%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 02:22:02 PM UTC 2026
% Result : Theorem 1.21s 0.72s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:01:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.21/0.72 % Refutation found
% 1.21/0.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.21/0.72 % SZS output start CNFRefutation for theBenchmark
% 1.21/0.72 fof(f5,axiom,(
% 1.21/0.72 (! [A] :( ( relation(A)& function(A) )=> ( relation(function_inverse(A))& function(function_inverse(A)) ) ) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f9,axiom,(
% 1.21/0.72 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f19,axiom,(
% 1.21/0.72 (? [A] :( relation(A)& function(A) ) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f23,axiom,(
% 1.21/0.72 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f27,axiom,(
% 1.21/0.72 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f31,axiom,(
% 1.21/0.72 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(B))=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) )) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f35,axiom,(
% 1.21/0.72 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> (! [B] :( ( relation(B)& function(B) )=> ( B = function_inverse(A)<=> ( relation_dom(B) = relation_rng(A)& (! [C,D] :( ( ( in(C,relation_rng(A))& D = apply(B,C) )=> ( in(D,relation_dom(A))& C = apply(A,D) ) )& ( ( in(D,relation_dom(A))& C = apply(A,D) )=> ( in(C,relation_rng(A))& D = apply(B,C) ) ) ) )) ) ) )) ) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f36,axiom,(
% 1.21/0.72 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> ( relation_rng(A) = relation_dom(function_inverse(A))& relation_dom(A) = relation_rng(function_inverse(A)) ) ) ) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f37,conjecture,(
% 1.21/0.72 (! [A,B] :( ( relation(B)& function(B) )=> ( ( one_to_one(B)& in(A,relation_rng(B)) )=> ( A = apply(B,apply(function_inverse(B),A))& A = apply(relation_composition(function_inverse(B),B),A) ) ) ) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f38,negated_conjecture,(
% 1.21/0.72 ~((! [A,B] :( ( relation(B)& function(B) )=> ( ( one_to_one(B)& in(A,relation_rng(B)) )=> ( A = apply(B,apply(function_inverse(B),A))& A = apply(relation_composition(function_inverse(B),B),A) ) ) ) ))),
% 1.21/0.72 inference(negated_conjecture,[status(cth)],[f37])).
% 1.21/0.72 fof(f41,axiom,(
% 1.21/0.72 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 1.21/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.21/0.72 fof(f53,plain,(
% 1.21/0.72 ![A]: ((~relation(A)|~function(A))|(relation(function_inverse(A))&function(function_inverse(A))))),
% 1.21/0.72 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 1.21/0.72 fof(f54,plain,(
% 1.21/0.72 ![X0]: (~relation(X0)|~function(X0)|relation(function_inverse(X0)))),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f53])).
% 1.21/0.72 fof(f55,plain,(
% 1.21/0.72 ![X0]: (~relation(X0)|~function(X0)|function(function_inverse(X0)))),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f53])).
% 1.21/0.72 fof(f63,plain,(
% 1.21/0.72 empty(empty_set)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f9])).
% 1.21/0.72 fof(f64,plain,(
% 1.21/0.72 relation(empty_set)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f9])).
% 1.21/0.72 fof(f86,plain,(
% 1.21/0.72 (relation(sK1_skl)&function(sK1_skl))),
% 1.21/0.72 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(A,sK1_skl)],[f19])).
% 1.21/0.72 fof(f87,plain,(
% 1.21/0.72 relation(sK1_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f86])).
% 1.21/0.72 fof(f98,plain,(
% 1.21/0.72 ((relation(sK5_skl)&empty(sK5_skl))&function(sK5_skl))),
% 1.21/0.72 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f23])).
% 1.21/0.72 fof(f100,plain,(
% 1.21/0.72 empty(sK5_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f98])).
% 1.21/0.72 fof(f110,plain,(
% 1.21/0.72 ((relation(sK9_skl)&function(sK9_skl))&one_to_one(sK9_skl))),
% 1.21/0.72 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f27])).
% 1.21/0.72 fof(f111,plain,(
% 1.21/0.72 relation(sK9_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f110])).
