%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET016+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:11:11 PM UTC 2026
% Result : Theorem 31.68s 4.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET016+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:38:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 31.68/4.46 % Refutation found
% 31.68/4.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 31.68/4.46 % SZS output start CNFRefutation for theBenchmark
% 31.68/4.46 fof(f1,axiom,(
% 31.68/4.46 (! [X,Y] :( subclass(X,Y)<=> (! [U] :( member(U,X)=> member(U,Y) ) )) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f2,axiom,(
% 31.68/4.46 (! [X] : subclass(X,universal_class) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f4,axiom,(
% 31.68/4.46 (! [U,X,Y] :( member(U,unordered_pair(X,Y))<=> ( member(U,universal_class)& ( U = X| U = Y ) ) ) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f5,axiom,(
% 31.68/4.46 (! [X,Y] : member(unordered_pair(X,Y),universal_class) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f6,axiom,(
% 31.68/4.46 (! [X] : singleton(X) = unordered_pair(X,X) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f7,axiom,(
% 31.68/4.46 (! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f8,axiom,(
% 31.68/4.46 (! [U,V,X,Y] :( member(ordered_pair(U,V),cross_product(X,Y))<=> ( member(U,X)& member(V,Y) ) ) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f9,axiom,(
% 31.68/4.46 (! [X,Y] :( ( member(X,universal_class)& member(Y,universal_class) )=> ( first(ordered_pair(X,Y)) = X& second(ordered_pair(X,Y)) = Y ) ) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f14,axiom,(
% 31.68/4.46 (! [X,Z] :( member(Z,complement(X))<=> ( member(Z,universal_class)& ~ member(Z,X) ) ) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f16,axiom,(
% 31.68/4.46 (! [X] : ~ member(X,null_class) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f29,axiom,(
% 31.68/4.46 (! [X] :( inductive(X)<=> ( member(null_class,X)& subclass(image(successor_relation,X),X) ) ) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f41,axiom,(
% 31.68/4.46 (! [X] :( X != null_class=> (? [U] :( member(U,universal_class)& member(U,X)& disjoint(U,X) ) )) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f44,conjecture,(
% 31.68/4.46 (! [W,X,Y,Z] :( ( ordered_pair(W,X) = ordered_pair(Y,Z)& member(W,universal_class) )=> W = Y ) )),
% 31.68/4.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.68/4.46 fof(f45,negated_conjecture,(
% 31.68/4.46 ~((! [W,X,Y,Z] :( ( ordered_pair(W,X) = ordered_pair(Y,Z)& member(W,universal_class) )=> W = Y ) ))),
% 31.68/4.46 inference(negated_conjecture,[status(cth)],[f44])).
% 31.68/4.46 fof(f46,plain,(
% 31.68/4.46 ![X,Y]: (subclass(X,Y)<=>(![U]: (~member(U,X)|member(U,Y))))),
% 31.68/4.46 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 31.68/4.46 fof(f47,plain,(
% 31.68/4.46 ![X,Y]: ((~subclass(X,Y)|(![U]: (~member(U,X)|member(U,Y))))&(subclass(X,Y)|(?[U]: (member(U,X)&~member(U,Y)))))),
% 31.68/4.46 inference(NNF_transformation,[status(thm)],[f46])).
% 31.68/4.46 fof(f48,plain,(
% 31.68/4.46 (![X,Y]: (~subclass(X,Y)|(![U]: (~member(U,X)|member(U,Y)))))&(![X,Y]: (subclass(X,Y)|(?[U]: (member(U,X)&~member(U,Y)))))),
% 31.68/4.46 inference(miniscoping,[status(thm)],[f47])).
% 31.68/4.46 fof(f49,plain,(
% 31.68/4.46 (![X,Y]: (~subclass(X,Y)|(![U]: (~member(U,X)|member(U,Y)))))&(![X,Y]: (subclass(X,Y)|(member(sK0_skl(Y,X),X)&~member(sK0_skl(Y,X),Y))))),
% 31.68/4.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(U,sK0_skl(Y,X))],[f48])).
% 31.68/4.46 fof(f50,plain,(
% 31.68/4.46 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f49])).
% 31.68/4.46 fof(f53,plain,(
% 31.68/4.46 ![X0]: (subclass(X0,universal_class))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f2])).
% 31.68/4.46 fof(f59,plain,(
% 31.68/4.46 ![U,X,Y]: ((~member(U,unordered_pair(X,Y))|(member(U,universal_class)&(U=X|U=Y)))&(member(U,unordered_pair(X,Y))|(~member(U,universal_class)|(~U=X&~U=Y))))),
% 31.68/4.46 inference(NNF_transformation,[status(thm)],[f4])).
