%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU002+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:21:34 PM UTC 2026
% Result : Theorem 6.71s 6.27s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU002+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n005.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 05:46:09 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.38 % Drodi V4.1.1
% 6.71/6.27 % Refutation found
% 6.71/6.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.71/6.27 % SZS output start CNFRefutation for theBenchmark
% 6.71/6.27 fof(f2,axiom,(
% 6.71/6.27 (! [A] :( empty(A)=> function(A) ) )),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f4,axiom,(
% 6.71/6.27 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(D,relation_dom(A))& C = apply(A,D) ) )) )) )) )),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f5,axiom,(
% 6.71/6.27 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f8,axiom,(
% 6.71/6.27 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f9,axiom,(
% 6.71/6.27 (! [A,B] :( ( relation(A)& function(A)& relation(B)& function(B) )=> ( relation(relation_composition(A,B))& function(relation_composition(A,B)) ) ) )),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f28,axiom,(
% 6.71/6.27 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(relation_composition(C,B)))<=> ( in(A,relation_dom(C))& in(apply(C,A),relation_dom(B)) ) ) ) )) )),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f29,axiom,(
% 6.71/6.27 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(relation_composition(C,B)))=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) )) )),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f30,conjecture,(
% 6.71/6.27 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_rng(relation_composition(C,B)))=> in(A,relation_rng(B)) ) ) )) )),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f31,negated_conjecture,(
% 6.71/6.27 ~((! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_rng(relation_composition(C,B)))=> in(A,relation_rng(B)) ) ) )) ))),
% 6.71/6.27 inference(negated_conjecture,[status(cth)],[f30])).
% 6.71/6.27 fof(f37,axiom,(
% 6.71/6.27 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 6.71/6.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.71/6.27 fof(f41,plain,(
% 6.71/6.27 ![A]: (~empty(A)|function(A))),
% 6.71/6.27 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 6.71/6.27 fof(f42,plain,(
% 6.71/6.27 ![X0]: (~empty(X0)|function(X0))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f41])).
% 6.71/6.27 fof(f45,plain,(
% 6.71/6.27 ![A]: ((~relation(A)|~function(A))|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))),
% 6.71/6.27 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 6.71/6.27 fof(f46,plain,(
% 6.71/6.27 ![A]: ((~relation(A)|~function(A))|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))&(in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D)))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 6.71/6.27 inference(NNF_transformation,[status(thm)],[f45])).
% 6.71/6.27 fof(f47,plain,(
% 6.71/6.27 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 6.71/6.27 inference(miniscoping,[status(thm)],[f46])).
% 6.71/6.27 fof(f48,plain,(
% 6.71/6.27 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(in(sK0_skl(C,B,A),relation_dom(A))&C=apply(A,sK0_skl(C,B,A)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|((~in(sK1_skl(B,A),B)|(![D]: (~in(D,relation_dom(A))|~sK1_skl(B,A)=apply(A,D))))&(in(sK1_skl(B,A),B)|(in(sK2_skl(B,A),relation_dom(A))&sK1_skl(B,A)=apply(A,sK2_skl(B,A)))))))))),
% 6.71/6.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(C,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f47])).
% 6.71/6.27 fof(f49,plain,(
% 6.71/6.27 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(sK0_skl(X2,X1,X0),relation_dom(X0)))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f48])).
% 6.71/6.27 fof(f50,plain,(
% 6.71/6.27 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|~in(X2,X1)|X2=apply(X0,sK0_skl(X2,X1,X0)))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f48])).
% 6.71/6.27 fof(f51,plain,(
% 6.71/6.27 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|in(X2,X1)|~in(X3,relation_dom(X0))|~X2=apply(X0,X3))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f48])).
% 6.71/6.27 fof(f55,plain,(
% 6.71/6.27 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 6.71/6.27 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 6.71/6.27 fof(f56,plain,(
% 6.71/6.27 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f55])).
