%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM403+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 : n008.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 69.85s 9.35s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM403+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 02:27:54 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 69.85/9.35 % Refutation found
% 69.85/9.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 69.85/9.35 % SZS output start CNFRefutation for theBenchmark
% 69.85/9.35 fof(f11,axiom,(
% 69.85/9.35 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 69.85/9.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 69.85/9.35 fof(f12,axiom,(
% 69.85/9.35 (! [A,B] :( B = union(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(C,D)& in(D,A) ) )) )) )),
% 69.85/9.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 69.85/9.35 fof(f20,axiom,(
% 69.85/9.35 (! [A] :( ordinal(A)=> ( ~ empty(succ(A))& epsilon_transitive(succ(A))& epsilon_connected(succ(A))& ordinal(succ(A)) ) ) )),
% 69.85/9.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 69.85/9.35 fof(f38,axiom,(
% 69.85/9.35 (! [A,B] :( ( ordinal(A)& ordinal(B) )=> ( ordinal_subset(A,B)<=> subset(A,B) ) ) )),
% 69.85/9.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 69.85/9.35 fof(f45,axiom,(
% 69.85/9.35 (! [A] :( ordinal(A)=> (! [B] :( ordinal(B)=> ( in(A,succ(B))<=> ordinal_subset(A,B) ) ) )) )),
% 69.85/9.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 69.85/9.35 fof(f46,axiom,(
% 69.85/9.35 (! [A] :( (! [B] :( in(B,A)=> ordinal(B) ))=> ordinal(union(A)) ) )),
% 69.85/9.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 69.85/9.35 fof(f47,conjecture,(
% 69.85/9.35 (! [A] :~ ( (! [B] :( in(B,A)=> ordinal(B) ))& (! [B] :( ordinal(B)=> ~ subset(A,B) ) )) )),
% 69.85/9.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 69.85/9.35 fof(f48,negated_conjecture,(
% 69.85/9.35 ~((! [A] :~ ( (! [B] :( in(B,A)=> ordinal(B) ))& (! [B] :( ordinal(B)=> ~ subset(A,B) ) )) ))),
% 69.85/9.35 inference(negated_conjecture,[status(cth)],[f47])).
% 69.85/9.35 fof(f78,plain,(
% 69.85/9.35 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 69.85/9.35 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 69.85/9.35 fof(f79,plain,(
% 69.85/9.35 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 69.85/9.35 inference(NNF_transformation,[status(thm)],[f78])).
% 69.85/9.35 fof(f80,plain,(
% 69.85/9.35 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 69.85/9.35 inference(miniscoping,[status(thm)],[f79])).
% 69.85/9.35 fof(f81,plain,(
% 69.85/9.35 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK0_skl(B,A),A)&~in(sK0_skl(B,A),B))))),
% 69.85/9.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f80])).
% 69.85/9.35 fof(f83,plain,(
% 69.85/9.35 ![X0,X1]: (subset(X0,X1)|in(sK0_skl(X1,X0),X0))),
% 69.85/9.35 inference(cnf_transformation,[status(thm)],[f81])).
% 69.85/9.35 fof(f84,plain,(
% 69.85/9.35 ![X0,X1]: (subset(X0,X1)|~in(sK0_skl(X1,X0),X1))),
% 69.85/9.35 inference(cnf_transformation,[status(thm)],[f81])).
% 69.85/9.35 fof(f85,plain,(
% 69.85/9.35 ![A,B]: ((~B=union(A)|(![C]: ((~in(C,B)|(?[D]: (in(C,D)&in(D,A))))&(in(C,B)|(![D]: (~in(C,D)|~in(D,A)))))))&(B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 69.85/9.35 inference(NNF_transformation,[status(thm)],[f12])).
% 69.85/9.35 fof(f86,plain,(
% 69.85/9.35 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(?[D]: (in(C,D)&in(D,A)))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 69.85/9.35 inference(miniscoping,[status(thm)],[f85])).