% 31.68/4.46 fof(f60,plain,(
% 31.68/4.46 (![U,X,Y]: (~member(U,unordered_pair(X,Y))|(member(U,universal_class)&(U=X|U=Y))))&(![U,X,Y]: (member(U,unordered_pair(X,Y))|(~member(U,universal_class)|(~U=X&~U=Y))))),
% 31.68/4.46 inference(miniscoping,[status(thm)],[f59])).
% 31.68/4.46 fof(f62,plain,(
% 31.68/4.46 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f60])).
% 31.68/4.46 fof(f63,plain,(
% 31.68/4.46 ![X0,X1,X2]: (member(X0,unordered_pair(X1,X2))|~member(X0,universal_class)|~X0=X1)),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f60])).
% 31.68/4.46 fof(f65,plain,(
% 31.68/4.46 ![X0,X1]: (member(unordered_pair(X0,X1),universal_class))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f5])).
% 31.68/4.46 fof(f66,plain,(
% 31.68/4.46 ![X0]: (singleton(X0)=unordered_pair(X0,X0))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f6])).
% 31.68/4.46 fof(f67,plain,(
% 31.68/4.46 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f7])).
% 31.68/4.46 fof(f68,plain,(
% 31.68/4.46 ![U,V,X,Y]: ((~member(ordered_pair(U,V),cross_product(X,Y))|(member(U,X)&member(V,Y)))&(member(ordered_pair(U,V),cross_product(X,Y))|(~member(U,X)|~member(V,Y))))),
% 31.68/4.46 inference(NNF_transformation,[status(thm)],[f8])).
% 31.68/4.46 fof(f69,plain,(
% 31.68/4.46 (![U,V,X,Y]: (~member(ordered_pair(U,V),cross_product(X,Y))|(member(U,X)&member(V,Y))))&(![U,V,X,Y]: (member(ordered_pair(U,V),cross_product(X,Y))|(~member(U,X)|~member(V,Y))))),
% 31.68/4.46 inference(miniscoping,[status(thm)],[f68])).
% 31.68/4.46 fof(f70,plain,(
% 31.68/4.46 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X0,X2))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f69])).
% 31.68/4.46 fof(f72,plain,(
% 31.68/4.46 ![X0,X1,X2,X3]: (member(ordered_pair(X0,X1),cross_product(X2,X3))|~member(X0,X2)|~member(X1,X3))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f69])).
% 31.68/4.46 fof(f73,plain,(
% 31.68/4.46 ![X,Y]: ((~member(X,universal_class)|~member(Y,universal_class))|(first(ordered_pair(X,Y))=X&second(ordered_pair(X,Y))=Y))),
% 31.68/4.46 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 31.68/4.46 fof(f74,plain,(
% 31.68/4.46 ![X0,X1]: (~member(X0,universal_class)|~member(X1,universal_class)|first(ordered_pair(X0,X1))=X0)),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f73])).
% 31.68/4.46 fof(f90,plain,(
% 31.68/4.46 ![X,Z]: ((~member(Z,complement(X))|(member(Z,universal_class)&~member(Z,X)))&(member(Z,complement(X))|(~member(Z,universal_class)|member(Z,X))))),
% 31.68/4.46 inference(NNF_transformation,[status(thm)],[f14])).
% 31.68/4.46 fof(f91,plain,(
% 31.68/4.46 (![X,Z]: (~member(Z,complement(X))|(member(Z,universal_class)&~member(Z,X))))&(![X,Z]: (member(Z,complement(X))|(~member(Z,universal_class)|member(Z,X))))),
% 31.68/4.46 inference(miniscoping,[status(thm)],[f90])).
% 31.68/4.46 fof(f93,plain,(
% 31.68/4.46 ![X0,X1]: (~member(X0,complement(X1))|~member(X0,X1))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f91])).
% 31.68/4.46 fof(f94,plain,(
% 31.68/4.46 ![X0,X1]: (member(X0,complement(X1))|~member(X0,universal_class)|member(X0,X1))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f91])).
% 31.68/4.46 fof(f96,plain,(
% 31.68/4.46 ![X0]: (~member(X0,null_class))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f16])).
% 31.68/4.46 fof(f130,plain,(
% 31.68/4.46 ![X]: ((~inductive(X)|(member(null_class,X)&subclass(image(successor_relation,X),X)))&(inductive(X)|(~member(null_class,X)|~subclass(image(successor_relation,X),X))))),
% 31.68/4.46 inference(NNF_transformation,[status(thm)],[f29])).
% 31.68/4.46 fof(f131,plain,(
% 31.68/4.46 (![X]: (~inductive(X)|(member(null_class,X)&subclass(image(successor_relation,X),X))))&(![X]: (inductive(X)|(~member(null_class,X)|~subclass(image(successor_relation,X),X))))),
% 31.68/4.46 inference(miniscoping,[status(thm)],[f130])).