% 6.71/6.27 fof(f62,plain,(
% 6.71/6.27 empty(empty_set)),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f8])).
% 6.71/6.27 fof(f63,plain,(
% 6.71/6.27 relation(empty_set)),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f8])).
% 6.71/6.27 fof(f65,plain,(
% 6.71/6.27 ![A,B]: ((((~relation(A)|~function(A))|~relation(B))|~function(B))|(relation(relation_composition(A,B))&function(relation_composition(A,B))))),
% 6.71/6.27 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 6.71/6.27 fof(f67,plain,(
% 6.71/6.27 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|function(relation_composition(X0,X1)))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f65])).
% 6.71/6.27 fof(f112,plain,(
% 6.71/6.27 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(in(A,relation_dom(relation_composition(C,B)))<=>(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B)))))))),
% 6.71/6.27 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 6.71/6.27 fof(f113,plain,(
% 6.71/6.27 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~in(A,relation_dom(relation_composition(C,B)))|(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B))))&(in(A,relation_dom(relation_composition(C,B)))|(~in(A,relation_dom(C))|~in(apply(C,A),relation_dom(B))))))))),
% 6.71/6.27 inference(NNF_transformation,[status(thm)],[f112])).
% 6.71/6.27 fof(f114,plain,(
% 6.71/6.27 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~in(A,relation_dom(relation_composition(C,B)))|(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B)))))&(![A]: (in(A,relation_dom(relation_composition(C,B)))|(~in(A,relation_dom(C))|~in(apply(C,A),relation_dom(B)))))))))),
% 6.71/6.27 inference(miniscoping,[status(thm)],[f113])).
% 6.71/6.27 fof(f116,plain,(
% 6.71/6.27 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~in(X2,relation_dom(relation_composition(X1,X0)))|in(apply(X1,X2),relation_dom(X0)))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f114])).
% 6.71/6.27 fof(f118,plain,(
% 6.71/6.27 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(~in(A,relation_dom(relation_composition(C,B)))|apply(relation_composition(C,B),A)=apply(B,apply(C,A))))))),
% 6.71/6.27 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 6.71/6.27 fof(f119,plain,(
% 6.71/6.27 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(![A]: (~in(A,relation_dom(relation_composition(C,B)))|apply(relation_composition(C,B),A)=apply(B,apply(C,A)))))))),
% 6.71/6.27 inference(miniscoping,[status(thm)],[f118])).
% 6.71/6.27 fof(f120,plain,(
% 6.71/6.27 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~in(X2,relation_dom(relation_composition(X1,X0)))|apply(relation_composition(X1,X0),X2)=apply(X0,apply(X1,X2)))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f119])).
% 6.71/6.27 fof(f121,plain,(
% 6.71/6.27 (?[A,B]: ((relation(B)&function(B))&(?[C]: ((relation(C)&function(C))&(in(A,relation_rng(relation_composition(C,B)))&~in(A,relation_rng(B)))))))),
% 6.71/6.27 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 6.71/6.27 fof(f122,plain,(
% 6.71/6.27 ?[B]: ((relation(B)&function(B))&(?[C]: ((relation(C)&function(C))&(?[A]: (in(A,relation_rng(relation_composition(C,B)))&~in(A,relation_rng(B)))))))),
% 6.71/6.27 inference(miniscoping,[status(thm)],[f121])).
% 6.71/6.27 fof(f123,plain,(
% 6.71/6.27 ((relation(sK12_skl)&function(sK12_skl))&((relation(sK13_skl)&function(sK13_skl))&(in(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)))&~in(sK14_skl,relation_rng(sK12_skl)))))),
% 6.71/6.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(B,sK12_skl),skolemize(C,sK13_skl),skolemize(A,sK14_skl)],[f122])).
% 6.71/6.27 fof(f124,plain,(
% 6.71/6.27 relation(sK12_skl)),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f123])).