% 69.85/9.35 fof(f87,plain,(
% 69.85/9.35 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(in(C,sK1_skl(C,B,A))&in(sK1_skl(C,B,A),A))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|((~in(sK2_skl(B,A),B)|(![D]: (~in(sK2_skl(B,A),D)|~in(D,A))))&(in(sK2_skl(B,A),B)|(in(sK2_skl(B,A),sK3_skl(B,A))&in(sK3_skl(B,A),A))))))),
% 69.85/9.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f86])).
% 69.85/9.35 fof(f90,plain,(
% 69.85/9.35 ![X0,X1,X2,X3]: (~X0=union(X1)|in(X2,X0)|~in(X2,X3)|~in(X3,X1))),
% 69.85/9.35 inference(cnf_transformation,[status(thm)],[f87])).
% 69.85/9.35 fof(f114,plain,(
% 69.85/9.35 ![A]: (~ordinal(A)|(((~empty(succ(A))&epsilon_transitive(succ(A)))&epsilon_connected(succ(A)))&ordinal(succ(A))))),
% 69.85/9.35 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 69.85/9.35 fof(f118,plain,(
% 69.85/9.35 ![X0]: (~ordinal(X0)|ordinal(succ(X0)))),
% 69.85/9.35 inference(cnf_transformation,[status(thm)],[f114])).
% 69.85/9.35 fof(f179,plain,(
% 69.85/9.35 ![A,B]: ((~ordinal(A)|~ordinal(B))|(ordinal_subset(A,B)<=>subset(A,B)))),
% 69.85/9.35 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 69.85/9.36 fof(f180,plain,(
% 69.85/9.36 ![A,B]: ((~ordinal(A)|~ordinal(B))|((~ordinal_subset(A,B)|subset(A,B))&(ordinal_subset(A,B)|~subset(A,B))))),
% 69.85/9.36 inference(NNF_transformation,[status(thm)],[f179])).
% 69.85/9.36 fof(f182,plain,(
% 69.85/9.36 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|ordinal_subset(X0,X1)|~subset(X0,X1))),
% 69.85/9.36 inference(cnf_transformation,[status(thm)],[f180])).
% 69.85/9.36 fof(f195,plain,(
% 69.85/9.36 ![A]: (~ordinal(A)|(![B]: (~ordinal(B)|(in(A,succ(B))<=>ordinal_subset(A,B)))))),
% 69.85/9.36 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 69.85/9.36 fof(f196,plain,(
% 69.85/9.36 ![A]: (~ordinal(A)|(![B]: (~ordinal(B)|((~in(A,succ(B))|ordinal_subset(A,B))&(in(A,succ(B))|~ordinal_subset(A,B))))))),
% 69.85/9.36 inference(NNF_transformation,[status(thm)],[f195])).
% 69.85/9.36 fof(f198,plain,(
% 69.85/9.36 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|in(X0,succ(X1))|~ordinal_subset(X0,X1))),
% 69.85/9.36 inference(cnf_transformation,[status(thm)],[f196])).
% 69.85/9.36 fof(f199,plain,(
% 69.85/9.36 ![A]: ((?[B]: (in(B,A)&~ordinal(B)))|ordinal(union(A)))),
% 69.85/9.36 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 69.85/9.36 fof(f200,plain,(
% 69.85/9.36 ![A]: ((in(sK18_skl(A),A)&~ordinal(sK18_skl(A)))|ordinal(union(A)))),
% 69.85/9.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(B,sK18_skl(A))],[f199])).
% 69.85/9.36 fof(f201,plain,(
% 69.85/9.36 ![X0]: (in(sK18_skl(X0),X0)|ordinal(union(X0)))),
% 69.85/9.36 inference(cnf_transformation,[status(thm)],[f200])).
