%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:22:07 PM UTC 2026
% Result : Theorem 0.02s 0.59s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n003.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.02/0.56 % CPULimit : 300
% 0.02/0.56 % WCLimit : 300
% 0.02/0.56 % DateTime : Mon Sep 21 06:04:31 UTC 2026
% 0.02/0.56 % CPUTime :
% 0.02/0.57 % Drodi V4.1.1
% 0.02/0.59 % Refutation found
% 0.02/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.59 % SZS output start CNFRefutation for theBenchmark
% 0.02/0.59 fof(f2,axiom,(
% 0.02/0.59 (! [A] :( relation(A)=> ( antisymmetric(A)<=> is_antisymmetric_in(A,relation_field(A)) ) ) )),
% 0.02/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.59 fof(f3,axiom,(
% 0.02/0.59 (! [A] :( relation(A)=> ( connected(A)<=> is_connected_in(A,relation_field(A)) ) ) )),
% 0.02/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.59 fof(f4,axiom,(
% 0.02/0.59 (! [A] :( relation(A)=> ( transitive(A)<=> is_transitive_in(A,relation_field(A)) ) ) )),
% 0.02/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.59 fof(f5,axiom,(
% 0.02/0.59 (! [A] :( relation(A)=> ( well_ordering(A)<=> ( reflexive(A)& transitive(A)& antisymmetric(A)& connected(A)& well_founded_relation(A) ) ) ) )),
% 0.02/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.59 fof(f6,axiom,(
% 0.02/0.59 (! [A] :( relation(A)=> (! [B] :( well_orders(A,B)<=> ( is_reflexive_in(A,B)& is_transitive_in(A,B)& is_antisymmetric_in(A,B)& is_connected_in(A,B)& is_well_founded_in(A,B) ) ) )) )),
% 0.02/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.59 fof(f8,axiom,(
% 0.02/0.59 (! [A] :( relation(A)=> ( reflexive(A)<=> is_reflexive_in(A,relation_field(A)) ) ) )),
% 0.02/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.59 fof(f14,axiom,(
% 0.02/0.59 (! [A] :( relation(A)=> ( well_founded_relation(A)<=> is_well_founded_in(A,relation_field(A)) ) ) )),
% 0.02/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.59 fof(f15,conjecture,(
% 0.02/0.59 (! [A] :( relation(A)=> ( well_orders(A,relation_field(A))<=> well_ordering(A) ) ) )),
% 0.02/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.59 fof(f16,negated_conjecture,(
% 0.02/0.59 ~((! [A] :( relation(A)=> ( well_orders(A,relation_field(A))<=> well_ordering(A) ) ) ))),
% 0.02/0.59 inference(negated_conjecture,[status(cth)],[f15])).
% 0.02/0.59 fof(f18,plain,(
% 0.02/0.59 ![A]: (~relation(A)|(antisymmetric(A)<=>is_antisymmetric_in(A,relation_field(A))))),
% 0.02/0.59 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.02/0.59 fof(f19,plain,(
% 0.02/0.59 ![A]: (~relation(A)|((~antisymmetric(A)|is_antisymmetric_in(A,relation_field(A)))&(antisymmetric(A)|~is_antisymmetric_in(A,relation_field(A)))))),
% 0.02/0.59 inference(NNF_transformation,[status(thm)],[f18])).
% 0.02/0.59 fof(f20,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~antisymmetric(X0)|is_antisymmetric_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f19])).
% 0.02/0.59 fof(f21,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|antisymmetric(X0)|~is_antisymmetric_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f19])).
% 0.02/0.59 fof(f22,plain,(
% 0.02/0.59 ![A]: (~relation(A)|(connected(A)<=>is_connected_in(A,relation_field(A))))),
% 0.02/0.59 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.02/0.59 fof(f23,plain,(
% 0.02/0.59 ![A]: (~relation(A)|((~connected(A)|is_connected_in(A,relation_field(A)))&(connected(A)|~is_connected_in(A,relation_field(A)))))),
% 0.02/0.59 inference(NNF_transformation,[status(thm)],[f22])).