% 1.21/0.72 fof(f112,plain,(
% 1.21/0.72 function(sK9_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f110])).
% 1.21/0.72 fof(f113,plain,(
% 1.21/0.72 one_to_one(sK9_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f110])).
% 1.21/0.72 fof(f121,plain,(
% 1.21/0.72 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(~in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A))))))),
% 1.21/0.72 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 1.21/0.72 fof(f122,plain,(
% 1.21/0.72 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(![A]: (~in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A)))))))),
% 1.21/0.72 inference(miniscoping,[status(thm)],[f121])).
% 1.21/0.72 fof(f123,plain,(
% 1.21/0.72 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~in(X2,relation_dom(X0))|apply(relation_composition(X0,X1),X2)=apply(X1,apply(X0,X2)))),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f122])).
% 1.21/0.72 fof(f133,plain,(
% 1.21/0.72 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|(B=function_inverse(A)<=>(relation_dom(B)=relation_rng(A)&(![C,D]: (((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D)))&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))))))),
% 1.21/0.72 inference(pre_NNF_transformation,[status(thm)],[f35])).
% 1.21/0.72 fof(f134,definition,(
% 1.21/0.72 ![A,B,C,D]: (sP0_prd(D,C,B,A)<=>((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D))))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 1.21/0.72 fof(f135,plain,(
% 1.21/0.72 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|(B=function_inverse(A)<=>(relation_dom(B)=relation_rng(A)&(![C,D]: (sP0_prd(D,C,B,A)&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))))))),
% 1.21/0.72 inference(formula_renaming,[status(thm)],[f133,f134])).
% 1.21/0.72 fof(f136,plain,(
% 1.21/0.72 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&(![C,D]: (sP0_prd(D,C,B,A)&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|(?[C,D]: (~sP0_prd(D,C,B,A)|((in(D,relation_dom(A))&C=apply(A,D))&(~in(C,relation_rng(A))|~D=apply(B,C))))))))))))),
% 1.21/0.72 inference(NNF_transformation,[status(thm)],[f135])).
% 1.21/0.72 fof(f137,plain,(
% 1.21/0.72 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&((![C,D]: sP0_prd(D,C,B,A))&(![C,D]: ((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|((?[C,D]: ~sP0_prd(D,C,B,A))|(?[C,D]: ((in(D,relation_dom(A))&C=apply(A,D))&(~in(C,relation_rng(A))|~D=apply(B,C))))))))))))),
% 1.21/0.72 inference(miniscoping,[status(thm)],[f136])).
% 1.21/0.72 fof(f138,plain,(
% 1.21/0.72 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&((![C,D]: sP0_prd(D,C,B,A))&(![C,D]: ((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|(~sP0_prd(sK12_skl(B,A),sK11_skl(B,A),B,A)|((in(sK14_skl(B,A),relation_dom(A))&sK13_skl(B,A)=apply(A,sK14_skl(B,A)))&(~in(sK13_skl(B,A),relation_rng(A))|~sK14_skl(B,A)=apply(B,sK13_skl(B,A))))))))))))),
% 1.21/0.72 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(C,sK11_skl(B,A)),skolemize(D,sK12_skl(B,A)),skolemize(C,sK13_skl(B,A)),skolemize(D,sK14_skl(B,A))],[f137])).
% 1.21/0.72 fof(f140,plain,(
% 1.21/0.72 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~relation(X1)|~function(X1)|~X1=function_inverse(X0)|sP0_prd(X2,X3,X1,X0))),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f138])).
% 1.21/0.72 fof(f146,plain,(
% 1.21/0.72 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(relation_rng(A)=relation_dom(function_inverse(A))&relation_dom(A)=relation_rng(function_inverse(A)))))),
% 1.21/0.72 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 1.21/0.72 fof(f147,plain,(
% 1.21/0.72 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_rng(X0)=relation_dom(function_inverse(X0)))),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f146])).