% 31.68/4.46 fof(f132,plain,(
% 31.68/4.46 ![X0]: (~inductive(X0)|member(null_class,X0))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f131])).
% 31.68/4.46 fof(f134,plain,(
% 31.68/4.46 ![X0]: (inductive(X0)|~member(null_class,X0)|~subclass(image(successor_relation,X0),X0))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f131])).
% 31.68/4.46 fof(f181,plain,(
% 31.68/4.46 ![X]: (X=null_class|(?[U]: ((member(U,universal_class)&member(U,X))&disjoint(U,X))))),
% 31.68/4.46 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 31.68/4.46 fof(f182,plain,(
% 31.68/4.46 ![X]: (X=null_class|((member(sK5_skl(X),universal_class)&member(sK5_skl(X),X))&disjoint(sK5_skl(X),X)))),
% 31.68/4.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(U,sK5_skl(X))],[f181])).
% 31.68/4.46 fof(f183,plain,(
% 31.68/4.46 ![X0]: (X0=null_class|member(sK5_skl(X0),universal_class))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f182])).
% 31.68/4.46 fof(f184,plain,(
% 31.68/4.46 ![X0]: (X0=null_class|member(sK5_skl(X0),X0))),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f182])).
% 31.68/4.46 fof(f191,plain,(
% 31.68/4.46 (?[W,X,Y,Z]: ((ordered_pair(W,X)=ordered_pair(Y,Z)&member(W,universal_class))&~W=Y))),
% 31.68/4.46 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 31.68/4.46 fof(f192,plain,(
% 31.68/4.46 ?[W,Y]: (((?[X,Z]: ordered_pair(W,X)=ordered_pair(Y,Z))&member(W,universal_class))&~W=Y)),
% 31.68/4.46 inference(miniscoping,[status(thm)],[f191])).
% 31.68/4.46 fof(f193,plain,(
% 31.68/4.46 ((ordered_pair(sK7_skl,sK9_skl)=ordered_pair(sK8_skl,sK10_skl)&member(sK7_skl,universal_class))&~sK7_skl=sK8_skl)),
% 31.68/4.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl,sK10_skl]),skolemize(W,sK7_skl),skolemize(Y,sK8_skl),skolemize(X,sK9_skl),skolemize(Z,sK10_skl)],[f192])).
% 31.68/4.46 fof(f194,plain,(
% 31.68/4.46 ordered_pair(sK7_skl,sK9_skl)=ordered_pair(sK8_skl,sK10_skl)),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f193])).
% 31.68/4.46 fof(f195,plain,(
% 31.68/4.46 member(sK7_skl,universal_class)),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f193])).
% 31.68/4.46 fof(f196,plain,(
% 31.68/4.46 ~sK7_skl=sK8_skl),
% 31.68/4.46 inference(cnf_transformation,[status(thm)],[f193])).
% 31.68/4.46 fof(f199,plain,(
% 31.68/4.46 ![X0,X1]: (member(X0,unordered_pair(X0,X1))|~member(X0,universal_class))),
% 31.68/4.46 inference(destructive_equality_resolution,[status(thm)],[f63])).
% 31.68/4.46 fof(f221,plain,(
% 31.68/4.46 ![X0]: (member(singleton(X0),universal_class))),
% 31.68/4.46 inference(paramodulation,[status(thm)],[f66,f65])).
% 31.68/4.46 fof(f300,definition,(
% 31.68/4.46 sQ6_spl <=> (member(null_class,universal_class))),
% 31.68/4.46 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 31.68/4.46 fof(f302,plain,(
% 31.68/4.46 ~member(null_class,universal_class)|sQ6_spl),
% 31.68/4.46 inference(component_clause,[status(thm)],[f300])).
% 31.68/4.46 fof(f311,plain,(
% 31.68/4.46 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1|X0=X1)),
% 31.68/4.46 inference(paramodulation,[status(thm)],[f66,f62])).
% 31.68/4.46 fof(f312,plain,(
% 31.68/4.46 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 31.68/4.46 inference(duplicate_literals_removal,[status(thm)],[f311])).
% 31.68/4.46 fof(f316,plain,(
% 31.68/4.46 ![X0]: (member(null_class,unordered_pair(null_class,X0))|~inductive(universal_class))),
% 31.68/4.46 inference(resolution,[status(thm)],[f199,f132])).
% 31.68/4.46 fof(f317,plain,(
% 31.68/4.46 ![X0,X1]: (member(singleton(X0),unordered_pair(singleton(X0),X1)))),
% 31.68/4.46 inference(resolution,[status(thm)],[f199,f221])).
% 31.68/4.46 fof(f319,plain,(
% 31.68/4.46 ![X0]: (member(sK7_skl,unordered_pair(sK7_skl,X0)))),
% 31.68/4.46 inference(resolution,[status(thm)],[f199,f195])).