% 0.02/0.59 fof(f24,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~connected(X0)|is_connected_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f23])).
% 0.02/0.59 fof(f25,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|connected(X0)|~is_connected_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f23])).
% 0.02/0.59 fof(f26,plain,(
% 0.02/0.59 ![A]: (~relation(A)|(transitive(A)<=>is_transitive_in(A,relation_field(A))))),
% 0.02/0.59 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.02/0.59 fof(f27,plain,(
% 0.02/0.59 ![A]: (~relation(A)|((~transitive(A)|is_transitive_in(A,relation_field(A)))&(transitive(A)|~is_transitive_in(A,relation_field(A)))))),
% 0.02/0.59 inference(NNF_transformation,[status(thm)],[f26])).
% 0.02/0.59 fof(f28,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~transitive(X0)|is_transitive_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f27])).
% 0.02/0.59 fof(f29,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|transitive(X0)|~is_transitive_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f27])).
% 0.02/0.59 fof(f30,plain,(
% 0.02/0.59 ![A]: (~relation(A)|(well_ordering(A)<=>((((reflexive(A)&transitive(A))&antisymmetric(A))&connected(A))&well_founded_relation(A))))),
% 0.02/0.59 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.02/0.59 fof(f31,plain,(
% 0.02/0.59 ![A]: (~relation(A)|((~well_ordering(A)|((((reflexive(A)&transitive(A))&antisymmetric(A))&connected(A))&well_founded_relation(A)))&(well_ordering(A)|((((~reflexive(A)|~transitive(A))|~antisymmetric(A))|~connected(A))|~well_founded_relation(A)))))),
% 0.02/0.59 inference(NNF_transformation,[status(thm)],[f30])).
% 0.02/0.59 fof(f32,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~well_ordering(X0)|reflexive(X0))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f31])).
% 0.02/0.59 fof(f33,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~well_ordering(X0)|transitive(X0))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f31])).
% 0.02/0.59 fof(f34,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~well_ordering(X0)|antisymmetric(X0))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f31])).
% 0.02/0.59 fof(f35,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~well_ordering(X0)|connected(X0))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f31])).
% 0.02/0.59 fof(f36,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~well_ordering(X0)|well_founded_relation(X0))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f31])).
% 0.02/0.59 fof(f37,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|well_ordering(X0)|~reflexive(X0)|~transitive(X0)|~antisymmetric(X0)|~connected(X0)|~well_founded_relation(X0))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f31])).
% 0.02/0.59 fof(f38,plain,(
% 0.02/0.59 ![A]: (~relation(A)|(![B]: (well_orders(A,B)<=>((((is_reflexive_in(A,B)&is_transitive_in(A,B))&is_antisymmetric_in(A,B))&is_connected_in(A,B))&is_well_founded_in(A,B)))))),
% 0.02/0.59 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.02/0.59 fof(f39,plain,(
% 0.02/0.59 ![A]: (~relation(A)|(![B]: ((~well_orders(A,B)|((((is_reflexive_in(A,B)&is_transitive_in(A,B))&is_antisymmetric_in(A,B))&is_connected_in(A,B))&is_well_founded_in(A,B)))&(well_orders(A,B)|((((~is_reflexive_in(A,B)|~is_transitive_in(A,B))|~is_antisymmetric_in(A,B))|~is_connected_in(A,B))|~is_well_founded_in(A,B))))))),
% 0.02/0.59 inference(NNF_transformation,[status(thm)],[f38])).