% 1.21/0.72 fof(f149,plain,(
% 1.21/0.72 (?[A,B]: ((relation(B)&function(B))&((one_to_one(B)&in(A,relation_rng(B)))&(~A=apply(B,apply(function_inverse(B),A))|~A=apply(relation_composition(function_inverse(B),B),A)))))),
% 1.21/0.72 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 1.21/0.72 fof(f150,plain,(
% 1.21/0.72 ?[B]: ((relation(B)&function(B))&(?[A]: ((one_to_one(B)&in(A,relation_rng(B)))&(~A=apply(B,apply(function_inverse(B),A))|~A=apply(relation_composition(function_inverse(B),B),A)))))),
% 1.21/0.72 inference(miniscoping,[status(thm)],[f149])).
% 1.21/0.72 fof(f151,plain,(
% 1.21/0.72 ((relation(sK15_skl)&function(sK15_skl))&((one_to_one(sK15_skl)&in(sK16_skl,relation_rng(sK15_skl)))&(~sK16_skl=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl))|~sK16_skl=apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl))))),
% 1.21/0.72 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(B,sK15_skl),skolemize(A,sK16_skl)],[f150])).
% 1.21/0.72 fof(f152,plain,(
% 1.21/0.72 relation(sK15_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f151])).
% 1.21/0.72 fof(f153,plain,(
% 1.21/0.72 function(sK15_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f151])).
% 1.21/0.72 fof(f154,plain,(
% 1.21/0.72 one_to_one(sK15_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f151])).
% 1.21/0.72 fof(f155,plain,(
% 1.21/0.72 in(sK16_skl,relation_rng(sK15_skl))),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f151])).
% 1.21/0.72 fof(f156,plain,(
% 1.21/0.72 ~sK16_skl=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl))|~sK16_skl=apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl)),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f151])).
% 1.21/0.72 fof(f162,plain,(
% 1.21/0.72 ![A,B]: (~in(A,B)|~empty(B))),
% 1.21/0.72 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 1.21/0.72 fof(f163,plain,(
% 1.21/0.72 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 1.21/0.72 inference(miniscoping,[status(thm)],[f162])).
% 1.21/0.72 fof(f164,plain,(
% 1.21/0.72 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f163])).
% 1.21/0.72 fof(f168,plain,(
% 1.21/0.72 ![A,B,C,D]: ((~sP0_prd(D,C,B,A)|((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D))))&(sP0_prd(D,C,B,A)|((in(C,relation_rng(A))&D=apply(B,C))&(~in(D,relation_dom(A))|~C=apply(A,D)))))),
% 1.21/0.72 inference(NNF_transformation,[status(thm)],[f134])).
% 1.21/0.72 fof(f169,plain,(
% 1.21/0.72 (![A,B,C,D]: (~sP0_prd(D,C,B,A)|((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D)))))&(![A,B,C,D]: (sP0_prd(D,C,B,A)|((in(C,relation_rng(A))&D=apply(B,C))&(~in(D,relation_dom(A))|~C=apply(A,D)))))),
% 1.21/0.72 inference(miniscoping,[status(thm)],[f168])).
% 1.21/0.72 fof(f171,plain,(
% 1.21/0.72 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|~in(X1,relation_rng(X3))|~X0=apply(X2,X1)|X1=apply(X3,X0))),
% 1.21/0.72 inference(cnf_transformation,[status(thm)],[f169])).
% 1.21/0.72 fof(f175,definition,(
% 1.21/0.72 sQ0_spl <=> (sK16_skl=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f177,plain,(
% 1.21/0.72 ~sK16_skl=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl))|sQ0_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f175])).
% 1.21/0.72 fof(f178,definition,(
% 1.21/0.72 sQ1_spl <=> (sK16_skl=apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f180,plain,(
% 1.21/0.72 ~sK16_skl=apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl)|sQ1_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f178])).
% 1.21/0.72 fof(f181,plain,(
% 1.21/0.72 ~sQ0_spl|~sQ1_spl),
% 1.21/0.72 inference(split_clause,[status(thm)],[f156,f175,f178])).