% 31.68/4.46 fof(f320,plain,(
% 31.68/4.46 ![X0,X1,X2]: (member(X0,unordered_pair(X0,X1))|~subclass(X2,universal_class)|~member(X0,X2))),
% 31.68/4.46 inference(resolution,[status(thm)],[f199,f50])).
% 31.68/4.46 fof(f328,definition,(
% 31.68/4.46 ![X0]: (sQ10_spl <=> (member(null_class,unordered_pair(null_class,X0))))),
% 31.68/4.46 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 31.68/4.46 fof(f329,plain,(
% 31.68/4.46 ![X0]: (member(null_class,unordered_pair(null_class,X0))|~sQ10_spl)),
% 31.68/4.46 inference(component_clause,[status(thm)],[f328])).
% 31.68/4.46 fof(f331,definition,(
% 31.68/4.46 sQ11_spl <=> (inductive(universal_class))),
% 31.68/4.46 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 31.68/4.46 fof(f334,plain,(
% 31.68/4.46 sQ10_spl|~sQ11_spl),
% 31.68/4.46 inference(split_clause,[status(thm)],[f316,f328,f331])).
% 31.68/4.46 fof(f335,plain,(
% 31.68/4.46 ![X0,X1,X2]: (member(X0,unordered_pair(X0,X1))|~member(X0,X2))),
% 31.68/4.46 inference(forward_subsumption_resolution,[status(thm)],[f320,f53])).
% 31.68/4.46 fof(f505,plain,(
% 31.68/4.46 ![X0,X1,X2]: (~member(X0,ordered_pair(X1,X2))|X0=singleton(X1)|X0=unordered_pair(X1,singleton(X2)))),
% 31.68/4.46 inference(paramodulation,[status(thm)],[f67,f62])).
% 31.68/4.46 fof(f578,plain,(
% 31.68/4.46 ![X0,X1]: (member(ordered_pair(sK8_skl,sK10_skl),cross_product(X0,X1))|~member(sK7_skl,X0)|~member(sK9_skl,X1))),
% 31.68/4.46 inference(paramodulation,[status(thm)],[f194,f72])).
% 31.68/4.46 fof(f587,plain,(
% 31.68/4.46 ![X0]: (~member(X0,universal_class)|first(ordered_pair(X0,sK7_skl))=X0)),
% 31.68/4.46 inference(resolution,[status(thm)],[f74,f195])).
% 31.68/4.46 fof(f595,plain,(
% 31.68/4.46 ![X0,X1]: (first(ordered_pair(X0,sK7_skl))=X0|~subclass(X1,universal_class)|~member(X0,X1))),
% 31.68/4.46 inference(resolution,[status(thm)],[f587,f50])).
% 31.68/4.46 fof(f596,plain,(
% 31.68/4.46 ![X0,X1]: (first(ordered_pair(X0,sK7_skl))=X0|~member(X0,X1))),
% 31.68/4.46 inference(forward_subsumption_resolution,[status(thm)],[f595,f53])).
% 31.68/4.46 fof(f624,definition,(
% 31.68/4.46 ![X1]: (sQ25_spl <=> (~member(sK8_skl,X1)))),
% 31.68/4.46 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 31.68/4.46 fof(f625,plain,(
% 31.68/4.46 ![X0]: (~member(sK8_skl,X0)|~sQ25_spl)),
% 31.68/4.46 inference(component_clause,[status(thm)],[f624])).
% 31.68/4.46 fof(f667,definition,(
% 31.68/4.47 sQ27_spl <=> (member(sK9_skl,universal_class))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f668,plain,(
% 31.68/4.47 member(sK9_skl,universal_class)|~sQ27_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f667])).
% 31.68/4.47 fof(f669,plain,(
% 31.68/4.47 ~member(sK9_skl,universal_class)|sQ27_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f667])).
% 31.68/4.47 fof(f732,plain,(
% 31.68/4.47 ![X0]: (first(ordered_pair(singleton(X0),sK7_skl))=singleton(X0))),
% 31.68/4.47 inference(resolution,[status(thm)],[f221,f596])).
% 31.68/4.47 fof(f772,plain,(
% 31.68/4.47 ![X0]: (~subclass(X0,universal_class)|~member(sK9_skl,X0)|sQ27_spl)),
% 31.68/4.47 inference(resolution,[status(thm)],[f669,f50])).
% 31.68/4.47 fof(f773,plain,(
% 31.68/4.47 ![X0]: (~member(sK9_skl,X0)|sQ27_spl)),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f772,f53])).
% 31.68/4.47 fof(f796,plain,(
% 31.68/4.47 member(null_class,singleton(null_class))|~sQ10_spl),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f66,f329])).