% 0.02/0.59 fof(f40,plain,(
% 0.02/0.59 ![A]: (~relation(A)|((![B]: (~well_orders(A,B)|((((is_reflexive_in(A,B)&is_transitive_in(A,B))&is_antisymmetric_in(A,B))&is_connected_in(A,B))&is_well_founded_in(A,B))))&(![B]: (well_orders(A,B)|((((~is_reflexive_in(A,B)|~is_transitive_in(A,B))|~is_antisymmetric_in(A,B))|~is_connected_in(A,B))|~is_well_founded_in(A,B))))))),
% 0.02/0.59 inference(miniscoping,[status(thm)],[f39])).
% 0.02/0.59 fof(f41,plain,(
% 0.02/0.59 ![X0,X1]: (~relation(X0)|~well_orders(X0,X1)|is_reflexive_in(X0,X1))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f40])).
% 0.02/0.59 fof(f42,plain,(
% 0.02/0.59 ![X0,X1]: (~relation(X0)|~well_orders(X0,X1)|is_transitive_in(X0,X1))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f40])).
% 0.02/0.59 fof(f43,plain,(
% 0.02/0.59 ![X0,X1]: (~relation(X0)|~well_orders(X0,X1)|is_antisymmetric_in(X0,X1))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f40])).
% 0.02/0.59 fof(f44,plain,(
% 0.02/0.59 ![X0,X1]: (~relation(X0)|~well_orders(X0,X1)|is_connected_in(X0,X1))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f40])).
% 0.02/0.59 fof(f45,plain,(
% 0.02/0.59 ![X0,X1]: (~relation(X0)|~well_orders(X0,X1)|is_well_founded_in(X0,X1))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f40])).
% 0.02/0.59 fof(f46,plain,(
% 0.02/0.59 ![X0,X1]: (~relation(X0)|well_orders(X0,X1)|~is_reflexive_in(X0,X1)|~is_transitive_in(X0,X1)|~is_antisymmetric_in(X0,X1)|~is_connected_in(X0,X1)|~is_well_founded_in(X0,X1))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f40])).
% 0.02/0.59 fof(f49,plain,(
% 0.02/0.59 ![A]: (~relation(A)|(reflexive(A)<=>is_reflexive_in(A,relation_field(A))))),
% 0.02/0.59 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.02/0.59 fof(f50,plain,(
% 0.02/0.59 ![A]: (~relation(A)|((~reflexive(A)|is_reflexive_in(A,relation_field(A)))&(reflexive(A)|~is_reflexive_in(A,relation_field(A)))))),
% 0.02/0.59 inference(NNF_transformation,[status(thm)],[f49])).
% 0.02/0.59 fof(f51,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~reflexive(X0)|is_reflexive_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f50])).
% 0.02/0.59 fof(f52,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|reflexive(X0)|~is_reflexive_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f50])).
% 0.02/0.59 fof(f55,plain,(
% 0.02/0.59 ![A]: (~relation(A)|(well_founded_relation(A)<=>is_well_founded_in(A,relation_field(A))))),
% 0.02/0.59 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.02/0.59 fof(f56,plain,(
% 0.02/0.59 ![A]: (~relation(A)|((~well_founded_relation(A)|is_well_founded_in(A,relation_field(A)))&(well_founded_relation(A)|~is_well_founded_in(A,relation_field(A)))))),
% 0.02/0.59 inference(NNF_transformation,[status(thm)],[f55])).
% 0.02/0.59 fof(f57,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|~well_founded_relation(X0)|is_well_founded_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f56])).
% 0.02/0.59 fof(f58,plain,(
% 0.02/0.59 ![X0]: (~relation(X0)|well_founded_relation(X0)|~is_well_founded_in(X0,relation_field(X0)))),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f56])).
% 0.02/0.59 fof(f59,plain,(
% 0.02/0.59 (?[A]: (relation(A)&(well_orders(A,relation_field(A))<~>well_ordering(A))))),
% 0.02/0.59 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.02/0.59 fof(f60,plain,(
% 0.02/0.59 ?[A]: (relation(A)&((well_orders(A,relation_field(A))|well_ordering(A))&(~well_orders(A,relation_field(A))|~well_ordering(A))))),
% 0.02/0.59 inference(NNF_transformation,[status(thm)],[f59])).
