%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM409+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 0.17s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM409+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
% 0.17/0.43 % Computer : n001.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 02:32:43 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.48 fof(f11,axiom,(
% 0.17/0.48 (! [A] :( ( relation(A)& function(A) )=> ( transfinite_sequence(A)<=> ordinal(relation_dom(A)) ) ) )),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f12,axiom,(
% 0.17/0.48 (! [A,B] :( ( relation(B)& function(B)& transfinite_sequence(B) )=> ( transfinite_sequence_of(B,A)<=> subset(relation_rng(B),A) ) ) )),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f16,axiom,(
% 0.17/0.48 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f19,axiom,(
% 0.17/0.48 ( relation(empty_set)& relation_empty_yielding(empty_set)& function(empty_set)& one_to_one(empty_set)& empty(empty_set)& epsilon_transitive(empty_set)& epsilon_connected(empty_set)& ordinal(empty_set) ) ),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f24,axiom,(
% 0.17/0.48 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f25,axiom,(
% 0.17/0.48 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f43,axiom,(
% 0.17/0.48 (! [A] : subset(empty_set,A) )),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f45,conjecture,(
% 0.17/0.48 (! [A] : transfinite_sequence_of(empty_set,A) )),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f46,negated_conjecture,(
% 0.17/0.48 ~((! [A] : transfinite_sequence_of(empty_set,A) ))),
% 0.17/0.48 inference(negated_conjecture,[status(cth)],[f45])).
% 0.17/0.48 fof(f50,axiom,(
% 0.17/0.48 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.17/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f82,plain,(
% 0.17/0.48 ![A]: ((~relation(A)|~function(A))|(transfinite_sequence(A)<=>ordinal(relation_dom(A))))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.17/0.48 fof(f83,plain,(
% 0.17/0.48 ![A]: ((~relation(A)|~function(A))|((~transfinite_sequence(A)|ordinal(relation_dom(A)))&(transfinite_sequence(A)|~ordinal(relation_dom(A)))))),
% 0.17/0.48 inference(NNF_transformation,[status(thm)],[f82])).
% 0.17/0.48 fof(f85,plain,(
% 0.17/0.48 ![X0]: (~relation(X0)|~function(X0)|transfinite_sequence(X0)|~ordinal(relation_dom(X0)))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f83])).
% 0.17/0.48 fof(f86,plain,(
% 0.17/0.48 ![A,B]: (((~relation(B)|~function(B))|~transfinite_sequence(B))|(transfinite_sequence_of(B,A)<=>subset(relation_rng(B),A)))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.17/0.48 fof(f87,plain,(
% 0.17/0.48 ![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))))),
% 0.17/0.48 inference(NNF_transformation,[status(thm)],[f86])).
% 0.17/0.48 fof(f88,plain,(
% 0.17/0.48 ![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)))))),
% 0.17/0.48 inference(miniscoping,[status(thm)],[f87])).
% 0.17/0.48 fof(f90,plain,(
% 0.17/0.48 ![X0,X1]: (~relation(X0)|~function(X0)|~transfinite_sequence(X0)|transfinite_sequence_of(X0,X1)|~subset(relation_rng(X0),X1))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f88])).
% 0.17/0.48 fof(f100,plain,(
% 0.17/0.48 empty(empty_set)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f16])).
% 0.17/0.48 fof(f101,plain,(
% 0.17/0.48 relation(empty_set)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f16])).
% 0.17/0.48 fof(f107,plain,(
% 0.17/0.48 function(empty_set)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.48 fof(f112,plain,(
% 0.17/0.48 ordinal(empty_set)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.48 fof(f121,plain,(
% 0.17/0.48 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.17/0.48 fof(f122,plain,(
% 0.17/0.48 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f121])).
% 0.17/0.48 fof(f124,plain,(
% 0.17/0.48 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.17/0.48 fof(f125,plain,(
% 0.17/0.48 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f124])).
% 0.17/0.48 fof(f186,plain,(
% 0.17/0.48 ![X0]: (subset(empty_set,X0))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f43])).
% 0.17/0.48 fof(f191,plain,(
% 0.17/0.48 (?[A]: ~transfinite_sequence_of(empty_set,A))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 0.17/0.48 fof(f192,plain,(
% 0.17/0.48 ~transfinite_sequence_of(empty_set,sK19_skl)),
% 0.17/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(A,sK19_skl)],[f191])).
