%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM412+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 : n017.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 0.16s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM412+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
% 0.16/0.42 % Computer : n017.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 02:22:41 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.47 % Refutation found
% 0.16/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.47 fof(f8,axiom,(
% 0.16/0.47 (! [A,B] :( ( relation(B)& function(B)& transfinite_sequence(B) )=> ( transfinite_sequence_of(B,A)<=> subset(relation_rng(B),A) ) ) )),
% 0.16/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f9,axiom,(
% 0.16/0.47 (! [A,B] :( ( relation(A)& function(A)& transfinite_sequence(A)& ordinal(B) )=> transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A)) ) )),
% 0.16/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f11,axiom,(
% 0.16/0.47 (! [A,B] :( transfinite_sequence_of(B,A)=> ( relation(B)& function(B)& transfinite_sequence(B) ) ) )),
% 0.16/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f42,axiom,(
% 0.16/0.47 (! [A,B] :( subset(A,B)=> (! [C] :( transfinite_sequence_of(C,A)=> transfinite_sequence_of(C,B) ) )) )),
% 0.16/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f43,conjecture,(
% 0.16/0.47 (! [A,B] :( transfinite_sequence_of(B,A)=> (! [C] :( ordinal(C)=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) )) )),
% 0.16/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f44,negated_conjecture,(
% 0.16/0.47 ~((! [A,B] :( transfinite_sequence_of(B,A)=> (! [C] :( ordinal(C)=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) )) ))),
% 0.16/0.47 inference(negated_conjecture,[status(cth)],[f43])).
% 0.16/0.47 fof(f69,plain,(
% 0.16/0.47 ![A,B]: (((~relation(B)|~function(B))|~transfinite_sequence(B))|(transfinite_sequence_of(B,A)<=>subset(relation_rng(B),A)))),
% 0.16/0.47 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.16/0.47 fof(f70,plain,(
% 0.16/0.47 ![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))))),
% 0.16/0.47 inference(NNF_transformation,[status(thm)],[f69])).
% 0.16/0.47 fof(f71,plain,(
% 0.16/0.47 ![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)))))),
% 0.16/0.47 inference(miniscoping,[status(thm)],[f70])).
% 0.16/0.47 fof(f72,plain,(
% 0.16/0.47 ![X0,X1]: (~relation(X0)|~function(X0)|~transfinite_sequence(X0)|~transfinite_sequence_of(X0,X1)|subset(relation_rng(X0),X1))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f71])).
% 0.16/0.47 fof(f74,plain,(
% 0.16/0.47 ![A,B]: ((((~relation(A)|~function(A))|~transfinite_sequence(A))|~ordinal(B))|transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A)))),
% 0.16/0.47 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.16/0.47 fof(f75,plain,(
% 0.16/0.47 ![X0,X1]: (~relation(X0)|~function(X0)|~transfinite_sequence(X0)|~ordinal(X1)|transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f74])).
% 0.16/0.47 fof(f79,plain,(
% 0.16/0.47 ![A,B]: (~transfinite_sequence_of(B,A)|((relation(B)&function(B))&transfinite_sequence(B)))),
% 0.16/0.47 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.16/0.47 fof(f80,plain,(
% 0.16/0.47 ![B]: ((![A]: ~transfinite_sequence_of(B,A))|((relation(B)&function(B))&transfinite_sequence(B)))),
% 0.16/0.47 inference(miniscoping,[status(thm)],[f79])).
% 0.16/0.47 fof(f81,plain,(
% 0.16/0.47 ![X0,X1]: (~transfinite_sequence_of(X0,X1)|relation(X0))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f80])).
% 0.16/0.47 fof(f82,plain,(
% 0.16/0.47 ![X0,X1]: (~transfinite_sequence_of(X0,X1)|function(X0))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f80])).
% 0.16/0.47 fof(f83,plain,(
% 0.16/0.47 ![X0,X1]: (~transfinite_sequence_of(X0,X1)|transfinite_sequence(X0))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f80])).
% 0.16/0.47 fof(f182,plain,(
% 0.16/0.47 ![A,B]: (~subset(A,B)|(![C]: (~transfinite_sequence_of(C,A)|transfinite_sequence_of(C,B))))),
% 0.16/0.47 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.16/0.47 fof(f183,plain,(
% 0.16/0.47 ![X0,X1,X2]: (~subset(X0,X1)|~transfinite_sequence_of(X2,X0)|transfinite_sequence_of(X2,X1))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f182])).
% 0.16/0.47 fof(f184,plain,(
% 0.16/0.47 (?[A,B]: (transfinite_sequence_of(B,A)&(?[C]: (ordinal(C)&~transfinite_sequence_of(tseq_dom_restriction(B,C),A)))))),
% 0.16/0.47 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 0.16/0.47 fof(f185,plain,(
% 0.16/0.47 (transfinite_sequence_of(sK17_skl,sK16_skl)&(ordinal(sK18_skl)&~transfinite_sequence_of(tseq_dom_restriction(sK17_skl,sK18_skl),sK16_skl)))),
% 0.16/0.48 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)],[f184])).