% 0.02/0.59 fof(f61,plain,(
% 0.02/0.59 (relation(sK0_skl)&((well_orders(sK0_skl,relation_field(sK0_skl))|well_ordering(sK0_skl))&(~well_orders(sK0_skl,relation_field(sK0_skl))|~well_ordering(sK0_skl))))),
% 0.02/0.59 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f60])).
% 0.02/0.59 fof(f62,plain,(
% 0.02/0.59 relation(sK0_skl)),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f61])).
% 0.02/0.59 fof(f63,plain,(
% 0.02/0.59 well_orders(sK0_skl,relation_field(sK0_skl))|well_ordering(sK0_skl)),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f61])).
% 0.02/0.59 fof(f64,plain,(
% 0.02/0.59 ~well_orders(sK0_skl,relation_field(sK0_skl))|~well_ordering(sK0_skl)),
% 0.02/0.59 inference(cnf_transformation,[status(thm)],[f61])).
% 0.02/0.59 fof(f65,definition,(
% 0.02/0.59 sQ0_spl <=> (well_orders(sK0_skl,relation_field(sK0_skl)))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f66,plain,(
% 0.02/0.59 well_orders(sK0_skl,relation_field(sK0_skl))|~sQ0_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f65])).
% 0.02/0.59 fof(f68,definition,(
% 0.02/0.59 sQ1_spl <=> (well_ordering(sK0_skl))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f69,plain,(
% 0.02/0.59 well_ordering(sK0_skl)|~sQ1_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f68])).
% 0.02/0.59 fof(f71,plain,(
% 0.02/0.59 sQ0_spl|sQ1_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f63,f65,f68])).
% 0.02/0.59 fof(f72,plain,(
% 0.02/0.59 ~sQ0_spl|~sQ1_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f64,f65,f68])).
% 0.02/0.59 fof(f79,plain,(
% 0.02/0.59 ~relation(sK0_skl)|reflexive(sK0_skl)|~sQ1_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f32,f69])).
% 0.02/0.59 fof(f80,definition,(
% 0.02/0.59 sQ2_spl <=> (relation(sK0_skl))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f82,plain,(
% 0.02/0.59 ~relation(sK0_skl)|sQ2_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f80])).
% 0.02/0.59 fof(f83,definition,(
% 0.02/0.59 sQ3_spl <=> (reflexive(sK0_skl))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f84,plain,(
% 0.02/0.59 reflexive(sK0_skl)|~sQ3_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f83])).
% 0.02/0.59 fof(f86,plain,(
% 0.02/0.59 ~sQ2_spl|sQ3_spl|~sQ1_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f79,f80,f83,f68])).
% 0.02/0.59 fof(f87,plain,(
% 0.02/0.59 $false|sQ2_spl),
% 0.02/0.59 inference(forward_subsumption_resolution,[status(thm)],[f82,f62])).
% 0.02/0.59 fof(f88,plain,(
% 0.02/0.59 sQ2_spl),
% 0.02/0.59 inference(contradiction_clause,[status(thm)],[f87])).
% 0.02/0.59 fof(f89,plain,(
% 0.02/0.59 ~relation(sK0_skl)|transitive(sK0_skl)|~sQ1_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f33,f69])).
% 0.02/0.59 fof(f90,definition,(
% 0.02/0.59 sQ4_spl <=> (transitive(sK0_skl))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f91,plain,(
% 0.02/0.59 transitive(sK0_skl)|~sQ4_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f90])).
% 0.02/0.59 fof(f93,plain,(
% 0.02/0.59 ~sQ2_spl|sQ4_spl|~sQ1_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f89,f80,f90,f68])).
% 0.02/0.59 fof(f96,plain,(
% 0.02/0.59 ~relation(sK0_skl)|is_reflexive_in(sK0_skl,relation_field(sK0_skl))|~sQ0_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f41,f66])).