% 6.71/6.27 fof(f125,plain,(
% 6.71/6.27 function(sK12_skl)),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f123])).
% 6.71/6.27 fof(f126,plain,(
% 6.71/6.27 relation(sK13_skl)),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f123])).
% 6.71/6.27 fof(f127,plain,(
% 6.71/6.27 function(sK13_skl)),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f123])).
% 6.71/6.27 fof(f128,plain,(
% 6.71/6.27 in(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f123])).
% 6.71/6.27 fof(f129,plain,(
% 6.71/6.27 ~in(sK14_skl,relation_rng(sK12_skl))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f123])).
% 6.71/6.27 fof(f144,plain,(
% 6.71/6.27 ![A,B]: (~in(A,B)|~empty(B))),
% 6.71/6.27 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 6.71/6.27 fof(f145,plain,(
% 6.71/6.27 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 6.71/6.27 inference(miniscoping,[status(thm)],[f144])).
% 6.71/6.27 fof(f146,plain,(
% 6.71/6.27 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 6.71/6.27 inference(cnf_transformation,[status(thm)],[f145])).
% 6.71/6.27 fof(f150,plain,(
% 6.71/6.27 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|in(sK0_skl(X1,relation_rng(X0),X0),relation_dom(X0)))),
% 6.71/6.27 inference(destructive_equality_resolution,[status(thm)],[f49])).
% 6.71/6.27 fof(f151,plain,(
% 6.71/6.27 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|X1=apply(X0,sK0_skl(X1,relation_rng(X0),X0)))),
% 6.71/6.27 inference(destructive_equality_resolution,[status(thm)],[f50])).
% 6.71/6.27 fof(f152,plain,(
% 6.71/6.27 ![X0,X1]: (~relation(X0)|~function(X0)|in(apply(X0,X1),relation_rng(X0))|~in(X1,relation_dom(X0)))),
% 6.71/6.27 inference(destructive_equality_resolution,[status(thm)],[f51])).
% 6.71/6.27 fof(f165,definition,(
% 6.71/6.27 sQ2_spl <=> (relation(sK13_skl))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f167,plain,(
% 6.71/6.27 ~relation(sK13_skl)|sQ2_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f165])).
% 6.71/6.27 fof(f172,definition,(
% 6.71/6.27 sQ4_spl <=> (relation(sK12_skl))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f174,plain,(
% 6.71/6.27 ~relation(sK12_skl)|sQ4_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f172])).
% 6.71/6.27 fof(f180,plain,(
% 6.71/6.27 $false|sQ4_spl),
% 6.71/6.27 inference(forward_subsumption_resolution,[status(thm)],[f174,f124])).
% 6.71/6.27 fof(f181,plain,(
% 6.71/6.27 sQ4_spl),
% 6.71/6.27 inference(contradiction_clause,[status(thm)],[f180])).
% 6.71/6.27 fof(f182,plain,(
% 6.71/6.27 $false|sQ2_spl),
% 6.71/6.27 inference(forward_subsumption_resolution,[status(thm)],[f167,f126])).
% 6.71/6.27 fof(f183,plain,(
% 6.71/6.27 sQ2_spl),
% 6.71/6.27 inference(contradiction_clause,[status(thm)],[f182])).
% 6.71/6.27 fof(f186,plain,(
% 6.71/6.27 ~relation(relation_composition(sK13_skl,sK12_skl))|~function(relation_composition(sK13_skl,sK12_skl))|sK14_skl=apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))),
% 6.71/6.27 inference(resolution,[status(thm)],[f128,f151])).
% 6.71/6.27 fof(f187,plain,(
% 6.71/6.27 ~relation(relation_composition(sK13_skl,sK12_skl))|~function(relation_composition(sK13_skl,sK12_skl))|in(sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)),relation_dom(relation_composition(sK13_skl,sK12_skl)))),
% 6.71/6.27 inference(resolution,[status(thm)],[f128,f150])).
