0.99 (! [A] :( epsilon_connected(A)<=> (! [B,C] :~ ( in(B,A)& in(C,A)& ~ in(B,C)& B != C& ~ in(C,B) ) )) )),
% 0.24/0.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.99 fof(f10,axiom,(
% 0.24/0.99 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.24/0.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.99 fof(f32,axiom,(
% 0.24/0.99 (! [A,B] :( ordinal(B)=> ( in(A,B)=> ordinal(A) ) ) )),
% 0.24/0.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.99 fof(f33,axiom,(
% 0.24/0.99 (! [A] :( ordinal(A)=> (! [B] :( ordinal(B)=> ~ ( ~ in(A,B)& A != B& ~ in(B,A) ) ) )) )),
% 0.24/0.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.99 fof(f35,conjecture,(
% 0.24/0.99 (! [A] :~ (! [B] :( in(B,A)<=> ordinal(B) ) ))),
% 0.24/0.99 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.99 fof(f36,negated_conjecture,(
% 0.24/0.99 ~((! [A] :~ (! [B] :( in(B,A)<=> ordinal(B) ) )))),
% 0.24/0.99 inference(negated_conjecture,[status(cth)],[f35])).
% 0.24/0.99 fof(f43,plain,(
% 0.24/0.99 ![A,B]: (~in(A,B)|~in(B,A))),
% 0.24/0.99 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.24/0.99 fof(f44,plain,(
% 0.24/0.99 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f43])).
% 0.24/0.99 fof(f56,plain,(
% 0.24/0.99 ![A]: ((~epsilon_transitive(A)|~epsilon_connected(A))|ordinal(A))),
% 0.24/0.99 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.24/0.99 fof(f57,plain,(
% 0.24/0.99 ![X0]: (~epsilon_transitive(X0)|~epsilon_connected(X0)|ordinal(X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f56])).
% 0.24/0.99 fof(f62,plain,(
% 0.24/0.99 ![A]: (epsilon_transitive(A)<=>(![B]: (~in(B,A)|subset(B,A))))),
% 0.24/0.99 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.24/0.99 fof(f63,plain,(
% 0.24/0.99 ![A]: ((~epsilon_transitive(A)|(![B]: (~in(B,A)|subset(B,A))))&(epsilon_transitive(A)|(?[B]: (in(B,A)&~subset(B,A)))))),
% 0.24/0.99 inference(NNF_transformation,[status(thm)],[f62])).
% 0.24/0.99 fof(f64,plain,(
% 0.24/0.99 (![A]: (~epsilon_transitive(A)|(![B]: (~in(B,A)|subset(B,A)))))&(![A]: (epsilon_transitive(A)|(?[B]: (in(B,A)&~subset(B,A)))))),
% 0.24/0.99 inference(miniscoping,[status(thm)],[f63])).
% 0.24/0.99 fof(f65,plain,(
% 0.24/0.99 (![A]: (~epsilon_transitive(A)|(![B]: (~in(B,A)|subset(B,A)))))&(![A]: (epsilon_transitive(A)|(in(sK0_skl(A),A)&~subset(sK0_skl(A),A))))),
% 0.24/0.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f64])).
% 0.24/0.99 fof(f67,plain,(
% 0.24/0.99 ![X0]: (epsilon_transitive(X0)|in(sK0_skl(X0),X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f65])).
% 0.24/0.99 fof(f68,plain,(
% 0.24/0.99 ![X0]: (epsilon_transitive(X0)|~subset(sK0_skl(X0),X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f65])).
% 0.24/0.99 fof(f69,plain,(
% 0.24/0.99 ![A]: (epsilon_connected(A)<=>(![B,C]: ((((~in(B,A)|~in(C,A))|in(B,C))|B=C)|in(C,B))))),
% 0.24/0.99 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.24/0.99 fof(f70,plain,(
% 0.24/0.99 ![A]: ((~epsilon_connected(A)|(![B,C]: ((((~in(B,A)|~in(C,A))|in(B,C))|B=C)|in(C,B))))&(epsilon_connected(A)|(?[B,C]: ((((in(B,A)&in(C,A))&~in(B,C))&~B=C)&~in(C,B)))))),
% 0.24/0.99 inference(NNF_transformation,[status(thm)],[f69])).