% 1.21/0.72 fof(f185,plain,(
% 1.21/0.72 ![X0,X2,X3]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~relation(function_inverse(X0))|~function(function_inverse(X0))|sP0_prd(X2,X3,function_inverse(X0),X0))),
% 1.21/0.72 inference(destructive_equality_resolution,[status(thm)],[f140])).
% 1.21/0.72 fof(f186,plain,(
% 1.21/0.72 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~function(function_inverse(X0))|sP0_prd(X1,X2,function_inverse(X0),X0))),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f185,f54])).
% 1.21/0.72 fof(f192,plain,(
% 1.21/0.72 ![X0,X1,X2]: (~sP0_prd(apply(X0,X1),X1,X0,X2)|~in(X1,relation_rng(X2))|X1=apply(X2,apply(X0,X1)))),
% 1.21/0.72 inference(destructive_equality_resolution,[status(thm)],[f171])).
% 1.21/0.72 fof(f202,plain,(
% 1.21/0.72 ~empty(relation_rng(sK15_skl))),
% 1.21/0.72 inference(resolution,[status(thm)],[f164,f155])).
% 1.21/0.72 fof(f204,plain,(
% 1.21/0.72 ~relation(sK15_skl)|~function(sK15_skl)|relation_rng(sK15_skl)=relation_dom(function_inverse(sK15_skl))),
% 1.21/0.72 inference(resolution,[status(thm)],[f147,f154])).
% 1.21/0.72 fof(f206,definition,(
% 1.21/0.72 sQ2_spl <=> (relation(sK15_skl))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f208,plain,(
% 1.21/0.72 ~relation(sK15_skl)|sQ2_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f206])).
% 1.21/0.72 fof(f209,definition,(
% 1.21/0.72 sQ3_spl <=> (function(sK15_skl))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f211,plain,(
% 1.21/0.72 ~function(sK15_skl)|sQ3_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f209])).
% 1.21/0.72 fof(f212,definition,(
% 1.21/0.72 sQ4_spl <=> (relation_rng(sK15_skl)=relation_dom(function_inverse(sK15_skl)))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f213,plain,(
% 1.21/0.72 relation_rng(sK15_skl)=relation_dom(function_inverse(sK15_skl))|~sQ4_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f212])).
% 1.21/0.72 fof(f215,plain,(
% 1.21/0.72 ~sQ2_spl|~sQ3_spl|sQ4_spl),
% 1.21/0.72 inference(split_clause,[status(thm)],[f204,f206,f209,f212])).
% 1.21/0.72 fof(f221,plain,(
% 1.21/0.72 ![X0,X1]: (~relation(function_inverse(sK15_skl))|~function(function_inverse(sK15_skl))|~relation(X0)|~function(X0)|~in(X1,relation_rng(sK15_skl))|apply(relation_composition(function_inverse(sK15_skl),X0),X1)=apply(X0,apply(function_inverse(sK15_skl),X1))|~sQ4_spl)),
% 1.21/0.72 inference(paramodulation,[status(thm)],[f213,f123])).
% 1.21/0.72 fof(f229,definition,(
% 1.21/0.72 sQ7_spl <=> (empty(relation_rng(sK15_skl)))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f230,plain,(
% 1.21/0.72 empty(relation_rng(sK15_skl))|~sQ7_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f229])).
% 1.21/0.72 fof(f233,definition,(
% 1.21/0.72 sQ8_spl <=> (relation(function_inverse(sK15_skl)))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f235,plain,(
% 1.21/0.72 ~relation(function_inverse(sK15_skl))|sQ8_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f233])).
% 1.21/0.72 fof(f237,definition,(
% 1.21/0.72 sQ9_spl <=> (function(function_inverse(sK15_skl)))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f239,plain,(
% 1.21/0.72 ~function(function_inverse(sK15_skl))|sQ9_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f237])).
% 1.21/0.72 fof(f240,definition,(
% 1.21/0.72 ![X0,X1]: (sQ10_spl <=> (~relation(X0)|~function(X0)|~in(X1,relation_rng(sK15_skl))|apply(relation_composition(function_inverse(sK15_skl),X0),X1)=apply(X0,apply(function_inverse(sK15_skl),X1))))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f241,plain,(
% 1.21/0.72 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(sK15_skl))|apply(relation_composition(function_inverse(sK15_skl),X0),X1)=apply(X0,apply(function_inverse(sK15_skl),X1))|~sQ10_spl)),
% 1.21/0.72 inference(component_clause,[status(thm)],[f240])).