% 0.02/0.59 fof(f97,definition,(
% 0.02/0.59 sQ5_spl <=> (is_reflexive_in(sK0_skl,relation_field(sK0_skl)))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f98,plain,(
% 0.02/0.59 is_reflexive_in(sK0_skl,relation_field(sK0_skl))|~sQ5_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f97])).
% 0.02/0.59 fof(f100,plain,(
% 0.02/0.59 ~sQ2_spl|sQ5_spl|~sQ0_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f96,f80,f97,f65])).
% 0.02/0.59 fof(f101,plain,(
% 0.02/0.59 ~relation(sK0_skl)|is_transitive_in(sK0_skl,relation_field(sK0_skl))|~sQ0_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f42,f66])).
% 0.02/0.59 fof(f102,definition,(
% 0.02/0.59 sQ6_spl <=> (is_transitive_in(sK0_skl,relation_field(sK0_skl)))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f103,plain,(
% 0.02/0.59 is_transitive_in(sK0_skl,relation_field(sK0_skl))|~sQ6_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f102])).
% 0.02/0.59 fof(f105,plain,(
% 0.02/0.59 ~sQ2_spl|sQ6_spl|~sQ0_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f101,f80,f102,f65])).
% 0.02/0.59 fof(f106,plain,(
% 0.02/0.59 ~relation(sK0_skl)|transitive(sK0_skl)|~sQ6_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f103,f29])).
% 0.02/0.59 fof(f107,plain,(
% 0.02/0.59 ~sQ2_spl|sQ4_spl|~sQ6_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f106,f80,f90,f102])).
% 0.02/0.59 fof(f108,plain,(
% 0.02/0.59 ~relation(sK0_skl)|is_transitive_in(sK0_skl,relation_field(sK0_skl))|~sQ4_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f91,f28])).
% 0.02/0.59 fof(f109,plain,(
% 0.02/0.59 ~sQ2_spl|sQ6_spl|~sQ4_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f108,f80,f102,f90])).
% 0.02/0.59 fof(f110,plain,(
% 0.02/0.59 ~relation(sK0_skl)|is_antisymmetric_in(sK0_skl,relation_field(sK0_skl))|~sQ0_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f43,f66])).
% 0.02/0.59 fof(f111,definition,(
% 0.02/0.59 sQ7_spl <=> (is_antisymmetric_in(sK0_skl,relation_field(sK0_skl)))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f112,plain,(
% 0.02/0.59 is_antisymmetric_in(sK0_skl,relation_field(sK0_skl))|~sQ7_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f111])).
% 0.02/0.59 fof(f114,plain,(
% 0.02/0.59 ~sQ2_spl|sQ7_spl|~sQ0_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f110,f80,f111,f65])).
% 0.02/0.59 fof(f115,plain,(
% 0.02/0.59 ~relation(sK0_skl)|antisymmetric(sK0_skl)|~sQ7_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f112,f21])).
% 0.02/0.59 fof(f116,definition,(
% 0.02/0.59 sQ8_spl <=> (antisymmetric(sK0_skl))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f117,plain,(
% 0.02/0.59 antisymmetric(sK0_skl)|~sQ8_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f116])).
% 0.02/0.59 fof(f119,plain,(
% 0.02/0.59 ~sQ2_spl|sQ8_spl|~sQ7_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f115,f80,f116,f111])).
% 0.02/0.59 fof(f120,plain,(
% 0.02/0.59 ~relation(sK0_skl)|is_antisymmetric_in(sK0_skl,relation_field(sK0_skl))|~sQ8_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f117,f20])).
% 0.02/0.59 fof(f121,plain,(
% 0.02/0.59 ~sQ2_spl|sQ7_spl|~sQ8_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f120,f80,f111,f116])).
% 0.02/0.59 fof(f122,plain,(
% 0.02/0.59 ~relation(sK0_skl)|is_connected_in(sK0_skl,relation_field(sK0_skl))|~sQ0_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f44,f66])).