% 0.24/0.99 fof(f71,plain,(
% 0.24/0.99 (![A]: (~epsilon_connected(A)|(![B,C]: ((((~in(B,A)|~in(C,A))|in(B,C))|B=C)|in(C,B)))))&(![A]: (epsilon_connected(A)|(?[B,C]: ((((in(B,A)&in(C,A))&~in(B,C))&~B=C)&~in(C,B)))))),
% 0.24/0.99 inference(miniscoping,[status(thm)],[f70])).
% 0.24/0.99 fof(f72,plain,(
% 0.24/0.99 (![A]: (~epsilon_connected(A)|(![B,C]: ((((~in(B,A)|~in(C,A))|in(B,C))|B=C)|in(C,B)))))&(![A]: (epsilon_connected(A)|((((in(sK1_skl(A),A)&in(sK2_skl(A),A))&~in(sK1_skl(A),sK2_skl(A)))&~sK1_skl(A)=sK2_skl(A))&~in(sK2_skl(A),sK1_skl(A)))))),
% 0.24/0.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(B,sK1_skl(A)),skolemize(C,sK2_skl(A))],[f71])).
% 0.24/0.99 fof(f74,plain,(
% 0.24/0.99 ![X0]: (epsilon_connected(X0)|in(sK1_skl(X0),X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f72])).
% 0.24/0.99 fof(f75,plain,(
% 0.24/0.99 ![X0]: (epsilon_connected(X0)|in(sK2_skl(X0),X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f72])).
% 0.24/0.99 fof(f76,plain,(
% 0.24/0.99 ![X0]: (epsilon_connected(X0)|~in(sK1_skl(X0),sK2_skl(X0)))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f72])).
% 0.24/0.99 fof(f77,plain,(
% 0.24/0.99 ![X0]: (epsilon_connected(X0)|~sK1_skl(X0)=sK2_skl(X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f72])).
% 0.24/0.99 fof(f78,plain,(
% 0.24/0.99 ![X0]: (epsilon_connected(X0)|~in(sK2_skl(X0),sK1_skl(X0)))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f72])).
% 0.24/0.99 fof(f79,plain,(
% 0.24/0.99 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.24/0.99 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.24/0.99 fof(f80,plain,(
% 0.24/0.99 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.24/0.99 inference(NNF_transformation,[status(thm)],[f79])).
% 0.24/0.99 fof(f81,plain,(
% 0.24/0.99 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.24/0.99 inference(miniscoping,[status(thm)],[f80])).
% 0.24/0.99 fof(f82,plain,(
% 0.24/0.99 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK3_skl(B,A),A)&~in(sK3_skl(B,A),B))))),
% 0.24/0.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B,A))],[f81])).
% 0.24/0.99 fof(f84,plain,(
% 0.24/0.99 ![X0,X1]: (subset(X0,X1)|in(sK3_skl(X1,X0),X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f82])).
% 0.24/0.99 fof(f85,plain,(
% 0.24/0.99 ![X0,X1]: (subset(X0,X1)|~in(sK3_skl(X1,X0),X1))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f82])).
% 0.24/0.99 fof(f160,plain,(
% 0.24/0.99 ![A,B]: (~ordinal(B)|(~in(A,B)|ordinal(A)))),
% 0.24/0.99 inference(pre_NNF_transformation,[status(thm)],[f32])).
% 0.24/0.99 fof(f161,plain,(
% 0.24/0.99 ![B]: (~ordinal(B)|(![A]: (~in(A,B)|ordinal(A))))),
% 0.24/0.99 inference(miniscoping,[status(thm)],[f160])).
% 0.24/0.99 fof(f162,plain,(
% 0.24/0.99 ![X0,X1]: (~ordinal(X0)|~in(X1,X0)|ordinal(X1))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f161])).
% 0.24/0.99 fof(f163,plain,(
% 0.24/0.99 ![A]: (~ordinal(A)|(![B]: (~ordinal(B)|((in(A,B)|A=B)|in(B,A)))))),
% 0.24/0.99 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 0.24/0.99 fof(f164,plain,(
% 0.24/0.99 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|in(X0,X1)|X0=X1|in(X1,X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f163])).
