TSTP Solution File: NUM409+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:29:02 EDT 2023
% Result : Theorem 0.16s 0.37s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 10:00:22 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 0.16/0.37 % Refutation found
% 0.16/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.37 fof(f6,axiom,(
% 0.16/0.37 (! [A] :( ( epsilon_transitive(A)& epsilon_connected(A) )=> ordinal(A) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f11,axiom,(
% 0.16/0.37 (! [A] :( ( relation(A)& function(A) )=> ( transfinite_sequence(A)<=> ordinal(relation_dom(A)) ) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f12,axiom,(
% 0.16/0.37 (! [A,B] :( ( relation(B)& function(B)& transfinite_sequence(B) )=> ( transfinite_sequence_of(B,A)<=> subset(relation_rng(B),A) ) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f16,axiom,(
% 0.16/0.37 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f19,axiom,(
% 0.16/0.37 ( 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) ) ),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f24,axiom,(
% 0.16/0.37 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f25,axiom,(
% 0.16/0.37 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f43,axiom,(
% 0.16/0.37 (! [A] : subset(empty_set,A) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f45,conjecture,(
% 0.16/0.37 (! [A] : transfinite_sequence_of(empty_set,A) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f46,negated_conjecture,(
% 0.16/0.37 ~((! [A] : transfinite_sequence_of(empty_set,A) ))),
% 0.16/0.37 inference(negated_conjecture,[status(cth)],[f45])).
% 0.16/0.37 fof(f50,axiom,(
% 0.16/0.37 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f66,plain,(
% 0.16/0.37 ![A]: ((~epsilon_transitive(A)|~epsilon_connected(A))|ordinal(A))),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.16/0.37 fof(f67,plain,(
% 0.16/0.37 ![X0]: (~epsilon_transitive(X0)|~epsilon_connected(X0)|ordinal(X0))),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f66])).
% 0.16/0.37 fof(f82,plain,(
% 0.16/0.37 ![A]: ((~relation(A)|~function(A))|(transfinite_sequence(A)<=>ordinal(relation_dom(A))))),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.16/0.37 fof(f83,plain,(
% 0.16/0.37 ![A]: ((~relation(A)|~function(A))|((~transfinite_sequence(A)|ordinal(relation_dom(A)))&(transfinite_sequence(A)|~ordinal(relation_dom(A)))))),
% 0.16/0.37 inference(NNF_transformation,[status(esa)],[f82])).
% 0.16/0.37 fof(f85,plain,(
% 0.16/0.37 ![X0]: (~relation(X0)|~function(X0)|transfinite_sequence(X0)|~ordinal(relation_dom(X0)))),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f83])).
% 0.16/0.37 fof(f86,plain,(
% 0.16/0.37 ![A,B]: (((~relation(B)|~function(B))|~transfinite_sequence(B))|(transfinite_sequence_of(B,A)<=>subset(relation_rng(B),A)))),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.16/0.37 fof(f87,plain,(
% 0.16/0.37 ![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))))),
% 0.16/0.37 inference(NNF_transformation,[status(esa)],[f86])).
% 0.16/0.37 fof(f88,plain,(
% 0.16/0.37 ![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)))))),
% 0.16/0.37 inference(miniscoping,[status(esa)],[f87])).
% 0.16/0.37 fof(f90,plain,(
% 0.16/0.37 ![X0,X1]: (~relation(X0)|~function(X0)|~transfinite_sequence(X0)|transfinite_sequence_of(X0,X1)|~subset(relation_rng(X0),X1))),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f88])).
% 0.16/0.37 fof(f100,plain,(
% 0.16/0.37 empty(empty_set)),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f16])).
% 0.16/0.37 fof(f101,plain,(
% 0.16/0.37 relation(empty_set)),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f16])).
% 0.16/0.37 fof(f107,plain,(
% 0.16/0.37 function(empty_set)),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f19])).
% 0.16/0.37 fof(f110,plain,(
% 0.16/0.37 epsilon_transitive(empty_set)),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f19])).
