%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM411+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 : n001.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 01:42:50 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM411+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
% 0.08/0.35 % Computer : n001.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 02:32:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.39 fof(f8,axiom,(
% 0.08/0.39 (! [A,B] :( ( relation(B)& function(B)& transfinite_sequence(B) )=> ( transfinite_sequence_of(B,A)<=> subset(relation_rng(B),A) ) ) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f9,axiom,(
% 0.08/0.39 (! [A,B] :( transfinite_sequence_of(B,A)=> ( relation(B)& function(B)& transfinite_sequence(B) ) ) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f35,axiom,(
% 0.08/0.39 (! [A,B,C] :( ( subset(A,B)& subset(B,C) )=> subset(A,C) ) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f38,conjecture,(
% 0.08/0.39 (! [A,B] :( subset(A,B)=> (! [C] :( transfinite_sequence_of(C,A)=> transfinite_sequence_of(C,B) ) )) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f39,negated_conjecture,(
% 0.08/0.39 ~((! [A,B] :( subset(A,B)=> (! [C] :( transfinite_sequence_of(C,A)=> transfinite_sequence_of(C,B) ) )) ))),
% 0.08/0.39 inference(negated_conjecture,[status(cth)],[f38])).
% 0.08/0.39 fof(f64,plain,(
% 0.08/0.39 ![A,B]: (((~relation(B)|~function(B))|~transfinite_sequence(B))|(transfinite_sequence_of(B,A)<=>subset(relation_rng(B),A)))),
% 0.08/0.39 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.08/0.39 fof(f65,plain,(
% 0.08/0.39 ![A,B]: (((~relation(B)|~function(B))|~transfinite_sequence(B))|((~transfinite_sequence_of(B,A)|subset(relation_rng(B),A))&(transfinite_sequence_of(B,A)|~subset(relation_rng(B),A))))),
% 0.08/0.39 inference(NNF_transformation,[status(thm)],[f64])).
% 0.08/0.39 fof(f66,plain,(
% 0.08/0.39 ![B]: (((~relation(B)|~function(B))|~transfinite_sequence(B))|((![A]: (~transfinite_sequence_of(B,A)|subset(relation_rng(B),A)))&(![A]: (transfinite_sequence_of(B,A)|~subset(relation_rng(B),A)))))),
% 0.08/0.39 inference(miniscoping,[status(thm)],[f65])).
% 0.08/0.39 fof(f67,plain,(
% 0.08/0.39 ![X0,X1]: (~relation(X0)|~function(X0)|~transfinite_sequence(X0)|~transfinite_sequence_of(X0,X1)|subset(relation_rng(X0),X1))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f66])).
% 0.08/0.39 fof(f68,plain,(
% 0.08/0.39 ![X0,X1]: (~relation(X0)|~function(X0)|~transfinite_sequence(X0)|transfinite_sequence_of(X0,X1)|~subset(relation_rng(X0),X1))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f66])).
% 0.08/0.39 fof(f69,plain,(
% 0.08/0.39 ![A,B]: (~transfinite_sequence_of(B,A)|((relation(B)&function(B))&transfinite_sequence(B)))),
% 0.08/0.39 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.08/0.39 fof(f70,plain,(
% 0.08/0.39 ![B]: ((![A]: ~transfinite_sequence_of(B,A))|((relation(B)&function(B))&transfinite_sequence(B)))),
% 0.08/0.39 inference(miniscoping,[status(thm)],[f69])).
% 0.08/0.39 fof(f71,plain,(
% 0.08/0.39 ![X0,X1]: (~transfinite_sequence_of(X0,X1)|relation(X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f70])).
% 0.08/0.39 fof(f72,plain,(
% 0.08/0.39 ![X0,X1]: (~transfinite_sequence_of(X0,X1)|function(X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f70])).
% 0.08/0.39 fof(f73,plain,(
% 0.08/0.39 ![X0,X1]: (~transfinite_sequence_of(X0,X1)|transfinite_sequence(X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f70])).
% 0.08/0.39 fof(f156,plain,(
% 0.08/0.39 ![A,B,C]: ((~subset(A,B)|~subset(B,C))|subset(A,C))),
% 0.08/0.39 inference(pre_NNF_transformation,[status(thm)],[f35])).
% 0.08/0.39 fof(f157,plain,(
% 0.08/0.39 ![A,C]: ((![B]: (~subset(A,B)|~subset(B,C)))|subset(A,C))),
% 0.08/0.39 inference(miniscoping,[status(thm)],[f156])).
% 0.08/0.39 fof(f158,plain,(
% 0.08/0.39 ![X0,X1,X2]: (~subset(X0,X1)|~subset(X1,X2)|subset(X0,X2))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f157])).