% 31.68/4.47 fof(f799,plain,(
% 31.68/4.47 first(ordered_pair(null_class,sK7_skl))=null_class|~sQ10_spl),
% 31.68/4.47 inference(resolution,[status(thm)],[f796,f596])).
% 31.68/4.47 fof(f803,plain,(
% 31.68/4.47 ![X0]: (singleton(X0)=null_class|sK5_skl(singleton(X0))=X0)),
% 31.68/4.47 inference(resolution,[status(thm)],[f184,f312])).
% 31.68/4.47 fof(f841,definition,(
% 31.68/4.47 ![X0]: (sQ34_spl <=> (~member(sK9_skl,X0)))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f842,plain,(
% 31.68/4.47 ![X0]: (~member(sK9_skl,X0)|~sQ34_spl)),
% 31.68/4.47 inference(component_clause,[status(thm)],[f841])).
% 31.68/4.47 fof(f852,plain,(
% 31.68/4.47 $false|~sQ34_spl|~sQ27_spl),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f668,f842])).
% 31.68/4.47 fof(f853,plain,(
% 31.68/4.47 ~sQ34_spl|~sQ27_spl),
% 31.68/4.47 inference(contradiction_clause,[status(thm)],[f852])).
% 31.68/4.47 fof(f1059,plain,(
% 31.68/4.47 ![X0]: (~member(sK8_skl,universal_class)|member(sK8_skl,X0)|~sQ25_spl)),
% 31.68/4.47 inference(resolution,[status(thm)],[f625,f94])).
% 31.68/4.47 fof(f1062,definition,(
% 31.68/4.47 sQ41_spl <=> (member(sK8_skl,universal_class))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f1064,plain,(
% 31.68/4.47 ~member(sK8_skl,universal_class)|sQ41_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f1062])).
% 31.68/4.47 fof(f1069,definition,(
% 31.68/4.47 ![X0]: (sQ43_spl <=> (member(sK8_skl,X0)))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f1070,plain,(
% 31.68/4.47 ![X0]: (member(sK8_skl,X0)|~sQ43_spl)),
% 31.68/4.47 inference(component_clause,[status(thm)],[f1069])).
% 31.68/4.47 fof(f1072,plain,(
% 31.68/4.47 ~sQ41_spl|sQ43_spl|~sQ25_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f1059,f1062,f1069,f624])).
% 31.68/4.47 fof(f1086,plain,(
% 31.68/4.47 ![X0]: (~subclass(X0,universal_class)|~member(sK8_skl,X0)|sQ41_spl)),
% 31.68/4.47 inference(resolution,[status(thm)],[f1064,f50])).
% 31.68/4.47 fof(f1087,plain,(
% 31.68/4.47 ![X0]: (~member(sK8_skl,X0)|sQ41_spl)),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f1086,f53])).
% 31.68/4.47 fof(f1141,plain,(
% 31.68/4.47 ![X0,X1]: (member(singleton(X0),ordered_pair(X0,X1)))),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f67,f317])).
% 31.68/4.47 fof(f1145,plain,(
% 31.68/4.47 member(singleton(sK7_skl),ordered_pair(sK8_skl,sK10_skl))),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f194,f1141])).
% 31.68/4.47 fof(f1156,plain,(
% 31.68/4.47 ![X0,X1]: (member(X0,singleton(X0))|~member(X0,X1))),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f66,f335])).
% 31.68/4.47 fof(f1288,plain,(
% 31.68/4.47 ![X0]: (singleton(X0)=null_class|member(X0,universal_class)|singleton(X0)=null_class)),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f803,f183])).
% 31.68/4.47 fof(f1290,plain,(
% 31.68/4.47 ![X0]: (singleton(X0)=null_class|member(X0,singleton(X0))|singleton(X0)=null_class)),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f803,f184])).
% 31.68/4.47 fof(f1293,plain,(
% 31.68/4.47 ![X0]: (singleton(X0)=null_class|member(X0,universal_class))),
% 31.68/4.47 inference(duplicate_literals_removal,[status(thm)],[f1288])).
% 31.68/4.47 fof(f1295,plain,(
% 31.68/4.47 ![X0]: (singleton(X0)=null_class|member(X0,singleton(X0)))),
% 31.68/4.47 inference(duplicate_literals_removal,[status(thm)],[f1290])).
% 31.68/4.47 fof(f1299,plain,(
% 31.68/4.47 singleton(sK8_skl)=null_class|sQ41_spl),
% 31.68/4.47 inference(resolution,[status(thm)],[f1293,f1087])).
% 31.68/4.47 fof(f1301,plain,(
% 31.68/4.47 singleton(sK9_skl)=null_class|sQ27_spl),
% 31.68/4.47 inference(resolution,[status(thm)],[f1293,f773])).