% 0.02/0.59 fof(f123,definition,(
% 0.02/0.59 sQ9_spl <=> (is_connected_in(sK0_skl,relation_field(sK0_skl)))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f124,plain,(
% 0.02/0.59 is_connected_in(sK0_skl,relation_field(sK0_skl))|~sQ9_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f123])).
% 0.02/0.59 fof(f126,plain,(
% 0.02/0.59 ~sQ2_spl|sQ9_spl|~sQ0_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f122,f80,f123,f65])).
% 0.02/0.59 fof(f127,plain,(
% 0.02/0.59 ~relation(sK0_skl)|connected(sK0_skl)|~sQ9_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f124,f25])).
% 0.02/0.59 fof(f128,definition,(
% 0.02/0.59 sQ10_spl <=> (connected(sK0_skl))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f129,plain,(
% 0.02/0.59 connected(sK0_skl)|~sQ10_spl),
% 0.02/0.59 inference(component_clause,[status(thm)],[f128])).
% 0.02/0.59 fof(f131,plain,(
% 0.02/0.59 ~sQ2_spl|sQ10_spl|~sQ9_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f127,f80,f128,f123])).
% 0.02/0.59 fof(f132,plain,(
% 0.02/0.59 ~relation(sK0_skl)|is_connected_in(sK0_skl,relation_field(sK0_skl))|~sQ10_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f129,f24])).
% 0.02/0.59 fof(f133,plain,(
% 0.02/0.59 ~sQ2_spl|sQ9_spl|~sQ10_spl),
% 0.02/0.59 inference(split_clause,[status(thm)],[f132,f80,f123,f128])).
% 0.02/0.59 fof(f134,plain,(
% 0.02/0.59 ~relation(sK0_skl)|is_well_founded_in(sK0_skl,relation_field(sK0_skl))|~sQ0_spl),
% 0.02/0.59 inference(resolution,[status(thm)],[f45,f66])).
% 0.02/0.59 fof(f135,definition,(
% 0.02/0.59 sQ11_spl <=> (is_well_founded_in(sK0_skl,relation_field(sK0_skl)))),
% 0.02/0.59 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.02/0.59 fof(f136,plain,(
% 0.02/0.59 is_well_founded_in(sK0_skl,relation_field(sK0_skl))|~sQ11_spl),
% 0.02/0.60 inference(component_clause,[status(thm)],[f135])).
% 0.02/0.60 fof(f138,plain,(
% 0.02/0.60 ~sQ2_spl|sQ11_spl|~sQ0_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f134,f80,f135,f65])).
% 0.02/0.60 fof(f141,plain,(
% 0.02/0.60 ~relation(sK0_skl)|reflexive(sK0_skl)|~sQ5_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f52,f98])).
% 0.02/0.60 fof(f144,plain,(
% 0.02/0.60 ~sQ2_spl|sQ3_spl|~sQ5_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f141,f80,f83,f97])).
% 0.02/0.60 fof(f146,plain,(
% 0.02/0.60 ~relation(sK0_skl)|is_reflexive_in(sK0_skl,relation_field(sK0_skl))|~sQ3_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f84,f51])).
% 0.02/0.60 fof(f147,plain,(
% 0.02/0.60 ~sQ2_spl|sQ5_spl|~sQ3_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f146,f80,f97,f83])).
% 0.02/0.60 fof(f150,plain,(
% 0.02/0.60 ~relation(sK0_skl)|well_founded_relation(sK0_skl)|~sQ11_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f58,f136])).
% 0.02/0.60 fof(f153,definition,(
% 0.02/0.60 sQ12_spl <=> (well_founded_relation(sK0_skl))),
% 0.02/0.60 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.02/0.60 fof(f154,plain,(
% 0.02/0.60 well_founded_relation(sK0_skl)|~sQ12_spl),
% 0.02/0.60 inference(component_clause,[status(thm)],[f153])).