% 1.21/0.72 fof(f243,plain,(
% 1.21/0.72 ~sQ8_spl|~sQ9_spl|sQ10_spl|~sQ4_spl),
% 1.21/0.72 inference(split_clause,[status(thm)],[f221,f233,f237,f240,f212])).
% 1.21/0.72 fof(f244,plain,(
% 1.21/0.72 $false|sQ3_spl),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f211,f153])).
% 1.21/0.72 fof(f245,plain,(
% 1.21/0.72 sQ3_spl),
% 1.21/0.72 inference(contradiction_clause,[status(thm)],[f244])).
% 1.21/0.72 fof(f254,plain,(
% 1.21/0.72 $false|sQ2_spl),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f208,f152])).
% 1.21/0.72 fof(f255,plain,(
% 1.21/0.72 sQ2_spl),
% 1.21/0.72 inference(contradiction_clause,[status(thm)],[f254])).
% 1.21/0.72 fof(f258,definition,(
% 1.21/0.72 sQ12_spl <=> (relation(sK9_skl))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f260,plain,(
% 1.21/0.72 ~relation(sK9_skl)|sQ12_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f258])).
% 1.21/0.72 fof(f261,definition,(
% 1.21/0.72 sQ13_spl <=> (function(sK9_skl))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f263,plain,(
% 1.21/0.72 ~function(sK9_skl)|sQ13_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f261])).
% 1.21/0.72 fof(f272,plain,(
% 1.21/0.72 $false|sQ13_spl),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f263,f112])).
% 1.21/0.72 fof(f273,plain,(
% 1.21/0.72 sQ13_spl),
% 1.21/0.72 inference(contradiction_clause,[status(thm)],[f272])).
% 1.21/0.72 fof(f274,plain,(
% 1.21/0.72 $false|sQ12_spl),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f260,f111])).
% 1.21/0.72 fof(f275,plain,(
% 1.21/0.72 sQ12_spl),
% 1.21/0.72 inference(contradiction_clause,[status(thm)],[f274])).
% 1.21/0.72 fof(f315,plain,(
% 1.21/0.72 ~relation(sK15_skl)|~function(sK15_skl)|sQ8_spl),
% 1.21/0.72 inference(resolution,[status(thm)],[f235,f54])).
% 1.21/0.72 fof(f316,plain,(
% 1.21/0.72 ~sQ2_spl|~sQ3_spl|sQ8_spl),
% 1.21/0.72 inference(split_clause,[status(thm)],[f315,f206,f209,f233])).
% 1.21/0.72 fof(f317,plain,(
% 1.21/0.72 $false|~sQ7_spl),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f230,f202])).
% 1.21/0.72 fof(f318,plain,(
% 1.21/0.72 ~sQ7_spl),
% 1.21/0.72 inference(contradiction_clause,[status(thm)],[f317])).
% 1.21/0.72 fof(f333,definition,(
% 1.21/0.72 sQ24_spl <=> (empty(sK5_skl))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f335,plain,(
% 1.21/0.72 ~empty(sK5_skl)|sQ24_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f333])).
% 1.21/0.72 fof(f367,plain,(
% 1.21/0.72 $false|sQ24_spl),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f335,f100])).
% 1.21/0.72 fof(f368,plain,(
% 1.21/0.72 sQ24_spl),
% 1.21/0.72 inference(contradiction_clause,[status(thm)],[f367])).
% 1.21/0.72 fof(f430,plain,(
% 1.21/0.72 ~relation(sK15_skl)|~function(sK15_skl)|sQ9_spl),
% 1.21/0.72 inference(resolution,[status(thm)],[f239,f55])).
% 1.21/0.72 fof(f432,plain,(
% 1.21/0.72 ~sQ2_spl|~sQ3_spl|sQ9_spl),
% 1.21/0.72 inference(split_clause,[status(thm)],[f430,f206,f209,f237])).