% 31.68/4.47 fof(f1312,plain,(
% 31.68/4.47 first(ordered_pair(null_class,sK7_skl))=singleton(sK8_skl)|sQ41_spl),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f1299,f732])).
% 31.68/4.47 fof(f1315,plain,(
% 31.68/4.47 member(null_class,universal_class)|sQ41_spl),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f1299,f221])).
% 31.68/4.47 fof(f1336,plain,(
% 31.68/4.47 ![X0]: (~member(sK8_skl,X0)|~sQ43_spl)),
% 31.68/4.47 inference(resolution,[status(thm)],[f1070,f93])).
% 31.68/4.47 fof(f1350,plain,(
% 31.68/4.47 $false|~sQ43_spl),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f1336,f1070])).
% 31.68/4.47 fof(f1351,plain,(
% 31.68/4.47 ~sQ43_spl),
% 31.68/4.47 inference(contradiction_clause,[status(thm)],[f1350])).
% 31.68/4.47 fof(f1607,definition,(
% 31.68/4.47 ![X0]: (sQ70_spl <=> (~member(sK7_skl,X0)))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f1608,plain,(
% 31.68/4.47 ![X0]: (~member(sK7_skl,X0)|~sQ70_spl)),
% 31.68/4.47 inference(component_clause,[status(thm)],[f1607])).
% 31.68/4.47 fof(f1623,plain,(
% 31.68/4.47 $false|~sQ70_spl),
% 31.68/4.47 inference(backward_subsumption_resolution,[status(thm)],[f319,f1608])).
% 31.68/4.47 fof(f1655,definition,(
% 31.68/4.47 sQ74_spl <=> (sK7_skl=sK8_skl)),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f1656,plain,(
% 31.68/4.47 sK7_skl=sK8_skl|~sQ74_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f1655])).
% 31.68/4.47 fof(f1659,plain,(
% 31.68/4.47 $false|~sQ74_spl),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f1656,f196])).
% 31.68/4.47 fof(f1660,plain,(
% 31.68/4.47 ~sQ74_spl),
% 31.68/4.47 inference(contradiction_clause,[status(thm)],[f1659])).
% 31.68/4.47 fof(f1724,plain,(
% 31.68/4.47 inductive(universal_class)|~member(null_class,universal_class)),
% 31.68/4.47 inference(resolution,[status(thm)],[f134,f53])).
% 31.68/4.47 fof(f1725,plain,(
% 31.68/4.47 sQ11_spl|~sQ6_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f1724,f331,f300])).
% 31.68/4.47 fof(f1784,definition,(
% 31.68/4.47 sQ79_spl <=> (singleton(sK9_skl)=null_class)),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f1785,plain,(
% 31.68/4.47 singleton(sK9_skl)=null_class|~sQ79_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f1784])).
% 31.68/4.47 fof(f1791,definition,(
% 31.68/4.47 sQ81_spl <=> (member(sK9_skl,null_class))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f1792,plain,(
% 31.68/4.47 member(sK9_skl,null_class)|~sQ81_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f1791])).
% 31.68/4.47 fof(f1919,plain,(
% 31.68/4.47 singleton(sK9_skl)=null_class|member(sK9_skl,null_class)|sQ27_spl),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f1301,f1295])).
% 31.68/4.47 fof(f1921,plain,(
% 31.68/4.47 sQ79_spl|sQ81_spl|sQ27_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f1919,f1784,f1791,f667])).
% 31.68/4.47 fof(f1924,plain,(
% 31.68/4.47 $false|~sQ81_spl),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f1792,f96])).
% 31.68/4.47 fof(f1925,plain,(
% 31.68/4.47 ~sQ81_spl),
% 31.68/4.47 inference(contradiction_clause,[status(thm)],[f1924])).
% 31.68/4.47 fof(f1939,plain,(
% 31.68/4.47 ~sQ70_spl),
% 31.68/4.47 inference(contradiction_clause,[status(thm)],[f1623])).
% 31.68/4.47 fof(f2340,plain,(
% 31.68/4.47 ![X0]: (member(null_class,ordered_pair(sK8_skl,X0))|sQ41_spl)),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f1299,f1141])).
% 31.68/4.47 fof(f2466,plain,(
% 31.68/4.47 $false|sQ41_spl|sQ6_spl),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f302,f1315])).
% 31.68/4.47 fof(f2467,plain,(
% 31.68/4.47 sQ41_spl|sQ6_spl),
% 31.68/4.47 inference(contradiction_clause,[status(thm)],[f2466])).
% 31.68/4.47 fof(f2555,plain,(
% 31.68/4.47 ![X0,X1]: (member(sK8_skl,X0)|~member(sK7_skl,X0)|~member(sK9_skl,X1))),
% 31.68/4.47 inference(resolution,[status(thm)],[f70,f578])).