% 6.71/6.27 fof(f189,definition,(
% 6.71/6.27 sQ6_spl <=> (relation(relation_composition(sK13_skl,sK12_skl)))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f191,plain,(
% 6.71/6.27 ~relation(relation_composition(sK13_skl,sK12_skl))|sQ6_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f189])).
% 6.71/6.27 fof(f192,definition,(
% 6.71/6.27 sQ7_spl <=> (function(relation_composition(sK13_skl,sK12_skl)))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f194,plain,(
% 6.71/6.27 ~function(relation_composition(sK13_skl,sK12_skl))|sQ7_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f192])).
% 6.71/6.27 fof(f195,definition,(
% 6.71/6.27 sQ8_spl <=> (sK14_skl=apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f196,plain,(
% 6.71/6.27 sK14_skl=apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))|~sQ8_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f195])).
% 6.71/6.27 fof(f198,plain,(
% 6.71/6.27 ~sQ6_spl|~sQ7_spl|sQ8_spl),
% 6.71/6.27 inference(split_clause,[status(thm)],[f186,f189,f192,f195])).
% 6.71/6.27 fof(f199,definition,(
% 6.71/6.27 sQ9_spl <=> (in(sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)),relation_dom(relation_composition(sK13_skl,sK12_skl))))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f200,plain,(
% 6.71/6.27 in(sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)),relation_dom(relation_composition(sK13_skl,sK12_skl)))|~sQ9_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f199])).
% 6.71/6.27 fof(f202,plain,(
% 6.71/6.27 ~sQ6_spl|~sQ7_spl|sQ9_spl),
% 6.71/6.27 inference(split_clause,[status(thm)],[f187,f189,f192,f199])).
% 6.71/6.27 fof(f212,definition,(
% 6.71/6.27 sQ11_spl <=> (function(sK12_skl))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f214,plain,(
% 6.71/6.27 ~function(sK12_skl)|sQ11_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f212])).
% 6.71/6.27 fof(f226,plain,(
% 6.71/6.27 ~relation(sK13_skl)|~function(sK13_skl)|~relation(sK12_skl)|~function(sK12_skl)|sQ7_spl),
% 6.71/6.27 inference(resolution,[status(thm)],[f194,f67])).
% 6.71/6.27 fof(f228,definition,(
% 6.71/6.27 sQ12_spl <=> (function(sK13_skl))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f230,plain,(
% 6.71/6.27 ~function(sK13_skl)|sQ12_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f228])).
% 6.71/6.27 fof(f231,plain,(
% 6.71/6.27 ~sQ2_spl|~sQ12_spl|~sQ4_spl|~sQ11_spl|sQ7_spl),
% 6.71/6.27 inference(split_clause,[status(thm)],[f226,f165,f228,f172,f212,f192])).
% 6.71/6.27 fof(f232,plain,(
% 6.71/6.27 $false|sQ11_spl),
% 6.71/6.27 inference(forward_subsumption_resolution,[status(thm)],[f214,f125])).
% 6.71/6.27 fof(f233,plain,(
% 6.71/6.27 sQ11_spl),
% 6.71/6.27 inference(contradiction_clause,[status(thm)],[f232])).
% 6.71/6.27 fof(f234,plain,(
% 6.71/6.27 $false|sQ12_spl),
% 6.71/6.27 inference(forward_subsumption_resolution,[status(thm)],[f230,f127])).
% 6.71/6.27 fof(f235,plain,(
% 6.71/6.27 sQ12_spl),
% 6.71/6.27 inference(contradiction_clause,[status(thm)],[f234])).
% 6.71/6.27 fof(f248,plain,(
% 6.71/6.27 ~relation(sK13_skl)|~relation(sK12_skl)|sQ6_spl),
% 6.71/6.27 inference(resolution,[status(thm)],[f191,f56])).