% 0.16/0.48 fof(f186,plain,(
% 0.16/0.48 transfinite_sequence_of(sK17_skl,sK16_skl)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f185])).
% 0.16/0.48 fof(f187,plain,(
% 0.16/0.48 ordinal(sK18_skl)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f185])).
% 0.16/0.48 fof(f188,plain,(
% 0.16/0.48 ~transfinite_sequence_of(tseq_dom_restriction(sK17_skl,sK18_skl),sK16_skl)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f185])).
% 0.16/0.48 fof(f203,plain,(
% 0.16/0.48 relation(sK17_skl)),
% 0.16/0.48 inference(resolution,[status(thm)],[f81,f186])).
% 0.16/0.48 fof(f204,plain,(
% 0.16/0.48 function(sK17_skl)),
% 0.16/0.48 inference(resolution,[status(thm)],[f82,f186])).
% 0.16/0.48 fof(f218,plain,(
% 0.16/0.48 ![X0,X1]: (~function(X0)|~transfinite_sequence(X0)|~transfinite_sequence_of(X0,X1)|subset(relation_rng(X0),X1))),
% 0.16/0.48 inference(forward_subsumption_resolution,[status(thm)],[f72,f81])).
% 0.16/0.48 fof(f219,plain,(
% 0.16/0.48 ~function(sK17_skl)|~transfinite_sequence(sK17_skl)|subset(relation_rng(sK17_skl),sK16_skl)),
% 0.16/0.48 inference(resolution,[status(thm)],[f218,f186])).
% 0.16/0.48 fof(f220,plain,(
% 0.16/0.48 ~transfinite_sequence(sK17_skl)|subset(relation_rng(sK17_skl),sK16_skl)),
% 0.16/0.48 inference(forward_subsumption_resolution,[status(thm)],[f219,f204])).
% 0.16/0.48 fof(f224,plain,(
% 0.16/0.48 transfinite_sequence(sK17_skl)),
% 0.16/0.48 inference(resolution,[status(thm)],[f83,f186])).
% 0.16/0.48 fof(f230,plain,(
% 0.16/0.48 ![X0]: (~relation(sK17_skl)|~function(sK17_skl)|~ordinal(X0)|transfinite_sequence_of(tseq_dom_restriction(sK17_skl,X0),relation_rng(sK17_skl)))),
% 0.16/0.48 inference(resolution,[status(thm)],[f224,f75])).
% 0.16/0.48 fof(f232,plain,(
% 0.16/0.48 ![X0]: (~function(sK17_skl)|~ordinal(X0)|transfinite_sequence_of(tseq_dom_restriction(sK17_skl,X0),relation_rng(sK17_skl)))),
% 0.16/0.48 inference(forward_subsumption_resolution,[status(thm)],[f230,f203])).
% 0.16/0.48 fof(f233,plain,(
% 0.16/0.48 subset(relation_rng(sK17_skl),sK16_skl)),
% 0.16/0.48 inference(forward_subsumption_resolution,[status(thm)],[f220,f224])).
% 0.16/0.48 fof(f244,plain,(
% 0.16/0.48 ![X0]: (~ordinal(X0)|transfinite_sequence_of(tseq_dom_restriction(sK17_skl,X0),relation_rng(sK17_skl)))),
% 0.16/0.48 inference(forward_subsumption_resolution,[status(thm)],[f232,f204])).
% 0.16/0.48 fof(f246,plain,(
% 0.16/0.48 transfinite_sequence_of(tseq_dom_restriction(sK17_skl,sK18_skl),relation_rng(sK17_skl))),
% 0.16/0.48 inference(resolution,[status(thm)],[f244,f187])).
% 0.16/0.48 fof(f507,plain,(
% 0.16/0.48 ![X0]: (~transfinite_sequence_of(X0,relation_rng(sK17_skl))|transfinite_sequence_of(X0,sK16_skl))),
% 0.16/0.48 inference(resolution,[status(thm)],[f183,f233])).
% 0.16/0.48 fof(f546,plain,(
% 0.16/0.48 transfinite_sequence_of(tseq_dom_restriction(sK17_skl,sK18_skl),sK16_skl)),
% 0.16/0.48 inference(resolution,[status(thm)],[f507,f246])).
% 0.16/0.48 fof(f549,plain,(
% 0.16/0.48 $false),
% 0.16/0.48 inference(forward_subsumption_resolution,[status(thm)],[f546,f188])).
% 0.16/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.51 % Elapsed time: 0.077909 seconds
% 0.16/0.51 % CPU time: 0.230436 seconds
% 0.16/0.51 % Total memory used: 83.654 MB
% 0.16/0.51 % Net memory used: 83.587 MB
%------------------------------------------------------------------------------