% 31.68/4.47 fof(f2558,definition,(
% 31.68/4.47 ![X0]: (sQ115_spl <=> (member(sK8_skl,X0)|~member(sK7_skl,X0)))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f2559,plain,(
% 31.68/4.47 ![X0]: (member(sK8_skl,X0)|~member(sK7_skl,X0)|~sQ115_spl)),
% 31.68/4.47 inference(component_clause,[status(thm)],[f2558])).
% 31.68/4.47 fof(f2561,plain,(
% 31.68/4.47 sQ115_spl|sQ34_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f2555,f2558,f841])).
% 31.68/4.47 fof(f2562,plain,(
% 31.68/4.47 ![X0]: (~member(sK7_skl,X0)|~sQ25_spl|~sQ115_spl)),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f2559,f625])).
% 31.68/4.47 fof(f2564,plain,(
% 31.68/4.47 $false|~sQ25_spl|~sQ115_spl),
% 31.68/4.47 inference(backward_subsumption_resolution,[status(thm)],[f319,f2562])).
% 31.68/4.47 fof(f2579,plain,(
% 31.68/4.47 ~sQ25_spl|~sQ115_spl),
% 31.68/4.47 inference(contradiction_clause,[status(thm)],[f2564])).
% 31.68/4.47 fof(f2833,plain,(
% 31.68/4.47 null_class=singleton(sK8_skl)|~sQ10_spl|sQ41_spl),
% 31.68/4.47 inference(forward_demodulation,[status(thm)],[f799,f1312])).
% 31.68/4.47 fof(f5323,plain,(
% 31.68/4.47 singleton(sK7_skl)=singleton(sK8_skl)|singleton(sK7_skl)=unordered_pair(sK8_skl,singleton(sK10_skl))),
% 31.68/4.47 inference(resolution,[status(thm)],[f505,f1145])).
% 31.68/4.47 fof(f5328,plain,(
% 31.68/4.47 ![X0]: (~member(X0,ordered_pair(sK8_skl,sK10_skl))|X0=singleton(sK7_skl)|X0=unordered_pair(sK7_skl,singleton(sK9_skl)))),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f194,f505])).
% 31.68/4.47 fof(f5350,definition,(
% 31.68/4.47 sQ195_spl <=> (singleton(sK7_skl)=singleton(sK8_skl))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f5351,plain,(
% 31.68/4.47 singleton(sK7_skl)=singleton(sK8_skl)|~sQ195_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f5350])).
% 31.68/4.47 fof(f5352,plain,(
% 31.68/4.47 ~singleton(sK7_skl)=singleton(sK8_skl)|sQ195_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f5350])).
% 31.68/4.47 fof(f5353,definition,(
% 31.68/4.47 sQ196_spl <=> (singleton(sK7_skl)=unordered_pair(sK8_skl,singleton(sK10_skl)))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f5354,plain,(
% 31.68/4.47 singleton(sK7_skl)=unordered_pair(sK8_skl,singleton(sK10_skl))|~sQ196_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f5353])).
% 31.68/4.47 fof(f5356,plain,(
% 31.68/4.47 sQ195_spl|sQ196_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f5323,f5350,f5353])).
% 31.68/4.47 fof(f5359,plain,(
% 31.68/4.47 ![X0]: (~member(X0,ordered_pair(sK8_skl,sK10_skl))|X0=singleton(sK7_skl)|X0=unordered_pair(sK7_skl,null_class)|~sQ79_spl)),
% 31.68/4.47 inference(forward_demodulation,[status(thm)],[f1785,f5328])).
% 31.68/4.47 fof(f5412,plain,(
% 31.68/4.47 ~singleton(sK7_skl)=null_class|~sQ10_spl|sQ41_spl|sQ195_spl),
% 31.68/4.47 inference(forward_demodulation,[status(thm)],[f2833,f5352])).
% 31.68/4.47 fof(f7107,plain,(
% 31.68/4.47 ![X0]: (member(sK8_skl,singleton(sK7_skl))|~member(sK8_skl,X0)|~sQ196_spl)),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f5354,f335])).
% 31.68/4.47 fof(f7144,definition,(
% 31.68/4.47 sQ262_spl <=> (member(sK8_skl,singleton(sK7_skl)))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f7145,plain,(
% 31.68/4.47 member(sK8_skl,singleton(sK7_skl))|~sQ262_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f7144])).
% 31.68/4.47 fof(f7147,plain,(
% 31.68/4.47 sQ262_spl|sQ25_spl|~sQ196_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f7107,f7144,f624,f5353])).
% 31.68/4.47 fof(f10100,plain,(
% 31.68/4.47 ![X0]: (member(sK7_skl,singleton(sK8_skl))|~member(sK7_skl,X0)|~sQ195_spl)),
% 31.68/4.47 inference(paramodulation,[status(thm)],[f5351,f1156])).