% 6.71/6.27 fof(f257,plain,(
% 6.71/6.27 ~sQ2_spl|~sQ4_spl|sQ6_spl),
% 6.71/6.27 inference(split_clause,[status(thm)],[f248,f165,f172,f189])).
% 6.71/6.27 fof(f266,plain,(
% 6.71/6.27 ![X0]: (~in(X0,empty_set))),
% 6.71/6.27 inference(resolution,[status(thm)],[f146,f62])).
% 6.71/6.27 fof(f415,definition,(
% 6.71/6.27 sQ28_spl <=> (empty_set=relation_rng(relation_composition(sK13_skl,sK12_skl)))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f416,plain,(
% 6.71/6.27 empty_set=relation_rng(relation_composition(sK13_skl,sK12_skl))|~sQ28_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f415])).
% 6.71/6.27 fof(f434,plain,(
% 6.71/6.27 in(sK14_skl,empty_set)|~sQ28_spl),
% 6.71/6.27 inference(backward_demodulation,[status(thm)],[f416,f128])).
% 6.71/6.27 fof(f449,plain,(
% 6.71/6.27 $false|~sQ28_spl),
% 6.71/6.27 inference(forward_subsumption_resolution,[status(thm)],[f434,f266])).
% 6.71/6.27 fof(f450,plain,(
% 6.71/6.27 ~sQ28_spl),
% 6.71/6.27 inference(contradiction_clause,[status(thm)],[f449])).
% 6.71/6.27 fof(f711,definition,(
% 6.71/6.27 sQ32_spl <=> (relation(empty_set))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f713,plain,(
% 6.71/6.27 ~relation(empty_set)|sQ32_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f711])).
% 6.71/6.27 fof(f714,definition,(
% 6.71/6.27 sQ33_spl <=> (function(empty_set))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f716,plain,(
% 6.71/6.27 ~function(empty_set)|sQ33_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f714])).
% 6.71/6.27 fof(f750,plain,(
% 6.71/6.27 ~relation(sK12_skl)|~function(sK12_skl)|~relation(sK13_skl)|~function(sK13_skl)|apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))=apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))))|~sQ9_spl),
% 6.71/6.27 inference(resolution,[status(thm)],[f200,f120])).
% 6.71/6.27 fof(f751,plain,(
% 6.71/6.27 ~relation(sK12_skl)|~function(sK12_skl)|~relation(sK13_skl)|~function(sK13_skl)|in(apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))),relation_dom(sK12_skl))|~sQ9_spl),
% 6.71/6.27 inference(resolution,[status(thm)],[f200,f116])).
% 6.71/6.27 fof(f755,definition,(
% 6.71/6.27 sQ41_spl <=> (apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))=apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f756,plain,(
% 6.71/6.27 apply(relation_composition(sK13_skl,sK12_skl),sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))=apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))))|~sQ41_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f755])).
% 6.71/6.27 fof(f758,plain,(
% 6.71/6.27 ~sQ4_spl|~sQ11_spl|~sQ2_spl|~sQ12_spl|sQ41_spl|~sQ9_spl),
% 6.71/6.27 inference(split_clause,[status(thm)],[f750,f172,f212,f165,f228,f755,f199])).
% 6.71/6.27 fof(f759,definition,(
% 6.71/6.27 sQ42_spl <=> (in(apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))),relation_dom(sK12_skl)))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f760,plain,(
% 6.71/6.27 in(apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))),relation_dom(sK12_skl))|~sQ42_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f759])).
% 6.71/6.27 fof(f762,plain,(
% 6.71/6.27 ~sQ4_spl|~sQ11_spl|~sQ2_spl|~sQ12_spl|sQ42_spl|~sQ9_spl),
% 6.71/6.27 inference(split_clause,[status(thm)],[f751,f172,f212,f165,f228,f759,f199])).