% 0.17/0.48 fof(f193,plain,(
% 0.17/0.48 ~transfinite_sequence_of(empty_set,sK19_skl)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f192])).
% 0.17/0.48 fof(f204,plain,(
% 0.17/0.48 ![A]: (~empty(A)|A=empty_set)),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 0.17/0.48 fof(f205,plain,(
% 0.17/0.48 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f204])).
% 0.17/0.48 fof(f272,plain,(
% 0.17/0.48 empty(relation_dom(empty_set))),
% 0.17/0.48 inference(resolution,[status(thm)],[f122,f100])).
% 0.17/0.48 fof(f275,plain,(
% 0.17/0.48 relation_dom(empty_set)=empty_set),
% 0.17/0.48 inference(resolution,[status(thm)],[f272,f205])).
% 0.17/0.48 fof(f281,plain,(
% 0.17/0.48 ~relation(empty_set)|~function(empty_set)|transfinite_sequence(empty_set)|~ordinal(empty_set)),
% 0.17/0.48 inference(paramodulation,[status(thm)],[f275,f85])).
% 0.17/0.48 fof(f284,plain,(
% 0.17/0.48 ~function(empty_set)|transfinite_sequence(empty_set)|~ordinal(empty_set)),
% 0.17/0.48 inference(forward_subsumption_resolution,[status(thm)],[f281,f101])).
% 0.17/0.48 fof(f298,plain,(
% 0.17/0.48 ~function(empty_set)|transfinite_sequence(empty_set)),
% 0.17/0.48 inference(resolution,[status(thm)],[f284,f112])).
% 0.17/0.48 fof(f303,plain,(
% 0.17/0.48 transfinite_sequence(empty_set)),
% 0.17/0.48 inference(forward_subsumption_resolution,[status(thm)],[f298,f107])).
% 0.17/0.48 fof(f304,plain,(
% 0.17/0.48 ![X0]: (~relation(empty_set)|~function(empty_set)|transfinite_sequence_of(empty_set,X0)|~subset(relation_rng(empty_set),X0))),
% 0.17/0.48 inference(resolution,[status(thm)],[f303,f90])).
% 0.17/0.48 fof(f306,plain,(
% 0.17/0.48 ![X0]: (~function(empty_set)|transfinite_sequence_of(empty_set,X0)|~subset(relation_rng(empty_set),X0))),
% 0.17/0.48 inference(forward_subsumption_resolution,[status(thm)],[f304,f101])).
% 0.17/0.48 fof(f307,plain,(
% 0.17/0.48 ![X0]: (transfinite_sequence_of(empty_set,X0)|~subset(relation_rng(empty_set),X0))),
% 0.17/0.48 inference(resolution,[status(thm)],[f306,f107])).
% 0.17/0.48 fof(f322,plain,(
% 0.17/0.48 empty(relation_rng(empty_set))),
% 0.17/0.48 inference(resolution,[status(thm)],[f125,f100])).
% 0.17/0.48 fof(f328,plain,(
% 0.17/0.48 relation_rng(empty_set)=empty_set),
% 0.17/0.48 inference(resolution,[status(thm)],[f322,f205])).
% 0.17/0.48 fof(f335,plain,(
% 0.17/0.48 ![X0]: (transfinite_sequence_of(empty_set,X0)|~subset(empty_set,X0))),
% 0.17/0.48 inference(backward_demodulation,[status(thm)],[f328,f307])).
% 0.17/0.48 fof(f340,plain,(
% 0.17/0.48 ![X0]: (transfinite_sequence_of(empty_set,X0))),
% 0.17/0.48 inference(forward_subsumption_resolution,[status(thm)],[f335,f186])).
% 0.17/0.48 fof(f341,plain,(
% 0.17/0.48 $false),
% 0.17/0.48 inference(backward_subsumption_resolution,[status(thm)],[f193,f340])).
% 0.17/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.50 % Elapsed time: 0.064448 seconds
% 0.17/0.50 % CPU time: 0.178624 seconds
% 0.17/0.50 % Total memory used: 72.471 MB
% 0.17/0.50 % Net memory used: 72.377 MB
%------------------------------------------------------------------------------