% 31.68/4.47 fof(f10121,definition,(
% 31.68/4.47 sQ332_spl <=> (member(sK7_skl,singleton(sK8_skl)))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f10122,plain,(
% 31.68/4.47 member(sK7_skl,singleton(sK8_skl))|~sQ332_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f10121])).
% 31.68/4.47 fof(f10124,plain,(
% 31.68/4.47 sQ332_spl|sQ70_spl|~sQ195_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f10100,f10121,f1607,f5350])).
% 31.68/4.47 fof(f10475,plain,(
% 31.68/4.47 sK7_skl=sK8_skl|~sQ332_spl),
% 31.68/4.47 inference(resolution,[status(thm)],[f10122,f312])).
% 31.68/4.47 fof(f10479,plain,(
% 31.68/4.47 sQ74_spl|~sQ332_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f10475,f1655,f10121])).
% 31.68/4.47 fof(f12274,definition,(
% 31.68/4.47 sQ363_spl <=> (singleton(sK7_skl)=null_class)),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f12275,plain,(
% 31.68/4.47 singleton(sK7_skl)=null_class|~sQ363_spl),
% 31.68/4.47 inference(component_clause,[status(thm)],[f12274])).
% 31.68/4.47 fof(f12283,plain,(
% 31.68/4.47 $false|~sQ10_spl|sQ41_spl|sQ195_spl|~sQ363_spl),
% 31.68/4.47 inference(forward_subsumption_resolution,[status(thm)],[f12275,f5412])).
% 31.68/4.47 fof(f12284,plain,(
% 31.68/4.47 ~sQ10_spl|sQ41_spl|sQ195_spl|~sQ363_spl),
% 31.68/4.47 inference(contradiction_clause,[status(thm)],[f12283])).
% 31.68/4.47 fof(f12924,plain,(
% 31.68/4.47 sK8_skl=sK7_skl|~sQ262_spl),
% 31.68/4.47 inference(resolution,[status(thm)],[f7145,f312])).
% 31.68/4.47 fof(f12928,plain,(
% 31.68/4.47 sQ74_spl|~sQ262_spl),
% 31.68/4.47 inference(split_clause,[status(thm)],[f12924,f1655,f7144])).
% 31.68/4.47 fof(f14803,plain,(
% 31.68/4.47 null_class=singleton(sK7_skl)|null_class=unordered_pair(sK7_skl,null_class)|~sQ79_spl|sQ41_spl),
% 31.68/4.47 inference(resolution,[status(thm)],[f5359,f2340])).
% 31.68/4.47 fof(f14819,definition,(
% 31.68/4.47 sQ407_spl <=> (null_class=unordered_pair(sK7_skl,null_class))),
% 31.68/4.47 introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition])).
% 31.68/4.47 fof(f14820,plain,(
% 31.68/4.50 null_class=unordered_pair(sK7_skl,null_class)|~sQ407_spl),
% 31.68/4.50 inference(component_clause,[status(thm)],[f14819])).
% 31.68/4.50 fof(f14822,plain,(
% 31.68/4.50 sQ363_spl|sQ407_spl|~sQ79_spl|sQ41_spl),
% 31.68/4.50 inference(split_clause,[status(thm)],[f14803,f12274,f14819,f1784,f1062])).
% 31.68/4.50 fof(f14978,plain,(
% 31.68/4.50 member(sK7_skl,null_class)|~sQ407_spl),
% 31.68/4.50 inference(paramodulation,[status(thm)],[f14820,f319])).
% 31.68/4.50 fof(f14997,plain,(
% 31.68/4.50 $false|~sQ407_spl),
% 31.68/4.50 inference(forward_subsumption_resolution,[status(thm)],[f14978,f96])).
% 31.68/4.50 fof(f14998,plain,(
% 31.68/4.50 ~sQ407_spl),
% 31.68/4.50 inference(contradiction_clause,[status(thm)],[f14997])).
% 31.68/4.50 fof(f14999,plain,(
% 31.68/4.50 $false),
% 31.68/4.50 inference(sat_refutation,[status(thm)],[f334,f853,f1072,f1351,f1660,f1725,f1921,f1925,f1939,f2467,f2561,f2579,f5356,f7147,f10124,f10479,f12284,f12928,f14822,f14998])).
% 31.68/4.50 % SZS output end CNFRefutation for theBenchmark.p
% 31.68/4.54 % Elapsed time: 4.163227 seconds
% 31.68/4.54 % CPU time: 32.688061 seconds
% 31.68/4.54 % Total memory used: 487.716 MB
% 31.68/4.54 % Net memory used: 434.520 MB
%------------------------------------------------------------------------------