% 0.08/0.39 fof(f165,plain,(
% 0.08/0.39 (?[A,B]: (subset(A,B)&(?[C]: (transfinite_sequence_of(C,A)&~transfinite_sequence_of(C,B)))))),
% 0.08/0.39 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 0.08/0.39 fof(f166,plain,(
% 0.08/0.39 (subset(sK16_skl,sK17_skl)&(transfinite_sequence_of(sK18_skl,sK16_skl)&~transfinite_sequence_of(sK18_skl,sK17_skl)))),
% 0.08/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(A,sK16_skl),skolemize(B,sK17_skl),skolemize(C,sK18_skl)],[f165])).
% 0.08/0.39 fof(f167,plain,(
% 0.08/0.39 subset(sK16_skl,sK17_skl)),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f166])).
% 0.08/0.39 fof(f168,plain,(
% 0.08/0.39 transfinite_sequence_of(sK18_skl,sK16_skl)),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f166])).
% 0.08/0.39 fof(f169,plain,(
% 0.08/0.39 ~transfinite_sequence_of(sK18_skl,sK17_skl)),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f166])).
% 0.08/0.39 fof(f185,plain,(
% 0.08/0.39 ![X0,X1]: (~function(X0)|~transfinite_sequence(X0)|~transfinite_sequence_of(X0,X1)|subset(relation_rng(X0),X1))),
% 0.08/0.39 inference(backward_subsumption_resolution,[status(thm)],[f67,f71])).
% 0.08/0.39 fof(f186,plain,(
% 0.08/0.39 ![X0,X1]: (~transfinite_sequence(X0)|~transfinite_sequence_of(X0,X1)|subset(relation_rng(X0),X1))),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f185,f72])).
% 0.08/0.39 fof(f187,plain,(
% 0.08/0.39 relation(sK18_skl)),
% 0.08/0.39 inference(resolution,[status(thm)],[f71,f168])).
% 0.08/0.39 fof(f188,plain,(
% 0.08/0.39 function(sK18_skl)),
% 0.08/0.39 inference(resolution,[status(thm)],[f72,f168])).
% 0.08/0.39 fof(f232,plain,(
% 0.08/0.39 transfinite_sequence(sK18_skl)),
% 0.08/0.39 inference(resolution,[status(thm)],[f73,f168])).
% 0.08/0.39 fof(f233,plain,(
% 0.08/0.39 ![X0]: (~relation(sK18_skl)|~function(sK18_skl)|transfinite_sequence_of(sK18_skl,X0)|~subset(relation_rng(sK18_skl),X0))),
% 0.08/0.39 inference(resolution,[status(thm)],[f232,f68])).
% 0.08/0.39 fof(f234,plain,(
% 0.08/0.39 ![X0]: (~transfinite_sequence_of(sK18_skl,X0)|subset(relation_rng(sK18_skl),X0))),
% 0.08/0.39 inference(resolution,[status(thm)],[f232,f186])).
% 0.08/0.39 fof(f235,plain,(
% 0.08/0.39 ![X0]: (~function(sK18_skl)|transfinite_sequence_of(sK18_skl,X0)|~subset(relation_rng(sK18_skl),X0))),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f233,f187])).
% 0.08/0.39 fof(f236,plain,(
% 0.08/0.39 ![X0]: (transfinite_sequence_of(sK18_skl,X0)|~subset(relation_rng(sK18_skl),X0))),
% 0.08/0.39 inference(resolution,[status(thm)],[f235,f188])).
% 0.08/0.39 fof(f238,plain,(
% 0.08/0.39 ![X0,X1]: (transfinite_sequence_of(sK18_skl,X0)|~subset(relation_rng(sK18_skl),X1)|~subset(X1,X0))),
% 0.08/0.39 inference(resolution,[status(thm)],[f236,f158])).
% 0.08/0.39 fof(f243,plain,(
% 0.08/0.39 ![X0,X1]: (transfinite_sequence_of(sK18_skl,X0)|~subset(X1,X0)|~transfinite_sequence_of(sK18_skl,X1))),
% 0.08/0.39 inference(resolution,[status(thm)],[f238,f234])).
% 0.08/0.39 fof(f247,plain,(
% 0.08/0.39 ![X0]: (transfinite_sequence_of(sK18_skl,X0)|~subset(sK16_skl,X0))),
% 0.08/0.39 inference(resolution,[status(thm)],[f243,f168])).
% 0.08/0.39 fof(f248,plain,(
% 0.08/0.39 transfinite_sequence_of(sK18_skl,sK17_skl)),
% 0.08/0.39 inference(resolution,[status(thm)],[f247,f167])).
% 0.08/0.39 fof(f251,plain,(
% 0.08/0.39 $false),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f248,f169])).
% 0.08/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.41 % Elapsed time: 0.055219 seconds
% 0.13/0.41 % CPU time: 0.109050 seconds
% 0.13/0.41 % Total memory used: 15.563 MB
% 0.13/0.41 % Net memory used: 15.551 MB
%------------------------------------------------------------------------------