% 0.24/0.99 fof(f167,plain,(
% 0.24/0.99 (?[A]: ![B]: (in(B,A)<=>ordinal(B)))),
% 0.24/0.99 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 0.24/0.99 fof(f168,plain,(
% 0.24/0.99 ?[A]: ![B]: ((~in(B,A)|ordinal(B))&(in(B,A)|~ordinal(B)))),
% 0.24/0.99 inference(NNF_transformation,[status(thm)],[f167])).
% 0.24/0.99 fof(f169,plain,(
% 0.24/0.99 ?[A]: ((![B]: (~in(B,A)|ordinal(B)))&(![B]: (in(B,A)|~ordinal(B))))),
% 0.24/0.99 inference(miniscoping,[status(thm)],[f168])).
% 0.24/0.99 fof(f170,plain,(
% 0.24/0.99 ((![B]: (~in(B,sK18_skl)|ordinal(B)))&(![B]: (in(B,sK18_skl)|~ordinal(B))))),
% 0.24/0.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(A,sK18_skl)],[f169])).
% 0.24/0.99 fof(f171,plain,(
% 0.24/0.99 ![X0]: (~in(X0,sK18_skl)|ordinal(X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f170])).
% 0.24/0.99 fof(f172,plain,(
% 0.24/0.99 ![X0]: (in(X0,sK18_skl)|~ordinal(X0))),
% 0.24/0.99 inference(cnf_transformation,[status(thm)],[f170])).
% 0.24/0.99 fof(f193,plain,(
% 0.24/0.99 epsilon_transitive(sK18_skl)|ordinal(sK0_skl(sK18_skl))),
% 0.24/0.99 inference(resolution,[status(thm)],[f67,f171])).
% 0.24/0.99 fof(f196,plain,(
% 0.24/0.99 ![X0]: (epsilon_transitive(sK18_skl)|~in(X0,sK0_skl(sK18_skl))|ordinal(X0))),
% 0.24/0.99 inference(resolution,[status(thm)],[f193,f162])).
% 0.24/0.99 fof(f269,plain,(
% 0.24/0.99 epsilon_connected(sK18_skl)|ordinal(sK1_skl(sK18_skl))),
% 0.24/0.99 inference(resolution,[status(thm)],[f74,f171])).
% 0.24/0.99 fof(f275,plain,(
% 0.24/0.99 epsilon_connected(sK18_skl)|ordinal(sK2_skl(sK18_skl))),
% 0.24/0.99 inference(resolution,[status(thm)],[f75,f171])).
% 0.24/0.99 fof(f281,plain,(
% 0.24/0.99 ![X0]: (epsilon_connected(sK18_skl)|~ordinal(X0)|in(X0,sK1_skl(sK18_skl))|X0=sK1_skl(sK18_skl)|in(sK1_skl(sK18_skl),X0))),
% 0.24/0.99 inference(resolution,[status(thm)],[f269,f164])).
% 0.24/0.99 fof(f294,plain,(
% 0.24/0.99 ![X0]: (subset(sK0_skl(sK18_skl),X0)|epsilon_transitive(sK18_skl)|ordinal(sK3_skl(X0,sK0_skl(sK18_skl))))),
% 0.24/0.99 inference(resolution,[status(thm)],[f84,f196])).
% 0.24/0.99 fof(f351,plain,(
% 0.24/0.99 epsilon_connected(sK18_skl)|in(sK2_skl(sK18_skl),sK1_skl(sK18_skl))|sK2_skl(sK18_skl)=sK1_skl(sK18_skl)|in(sK1_skl(sK18_skl),sK2_skl(sK18_skl))|epsilon_connected(sK18_skl)),
% 0.24/1.00 inference(resolution,[status(thm)],[f281,f275])).