% 0.16/0.37 fof(f111,plain,(
% 0.16/0.37 epsilon_connected(empty_set)),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f19])).
% 0.16/0.37 fof(f121,plain,(
% 0.16/0.37 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f24])).
% 0.16/0.37 fof(f122,plain,(
% 0.16/0.37 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f121])).
% 0.16/0.37 fof(f124,plain,(
% 0.16/0.37 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f25])).
% 0.16/0.37 fof(f125,plain,(
% 0.16/0.37 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f124])).
% 0.16/0.37 fof(f186,plain,(
% 0.16/0.37 ![X0]: (subset(empty_set,X0))),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f43])).
% 0.16/0.37 fof(f191,plain,(
% 0.16/0.37 (?[A]: ~transfinite_sequence_of(empty_set,A))),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f46])).
% 0.16/0.37 fof(f192,plain,(
% 0.16/0.37 ~transfinite_sequence_of(empty_set,sk0_19)),
% 0.16/0.37 inference(skolemization,[status(esa)],[f191])).
% 0.16/0.37 fof(f193,plain,(
% 0.16/0.37 ~transfinite_sequence_of(empty_set,sk0_19)),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f192])).
% 0.16/0.37 fof(f204,plain,(
% 0.16/0.37 ![A]: (~empty(A)|A=empty_set)),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f50])).
% 0.16/0.37 fof(f205,plain,(
% 0.16/0.37 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f204])).
% 0.16/0.37 fof(f304,plain,(
% 0.16/0.37 spl0_14 <=> epsilon_transitive(empty_set)),
% 0.16/0.37 introduced(split_symbol_definition)).
% 0.16/0.37 fof(f306,plain,(
% 0.16/0.37 ~epsilon_transitive(empty_set)|spl0_14),
% 0.16/0.37 inference(component_clause,[status(thm)],[f304])).
% 0.16/0.37 fof(f307,plain,(
% 0.16/0.37 spl0_15 <=> ordinal(empty_set)),
% 0.16/0.37 introduced(split_symbol_definition)).
% 0.16/0.37 fof(f310,plain,(
% 0.16/0.37 ~epsilon_transitive(empty_set)|ordinal(empty_set)),
% 0.16/0.37 inference(resolution,[status(thm)],[f67,f111])).
% 0.16/0.37 fof(f311,plain,(
% 0.16/0.37 ~spl0_14|spl0_15),
% 0.16/0.37 inference(split_clause,[status(thm)],[f310,f304,f307])).
% 0.16/0.37 fof(f312,plain,(
% 0.16/0.37 $false|spl0_14),
% 0.16/0.37 inference(forward_subsumption_resolution,[status(thm)],[f306,f110])).
% 0.16/0.37 fof(f313,plain,(
% 0.16/0.37 spl0_14),
% 0.16/0.37 inference(contradiction_clause,[status(thm)],[f312])).
% 0.16/0.37 fof(f346,plain,(
% 0.16/0.37 empty(relation_dom(empty_set))),
% 0.16/0.37 inference(resolution,[status(thm)],[f122,f100])).
% 0.16/0.37 fof(f353,plain,(
% 0.16/0.37 relation_dom(empty_set)=empty_set),
% 0.16/0.37 inference(resolution,[status(thm)],[f346,f205])).
% 0.16/0.37 fof(f385,plain,(
% 0.16/0.37 empty(relation_rng(empty_set))),
% 0.16/0.37 inference(resolution,[status(thm)],[f125,f100])).
% 0.16/0.37 fof(f394,plain,(
% 0.16/0.37 relation_rng(empty_set)=empty_set),
% 0.16/0.37 inference(resolution,[status(thm)],[f385,f205])).
% 0.16/0.37 fof(f451,plain,(
% 0.16/0.37 spl0_27 <=> relation(empty_set)),
% 0.16/0.37 introduced(split_symbol_definition)).
% 0.16/0.37 fof(f453,plain,(
% 0.16/0.37 ~relation(empty_set)|spl0_27),
% 0.16/0.37 inference(component_clause,[status(thm)],[f451])).