% 69.85/9.36 fof(f202,plain,(
% 69.85/9.36 ![X0]: (~ordinal(sK18_skl(X0))|ordinal(union(X0)))),
% 69.85/9.36 inference(cnf_transformation,[status(thm)],[f200])).
% 69.85/9.36 fof(f203,plain,(
% 69.85/9.36 (?[A]: ((![B]: (~in(B,A)|ordinal(B)))&(![B]: (~ordinal(B)|~subset(A,B)))))),
% 69.85/9.36 inference(pre_NNF_transformation,[status(thm)],[f48])).
% 69.85/9.36 fof(f204,plain,(
% 69.85/9.36 ((![B]: (~in(B,sK19_skl)|ordinal(B)))&(![B]: (~ordinal(B)|~subset(sK19_skl,B))))),
% 69.85/9.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(A,sK19_skl)],[f203])).
% 69.85/9.36 fof(f205,plain,(
% 69.85/9.36 ![X0]: (~in(X0,sK19_skl)|ordinal(X0))),
% 69.85/9.36 inference(cnf_transformation,[status(thm)],[f204])).
% 69.85/9.36 fof(f206,plain,(
% 69.85/9.36 ![X0]: (~ordinal(X0)|~subset(sK19_skl,X0))),
% 69.85/9.36 inference(cnf_transformation,[status(thm)],[f204])).
% 69.85/9.36 fof(f228,plain,(
% 69.85/9.36 ![X0,X1,X2]: (in(X0,union(X1))|~in(X0,X2)|~in(X2,X1))),
% 69.85/9.36 inference(destructive_equality_resolution,[status(thm)],[f90])).
% 69.85/9.36 fof(f313,plain,(
% 69.85/9.36 ![X0]: (subset(sK19_skl,X0)|ordinal(sK0_skl(X0,sK19_skl)))),
% 69.85/9.36 inference(resolution,[status(thm)],[f83,f205])).
% 69.85/9.36 fof(f414,plain,(
% 69.85/9.36 ![X0,X1,X2]: (in(X0,union(X1))|~in(X0,sK0_skl(X2,X1))|subset(X1,X2))),
% 69.85/9.36 inference(resolution,[status(thm)],[f228,f83])).
% 69.85/9.36 fof(f707,plain,(
% 69.85/9.36 ![X0,X1]: (~ordinal(sK0_skl(succ(X0),X1))|~ordinal(X0)|~ordinal_subset(sK0_skl(succ(X0),X1),X0)|subset(X1,succ(X0)))),
% 69.85/9.36 inference(resolution,[status(thm)],[f198,f84])).
% 69.85/9.36 fof(f826,plain,(
% 69.85/9.36 ordinal(union(sK19_skl))|ordinal(sK18_skl(sK19_skl))),
% 69.85/9.36 inference(resolution,[status(thm)],[f201,f205])).
% 69.85/9.36 fof(f832,plain,(
% 69.85/9.36 ordinal(union(sK19_skl))),
% 69.85/9.36 inference(forward_subsumption_resolution,[status(thm)],[f826,f202])).
% 69.85/9.36 fof(f837,plain,(
% 69.85/9.36 ordinal(succ(union(sK19_skl)))),
% 69.85/9.36 inference(resolution,[status(thm)],[f832,f118])).
% 69.85/9.36 fof(f852,plain,(
% 69.85/9.36 ~subset(sK19_skl,succ(union(sK19_skl)))),
% 69.85/9.36 inference(resolution,[status(thm)],[f837,f206])).
% 69.85/9.36 fof(f1295,plain,(
% 69.85/9.36 ![X0,X1,X2]: (in(sK0_skl(X0,sK0_skl(X1,X2)),union(X2))|subset(X2,X1)|subset(sK0_skl(X1,X2),X0))),
% 69.85/9.36 inference(resolution,[status(thm)],[f414,f83])).