% 0.24/1.00 fof(f359,plain,(
% 0.24/1.00 epsilon_connected(sK18_skl)|in(sK2_skl(sK18_skl),sK1_skl(sK18_skl))|sK2_skl(sK18_skl)=sK1_skl(sK18_skl)|in(sK1_skl(sK18_skl),sK2_skl(sK18_skl))),
% 0.24/1.00 inference(duplicate_literals_removal,[status(thm)],[f351])).
% 0.24/1.00 fof(f360,plain,(
% 0.24/1.00 epsilon_connected(sK18_skl)|sK2_skl(sK18_skl)=sK1_skl(sK18_skl)|in(sK1_skl(sK18_skl),sK2_skl(sK18_skl))),
% 0.24/1.00 inference(forward_subsumption_resolution,[status(thm)],[f359,f78])).
% 0.24/1.00 fof(f422,plain,(
% 0.24/1.00 ![X0]: (subset(sK0_skl(sK18_skl),X0)|epsilon_transitive(sK18_skl)|in(sK3_skl(X0,sK0_skl(sK18_skl)),sK18_skl))),
% 0.24/1.00 inference(resolution,[status(thm)],[f294,f172])).
% 0.24/1.00 fof(f762,plain,(
% 0.24/1.00 epsilon_connected(sK18_skl)|epsilon_connected(sK18_skl)|sK2_skl(sK18_skl)=sK1_skl(sK18_skl)),
% 0.24/1.00 inference(resolution,[status(thm)],[f76,f360])).
% 0.24/1.00 fof(f763,plain,(
% 0.24/1.00 epsilon_connected(sK18_skl)|sK2_skl(sK18_skl)=sK1_skl(sK18_skl)),
% 0.24/1.00 inference(duplicate_literals_removal,[status(thm)],[f762])).
% 0.24/1.00 fof(f764,plain,(
% 0.24/1.00 epsilon_connected(sK18_skl)),
% 0.24/1.00 inference(forward_subsumption_resolution,[status(thm)],[f763,f77])).
% 0.24/1.00 fof(f1125,plain,(
% 0.24/1.00 ~epsilon_transitive(sK18_skl)|ordinal(sK18_skl)),
% 0.24/1.00 inference(resolution,[status(thm)],[f764,f57])).
% 0.24/1.00 fof(f1137,plain,(
% 0.24/1.00 subset(sK0_skl(sK18_skl),sK18_skl)|subset(sK0_skl(sK18_skl),sK18_skl)|epsilon_transitive(sK18_skl)),
% 0.24/1.00 inference(resolution,[status(thm)],[f85,f422])).
% 0.24/1.00 fof(f1153,plain,(
% 0.24/1.00 subset(sK0_skl(sK18_skl),sK18_skl)|epsilon_transitive(sK18_skl)),
% 0.24/1.00 inference(duplicate_literals_removal,[status(thm)],[f1137])).
% 0.24/1.00 fof(f1154,plain,(
% 0.24/1.00 ordinal(sK18_skl)),
% 0.24/1.00 inference(backward_subsumption_resolution,[status(thm)],[f1125,f1155])).
% 0.24/1.00 fof(f1155,plain,(
% 0.24/1.00 epsilon_transitive(sK18_skl)),
% 0.24/1.00 inference(forward_subsumption_resolution,[status(thm)],[f1153,f68])).
% 0.24/1.00 fof(f1682,plain,(
% 0.24/1.00 in(sK18_skl,sK18_skl)),
% 0.24/1.00 inference(resolution,[status(thm)],[f1154,f172])).
% 0.24/1.00 fof(f2211,plain,(
% 0.24/1.00 ~in(sK18_skl,sK18_skl)),
% 0.24/1.00 inference(resolution,[status(thm)],[f1682,f44])).
% 0.24/1.00 fof(f2212,plain,(
% 0.24/1.00 $false),
% 0.24/1.00 inference(forward_subsumption_resolution,[status(thm)],[f2211,f1682])).
% 0.24/1.00 % SZS output end CNFRefutation for theBenchmark.p
% 0.31/1.05 % Elapsed time: 0.585755 seconds
% 0.31/1.05 % CPU time: 3.933282 seconds
% 0.31/1.05 % Total memory used: 114.009 MB
% 0.31/1.05 % Net memory used: 108.227 MB
%------------------------------------------------------------------------------