% 0.16/0.37 fof(f477,plain,(
% 0.16/0.37 $false|spl0_27),
% 0.16/0.37 inference(forward_subsumption_resolution,[status(thm)],[f453,f101])).
% 0.16/0.37 fof(f478,plain,(
% 0.16/0.37 spl0_27),
% 0.16/0.37 inference(contradiction_clause,[status(thm)],[f477])).
% 0.16/0.37 fof(f633,plain,(
% 0.16/0.37 spl0_35 <=> function(empty_set)),
% 0.16/0.37 introduced(split_symbol_definition)).
% 0.16/0.37 fof(f635,plain,(
% 0.16/0.37 ~function(empty_set)|spl0_35),
% 0.16/0.37 inference(component_clause,[status(thm)],[f633])).
% 0.16/0.37 fof(f636,plain,(
% 0.16/0.37 spl0_36 <=> transfinite_sequence(empty_set)),
% 0.16/0.37 introduced(split_symbol_definition)).
% 0.16/0.37 fof(f639,plain,(
% 0.16/0.37 ~relation(empty_set)|~function(empty_set)|transfinite_sequence(empty_set)|~ordinal(empty_set)),
% 0.16/0.37 inference(paramodulation,[status(thm)],[f353,f85])).
% 0.16/0.37 fof(f640,plain,(
% 0.16/0.37 ~spl0_27|~spl0_35|spl0_36|~spl0_15),
% 0.16/0.37 inference(split_clause,[status(thm)],[f639,f451,f633,f636,f307])).
% 0.16/0.37 fof(f641,plain,(
% 0.16/0.37 $false|spl0_35),
% 0.16/0.37 inference(forward_subsumption_resolution,[status(thm)],[f635,f107])).
% 0.16/0.37 fof(f642,plain,(
% 0.16/0.37 spl0_35),
% 0.16/0.37 inference(contradiction_clause,[status(thm)],[f641])).
% 0.16/0.37 fof(f929,plain,(
% 0.16/0.37 spl0_60 <=> transfinite_sequence_of(empty_set,X0)|~subset(empty_set,X0)),
% 0.16/0.37 introduced(split_symbol_definition)).
% 0.16/0.37 fof(f930,plain,(
% 0.16/0.37 ![X0]: (transfinite_sequence_of(empty_set,X0)|~subset(empty_set,X0)|~spl0_60)),
% 0.16/0.37 inference(component_clause,[status(thm)],[f929])).
% 0.16/0.37 fof(f932,plain,(
% 0.16/0.37 ![X0]: (~relation(empty_set)|~function(empty_set)|~transfinite_sequence(empty_set)|transfinite_sequence_of(empty_set,X0)|~subset(empty_set,X0))),
% 0.16/0.37 inference(paramodulation,[status(thm)],[f394,f90])).
% 0.16/0.38 fof(f933,plain,(
% 0.16/0.38 ~spl0_27|~spl0_35|~spl0_36|spl0_60),
% 0.16/0.38 inference(split_clause,[status(thm)],[f932,f451,f633,f636,f929])).
% 0.16/0.38 fof(f934,plain,(
% 0.16/0.38 ![X0]: (transfinite_sequence_of(empty_set,X0)|~spl0_60)),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f930,f186])).
% 0.16/0.38 fof(f950,plain,(
% 0.16/0.38 $false|~spl0_60),
% 0.16/0.38 inference(backward_subsumption_resolution,[status(thm)],[f193,f934])).
% 0.16/0.38 fof(f951,plain,(
% 0.16/0.38 ~spl0_60),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f950])).
% 0.16/0.38 fof(f952,plain,(
% 0.16/0.38 $false),
% 0.16/0.38 inference(sat_refutation,[status(thm)],[f311,f313,f478,f640,f642,f933,f951])).
% 0.16/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.37/0.60 % Elapsed time: 0.067625 seconds
% 0.37/0.60 % CPU time: 0.168717 seconds
% 0.37/0.60 % Memory used: 24.650 MB
%------------------------------------------------------------------------------