% 1.21/0.72 fof(f524,plain,(
% 1.21/0.72 ![X0]: (~relation(X0)|~function(X0)|apply(relation_composition(function_inverse(sK15_skl),X0),sK16_skl)=apply(X0,apply(function_inverse(sK15_skl),sK16_skl))|~sQ10_spl)),
% 1.21/0.72 inference(resolution,[status(thm)],[f241,f155])).
% 1.21/0.72 fof(f632,plain,(
% 1.21/0.72 ![X0,X1]: (~in(X0,relation_rng(X1))|X0=apply(X1,apply(function_inverse(X1),X0))|~relation(X1)|~function(X1)|~one_to_one(X1)|~function(function_inverse(X1)))),
% 1.21/0.72 inference(resolution,[status(thm)],[f192,f186])).
% 1.21/0.72 fof(f633,plain,(
% 1.21/0.72 ![X0,X1]: (~in(X0,relation_rng(X1))|X0=apply(X1,apply(function_inverse(X1),X0))|~relation(X1)|~function(X1)|~one_to_one(X1))),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f632,f55])).
% 1.21/0.72 fof(f648,plain,(
% 1.21/0.72 ~relation(sK15_skl)|apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl)=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl))|~sQ10_spl),
% 1.21/0.72 inference(resolution,[status(thm)],[f524,f153])).
% 1.21/0.72 fof(f655,definition,(
% 1.21/0.72 sQ56_spl <=> (relation(sK1_skl))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f657,plain,(
% 1.21/0.72 ~relation(sK1_skl)|sQ56_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f655])).
% 1.21/0.72 fof(f674,definition,(
% 1.21/0.72 sQ61_spl <=> (apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl)=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f675,plain,(
% 1.21/0.72 apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl)=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl))|~sQ61_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f674])).
% 1.21/0.72 fof(f677,plain,(
% 1.21/0.72 ~sQ2_spl|sQ61_spl|~sQ10_spl),
% 1.21/0.72 inference(split_clause,[status(thm)],[f648,f206,f674,f240])).
% 1.21/0.72 fof(f679,plain,(
% 1.21/0.72 $false|sQ56_spl),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f657,f87])).
% 1.21/0.72 fof(f680,plain,(
% 1.21/0.72 sQ56_spl),
% 1.21/0.72 inference(contradiction_clause,[status(thm)],[f679])).
% 1.21/0.72 fof(f781,definition,(
% 1.21/0.72 sQ64_spl <=> (relation(empty_set))),
% 1.21/0.72 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 1.21/0.72 fof(f783,plain,(
% 1.21/0.72 ~relation(empty_set)|sQ64_spl),
% 1.21/0.72 inference(component_clause,[status(thm)],[f781])).
% 1.21/0.72 fof(f788,plain,(
% 1.21/0.72 $false|sQ64_spl),
% 1.21/0.72 inference(forward_subsumption_resolution,[status(thm)],[f783,f64])).
% 1.21/0.72 fof(f789,plain,(
% 1.21/0.72 sQ64_spl),
% 1.21/0.72 inference(contradiction_clause,[status(thm)],[f788])).
% 1.21/0.72 fof(f818,plain,(
% 1.21/0.72 ![X0]: (~in(X0,relation_rng(sK15_skl))|X0=apply(sK15_skl,apply(function_inverse(sK15_skl),X0))|~relation(sK15_skl)|~function(sK15_skl))),
% 1.21/0.72 inference(resolution,[status(thm)],[f633,f154])).
% 1.21/0.72 fof(f824,definition,(
% 1.21/0.72 ![X0]: (sQ68_spl <=> (~in(X0,relation_rng(sK15_skl))|X0=apply(sK15_skl,apply(function_inverse(sK15_skl),X0))))),
% 1.21/0.73 introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition])).