% 6.71/6.27 fof(f765,plain,(
% 6.71/6.27 sK14_skl=apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl))))|~sQ8_spl|~sQ41_spl),
% 6.71/6.27 inference(forward_demodulation,[status(thm)],[f196,f756])).
% 6.71/6.27 fof(f1256,plain,(
% 6.71/6.27 ~empty(empty_set)|sQ33_spl),
% 6.71/6.27 inference(resolution,[status(thm)],[f716,f42])).
% 6.71/6.27 fof(f1257,plain,(
% 6.71/6.27 $false|sQ33_spl),
% 6.71/6.27 inference(forward_subsumption_resolution,[status(thm)],[f1256,f62])).
% 6.71/6.27 fof(f1258,plain,(
% 6.71/6.27 sQ33_spl),
% 6.71/6.27 inference(contradiction_clause,[status(thm)],[f1257])).
% 6.71/6.27 fof(f1259,plain,(
% 6.71/6.27 $false|sQ32_spl),
% 6.71/6.27 inference(forward_subsumption_resolution,[status(thm)],[f713,f63])).
% 6.71/6.27 fof(f1260,plain,(
% 6.71/6.27 sQ32_spl),
% 6.71/6.27 inference(contradiction_clause,[status(thm)],[f1259])).
% 6.71/6.27 fof(f2054,plain,(
% 6.71/6.27 ~relation(sK12_skl)|~function(sK12_skl)|in(apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))),relation_rng(sK12_skl))|~sQ42_spl),
% 6.71/6.27 inference(resolution,[status(thm)],[f760,f152])).
% 6.71/6.27 fof(f2057,definition,(
% 6.71/6.27 sQ153_spl <=> (in(apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))),relation_rng(sK12_skl)))),
% 6.71/6.27 introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition])).
% 6.71/6.27 fof(f2058,plain,(
% 6.71/6.27 in(apply(sK12_skl,apply(sK13_skl,sK0_skl(sK14_skl,relation_rng(relation_composition(sK13_skl,sK12_skl)),relation_composition(sK13_skl,sK12_skl)))),relation_rng(sK12_skl))|~sQ153_spl),
% 6.71/6.27 inference(component_clause,[status(thm)],[f2057])).
% 6.71/6.27 fof(f2060,plain,(
% 6.71/6.27 ~sQ4_spl|~sQ11_spl|sQ153_spl|~sQ42_spl),
% 6.71/6.27 inference(split_clause,[status(thm)],[f2054,f172,f212,f2057,f759])).
% 6.71/6.27 fof(f2061,plain,(
% 6.71/6.27 in(sK14_skl,relation_rng(sK12_skl))|~sQ8_spl|~sQ41_spl|~sQ153_spl),
% 6.71/6.27 inference(forward_demodulation,[status(thm)],[f765,f2058])).
% 6.71/6.27 fof(f2062,plain,(
% 6.71/6.27 $false|~sQ8_spl|~sQ41_spl|~sQ153_spl),
% 6.71/6.29 inference(forward_subsumption_resolution,[status(thm)],[f2061,f129])).
% 6.71/6.29 fof(f2063,plain,(
% 6.71/6.29 ~sQ8_spl|~sQ41_spl|~sQ153_spl),
% 6.71/6.29 inference(contradiction_clause,[status(thm)],[f2062])).
% 6.71/6.29 fof(f2064,plain,(
% 6.71/6.29 $false),
% 6.71/6.29 inference(sat_refutation,[status(thm)],[f181,f183,f198,f202,f231,f233,f235,f257,f450,f758,f762,f1258,f1260,f2060,f2063])).
% 6.71/6.29 % SZS output end CNFRefutation for theBenchmark.p
% 6.71/6.30 % Elapsed time: 0.910406 seconds
% 6.71/6.30 % CPU time: 7.018484 seconds
% 6.71/6.30 % Total memory used: 186.153 MB
% 6.71/6.30 % Net memory used: 176.156 MB
%------------------------------------------------------------------------------