% 69.85/9.36 fof(f2860,plain,(
% 69.85/9.36 ![X0]: (~ordinal(X0)|~ordinal_subset(sK0_skl(succ(X0),sK19_skl),X0)|subset(sK19_skl,succ(X0))|subset(sK19_skl,succ(X0)))),
% 69.85/9.36 inference(resolution,[status(thm)],[f707,f313])).
% 69.85/9.36 fof(f2863,plain,(
% 69.85/9.36 ![X0]: (~ordinal(X0)|~ordinal_subset(sK0_skl(succ(X0),sK19_skl),X0)|subset(sK19_skl,succ(X0)))),
% 69.85/9.36 inference(duplicate_literals_removal,[status(thm)],[f2860])).
% 69.85/9.36 fof(f4893,plain,(
% 69.85/9.36 ![X0]: (~ordinal(X0)|subset(sK19_skl,succ(X0))|~ordinal(sK0_skl(succ(X0),sK19_skl))|~ordinal(X0)|~subset(sK0_skl(succ(X0),sK19_skl),X0))),
% 69.85/9.36 inference(resolution,[status(thm)],[f2863,f182])).
% 69.85/9.36 fof(f4915,plain,(
% 69.85/9.36 ![X0]: (~ordinal(X0)|subset(sK19_skl,succ(X0))|~ordinal(sK0_skl(succ(X0),sK19_skl))|~subset(sK0_skl(succ(X0),sK19_skl),X0))),
% 69.85/9.36 inference(duplicate_literals_removal,[status(thm)],[f4893])).
% 69.85/9.36 fof(f4916,plain,(
% 69.85/9.36 ![X0]: (~ordinal(X0)|subset(sK19_skl,succ(X0))|~subset(sK0_skl(succ(X0),sK19_skl),X0))),
% 69.85/9.42 inference(forward_subsumption_resolution,[status(thm)],[f4915,f313])).
% 69.85/9.42 fof(f7355,plain,(
% 69.85/9.42 ![X0,X1]: (subset(X0,X1)|subset(sK0_skl(X1,X0),union(X0))|subset(sK0_skl(X1,X0),union(X0)))),
% 69.85/9.42 inference(resolution,[status(thm)],[f1295,f84])).
% 69.85/9.42 fof(f7369,plain,(
% 69.85/9.42 ![X0,X1]: (subset(X0,X1)|subset(sK0_skl(X1,X0),union(X0)))),
% 69.85/9.42 inference(duplicate_literals_removal,[status(thm)],[f7355])).
% 69.85/9.42 fof(f9676,plain,(
% 69.85/9.42 ~ordinal(union(sK19_skl))|subset(sK19_skl,succ(union(sK19_skl)))|subset(sK19_skl,succ(union(sK19_skl)))),
% 69.85/9.42 inference(resolution,[status(thm)],[f4916,f7369])).
% 69.85/9.42 fof(f9678,plain,(
% 69.85/9.42 ~ordinal(union(sK19_skl))|subset(sK19_skl,succ(union(sK19_skl)))),
% 69.85/9.42 inference(duplicate_literals_removal,[status(thm)],[f9676])).
% 69.85/9.42 fof(f9680,plain,(
% 69.85/9.42 subset(sK19_skl,succ(union(sK19_skl)))),
% 69.85/9.42 inference(forward_subsumption_resolution,[status(thm)],[f9678,f832])).
% 69.85/9.42 fof(f9681,plain,(
% 69.85/9.42 $false),
% 69.85/9.42 inference(backward_subsumption_resolution,[status(thm)],[f852,f9680])).
% 69.85/9.42 % SZS output end CNFRefutation for theBenchmark.p
% 4.03/9.47 % Elapsed time: 9.098753 seconds
% 4.03/9.47 % CPU time: 71.479629 seconds
% 4.03/9.47 % Total memory used: 439.908 MB
% 4.03/9.47 % Net memory used: 399.325 MB
%------------------------------------------------------------------------------