% 1.21/0.73 fof(f825,plain,(
% 1.21/0.73 ![X0]: (~in(X0,relation_rng(sK15_skl))|X0=apply(sK15_skl,apply(function_inverse(sK15_skl),X0))|~sQ68_spl)),
% 1.21/0.73 inference(component_clause,[status(thm)],[f824])).
% 1.21/0.73 fof(f827,plain,(
% 1.21/0.73 sQ68_spl|~sQ2_spl|~sQ3_spl),
% 1.21/0.73 inference(split_clause,[status(thm)],[f818,f824,f206,f209])).
% 1.21/0.73 fof(f838,definition,(
% 1.21/0.73 sQ69_spl <=> (one_to_one(sK9_skl))),
% 1.21/0.73 introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 1.21/0.73 fof(f840,plain,(
% 1.21/0.73 ~one_to_one(sK9_skl)|sQ69_spl),
% 1.21/0.73 inference(component_clause,[status(thm)],[f838])).
% 1.21/0.73 fof(f850,definition,(
% 1.21/0.73 sQ72_spl <=> (empty(empty_set))),
% 1.21/0.73 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 1.21/0.73 fof(f852,plain,(
% 1.21/0.73 ~empty(empty_set)|sQ72_spl),
% 1.21/0.73 inference(component_clause,[status(thm)],[f850])).
% 1.21/0.73 fof(f859,plain,(
% 1.21/0.73 $false|sQ69_spl),
% 1.21/0.73 inference(forward_subsumption_resolution,[status(thm)],[f840,f113])).
% 1.21/0.73 fof(f860,plain,(
% 1.21/0.73 sQ69_spl),
% 1.21/0.73 inference(contradiction_clause,[status(thm)],[f859])).
% 1.21/0.73 fof(f861,plain,(
% 1.21/0.73 $false|sQ72_spl),
% 1.21/0.73 inference(forward_subsumption_resolution,[status(thm)],[f852,f63])).
% 1.21/0.73 fof(f862,plain,(
% 1.21/0.73 sQ72_spl),
% 1.21/0.73 inference(contradiction_clause,[status(thm)],[f861])).
% 1.21/0.73 fof(f952,plain,(
% 1.21/0.73 sK16_skl=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl))|~sQ68_spl),
% 1.21/0.73 inference(resolution,[status(thm)],[f825,f155])).
% 1.21/0.73 fof(f957,plain,(
% 1.21/0.73 $false|sQ0_spl|~sQ68_spl),
% 1.21/0.73 inference(forward_subsumption_resolution,[status(thm)],[f952,f177])).
% 1.21/0.73 fof(f958,plain,(
% 1.21/0.73 sQ0_spl|~sQ68_spl),
% 1.21/0.73 inference(contradiction_clause,[status(thm)],[f957])).
% 1.21/0.73 fof(f959,plain,(
% 1.21/0.73 ~sK16_skl=apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl))|~sQ61_spl|sQ1_spl),
% 1.21/0.73 inference(forward_demodulation,[status(thm)],[f675,f180])).
% 1.21/0.73 fof(f960,plain,(
% 1.21/0.73 $false|~sQ61_spl|sQ1_spl|~sQ68_spl),
% 1.21/0.73 inference(forward_subsumption_resolution,[status(thm)],[f952,f959])).
% 1.21/0.73 fof(f961,plain,(
% 1.21/0.73 ~sQ61_spl|sQ1_spl|~sQ68_spl),
% 1.21/0.73 inference(contradiction_clause,[status(thm)],[f960])).
% 1.21/0.73 fof(f962,plain,(
% 1.21/0.73 $false),
% 1.21/0.73 inference(sat_refutation,[status(thm)],[f181,f215,f243,f245,f255,f273,f275,f316,f318,f368,f432,f677,f680,f789,f827,f860,f862,f958,f961])).
% 1.21/0.73 % SZS output end CNFRefutation for theBenchmark.p
% 0.27/0.75 % Elapsed time: 0.365177 seconds
% 0.27/0.75 % CPU time: 2.474215 seconds
% 0.27/0.75 % Total memory used: 114.479 MB
% 0.27/0.75 % Net memory used: 112.465 MB
%------------------------------------------------------------------------------