% 0.02/0.60 fof(f156,plain,(
% 0.02/0.60 ~sQ2_spl|sQ12_spl|~sQ11_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f150,f80,f153,f135])).
% 0.02/0.60 fof(f158,plain,(
% 0.02/0.60 ~relation(sK0_skl)|is_well_founded_in(sK0_skl,relation_field(sK0_skl))|~sQ12_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f154,f57])).
% 0.02/0.60 fof(f159,plain,(
% 0.02/0.60 ~relation(sK0_skl)|well_ordering(sK0_skl)|~reflexive(sK0_skl)|~transitive(sK0_skl)|~antisymmetric(sK0_skl)|~connected(sK0_skl)|~sQ12_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f154,f37])).
% 0.02/0.60 fof(f160,plain,(
% 0.02/0.60 ~sQ2_spl|sQ11_spl|~sQ12_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f158,f80,f135,f153])).
% 0.02/0.60 fof(f161,plain,(
% 0.02/0.60 ~sQ2_spl|sQ1_spl|~sQ3_spl|~sQ4_spl|~sQ8_spl|~sQ10_spl|~sQ12_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f159,f80,f68,f83,f90,f116,f128,f153])).
% 0.02/0.60 fof(f162,plain,(
% 0.02/0.60 ~relation(sK0_skl)|well_founded_relation(sK0_skl)|~sQ1_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f69,f36])).
% 0.02/0.60 fof(f163,plain,(
% 0.02/0.60 ~relation(sK0_skl)|connected(sK0_skl)|~sQ1_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f69,f35])).
% 0.02/0.60 fof(f164,plain,(
% 0.02/0.60 ~relation(sK0_skl)|antisymmetric(sK0_skl)|~sQ1_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f69,f34])).
% 0.02/0.60 fof(f167,plain,(
% 0.02/0.60 ~sQ2_spl|sQ12_spl|~sQ1_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f162,f80,f153,f68])).
% 0.02/0.60 fof(f168,plain,(
% 0.02/0.60 ~sQ2_spl|sQ10_spl|~sQ1_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f163,f80,f128,f68])).
% 0.02/0.60 fof(f169,plain,(
% 0.02/0.60 ~sQ2_spl|sQ8_spl|~sQ1_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f164,f80,f116,f68])).
% 0.02/0.60 fof(f172,plain,(
% 0.02/0.60 ~relation(sK0_skl)|well_orders(sK0_skl,relation_field(sK0_skl))|~is_reflexive_in(sK0_skl,relation_field(sK0_skl))|~is_transitive_in(sK0_skl,relation_field(sK0_skl))|~is_antisymmetric_in(sK0_skl,relation_field(sK0_skl))|~is_connected_in(sK0_skl,relation_field(sK0_skl))|~sQ11_spl),
% 0.02/0.60 inference(resolution,[status(thm)],[f46,f136])).
% 0.02/0.60 fof(f175,plain,(
% 0.02/0.60 ~sQ2_spl|sQ0_spl|~sQ5_spl|~sQ6_spl|~sQ7_spl|~sQ9_spl|~sQ11_spl),
% 0.02/0.60 inference(split_clause,[status(thm)],[f172,f80,f65,f97,f102,f111,f123,f135])).
% 0.02/0.60 fof(f177,plain,(
% 0.02/0.60 $false),
% 0.02/0.60 inference(sat_refutation,[status(thm)],[f71,f72,f86,f88,f93,f100,f105,f107,f109,f114,f119,f121,f126,f131,f133,f138,f144,f147,f156,f160,f161,f167,f168,f169,f175])).
% 0.02/0.60 % SZS output end CNFRefutation for theBenchmark.p
% 0.02/0.62 % Elapsed time: 0.050394 seconds
% 0.02/0.62 % CPU time: 0.153873 seconds
% 0.02/0.62 % Total memory used: 102.231 MB
% 0.02/0.62 % Net memory used: 101.979 MB
%------------------------------------------------------------------------------