%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU014+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 : n011.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 02:21:35 PM UTC 2026
% Result : Theorem 57.79s 7.99s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU014+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
% 0.10/0.36 % Computer : n011.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:47:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 57.79/7.99 % Refutation found
% 57.79/7.99 % SZS status Theorem for theBenchmark: Theorem is valid
% 57.79/7.99 % SZS output start CNFRefutation for theBenchmark
% 57.79/7.99 fof(f2,axiom,(
% 57.79/7.99 (! [A] :( empty(A)=> function(A) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f4,axiom,(
% 57.79/7.99 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)<=> (! [B,C] :( ( in(B,relation_dom(A))& in(C,relation_dom(A))& apply(A,B) = apply(A,C) )=> B = C ) )) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f5,axiom,(
% 57.79/7.99 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f7,axiom,(
% 57.79/7.99 (! [A,B] :( ( empty(A)& relation(B) )=> ( empty(relation_composition(B,A))& relation(relation_composition(B,A)) ) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f8,axiom,(
% 57.79/7.99 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f9,axiom,(
% 57.79/7.99 (! [A,B] :( ( relation(A)& function(A)& relation(B)& function(B) )=> ( relation(relation_composition(A,B))& function(relation_composition(A,B)) ) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f10,axiom,(
% 57.79/7.99 (! [A] : ~ empty(powerset(A)) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f17,axiom,(
% 57.79/7.99 (! [A,B] :( ( empty(A)& relation(B) )=> ( empty(relation_composition(A,B))& relation(relation_composition(A,B)) ) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f18,axiom,(
% 57.79/7.99 (? [A] :( relation(A)& function(A) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f19,axiom,(
% 57.79/7.99 (? [A] :( empty(A)& relation(A) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f21,axiom,(
% 57.79/7.99 (? [A] : empty(A) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f22,axiom,(
% 57.79/7.99 (? [A] :( ~ empty(A)& relation(A) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f23,axiom,(
% 57.79/7.99 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f25,axiom,(
% 57.79/7.99 (? [A] :( relation(A)& relation_empty_yielding(A) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f28,axiom,(
% 57.79/7.99 (! [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)) ) ) )) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f30,axiom,(
% 57.79/7.99 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f31,axiom,(
% 57.79/7.99 (! [A] :( relation(A)=> (! [B] :( relation(B)=> ( subset(relation_rng(A),relation_dom(B))=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) )) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f32,conjecture,(
% 57.79/7.99 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( ( relation(B)& function(B) )=> ( ( one_to_one(relation_composition(B,A))& subset(relation_rng(B),relation_dom(A)) )=> one_to_one(B) ) ) )) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f33,negated_conjecture,(
% 57.79/7.99 ~((! [A] :( ( relation(A)& function(A) )=> (! [B] :( ( relation(B)& function(B) )=> ( ( one_to_one(relation_composition(B,A))& subset(relation_rng(B),relation_dom(A)) )=> one_to_one(B) ) ) )) ))),
% 57.79/7.99 inference(negated_conjecture,[status(cth)],[f32])).
% 57.79/7.99 fof(f36,axiom,(
% 57.79/7.99 (! [A] :( empty(A)=> A = empty_set ) )),
% 57.79/7.99 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 57.79/7.99 fof(f41,plain,(
% 57.79/7.99 ![A]: (~empty(A)|function(A))),
% 57.79/7.99 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 57.79/7.99 fof(f42,plain,(
% 57.79/7.99 ![X0]: (~empty(X0)|function(X0))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f41])).
% 57.79/7.99 fof(f45,plain,(
% 57.79/7.99 ![A]: ((~relation(A)|~function(A))|(one_to_one(A)<=>(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C))))),
% 57.79/7.99 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 57.79/7.99 fof(f46,plain,(
% 57.79/7.99 ![A]: ((~relation(A)|~function(A))|((~one_to_one(A)|(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C)))&(one_to_one(A)|(?[B,C]: (((in(B,relation_dom(A))&in(C,relation_dom(A)))&apply(A,B)=apply(A,C))&~B=C)))))),
% 57.79/7.99 inference(NNF_transformation,[status(thm)],[f45])).
% 57.79/7.99 fof(f47,plain,(
% 57.79/7.99 ![A]: ((~relation(A)|~function(A))|((~one_to_one(A)|(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C)))&(one_to_one(A)|(((in(sK0_skl(A),relation_dom(A))&in(sK1_skl(A),relation_dom(A)))&apply(A,sK0_skl(A))=apply(A,sK1_skl(A)))&~sK0_skl(A)=sK1_skl(A)))))),
% 57.79/7.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(B,sK0_skl(A)),skolemize(C,sK1_skl(A))],[f46])).
% 57.79/7.99 fof(f48,plain,(
% 57.79/7.99 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_dom(X0))|~in(X2,relation_dom(X0))|~apply(X0,X1)=apply(X0,X2)|X1=X2)),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f47])).
% 57.79/7.99 fof(f49,plain,(
% 57.79/7.99 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|in(sK0_skl(X0),relation_dom(X0)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f47])).
% 57.79/7.99 fof(f50,plain,(
% 57.79/7.99 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|in(sK1_skl(X0),relation_dom(X0)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f47])).
% 57.79/7.99 fof(f51,plain,(
% 57.79/7.99 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|apply(X0,sK0_skl(X0))=apply(X0,sK1_skl(X0)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f47])).
% 57.79/7.99 fof(f52,plain,(
% 57.79/7.99 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|~sK0_skl(X0)=sK1_skl(X0))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f47])).
% 57.79/7.99 fof(f53,plain,(
% 57.79/7.99 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 57.79/7.99 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 57.79/7.99 fof(f54,plain,(
% 57.79/7.99 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f53])).
% 57.79/7.99 fof(f57,plain,(
% 57.79/7.99 ![A,B]: ((~empty(A)|~relation(B))|(empty(relation_composition(B,A))&relation(relation_composition(B,A))))),
% 57.79/7.99 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 57.79/7.99 fof(f58,plain,(
% 57.79/7.99 ![X0,X1]: (~empty(X0)|~relation(X1)|empty(relation_composition(X1,X0)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f57])).
% 57.79/7.99 fof(f60,plain,(
% 57.79/7.99 empty(empty_set)),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f8])).
% 57.79/7.99 fof(f63,plain,(
% 57.79/7.99 ![A,B]: ((((~relation(A)|~function(A))|~relation(B))|~function(B))|(relation(relation_composition(A,B))&function(relation_composition(A,B))))),
% 57.79/7.99 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 57.79/7.99 fof(f65,plain,(
% 57.79/7.99 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|function(relation_composition(X0,X1)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f63])).
% 57.79/7.99 fof(f66,plain,(
% 57.79/7.99 ![X0]: (~empty(powerset(X0)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f10])).
% 57.79/7.99 fof(f80,plain,(
% 57.79/7.99 ![A,B]: ((~empty(A)|~relation(B))|(empty(relation_composition(A,B))&relation(relation_composition(A,B))))),
% 57.79/7.99 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 57.79/7.99 fof(f81,plain,(
% 57.79/7.99 ![X0,X1]: (~empty(X0)|~relation(X1)|empty(relation_composition(X0,X1)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f80])).
% 57.79/7.99 fof(f82,plain,(
% 57.79/7.99 ![X0,X1]: (~empty(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f80])).
% 57.79/7.99 fof(f83,plain,(
% 57.79/7.99 (relation(sK3_skl)&function(sK3_skl))),
% 57.79/7.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f18])).
% 57.79/7.99 fof(f84,plain,(
% 57.79/7.99 relation(sK3_skl)),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f83])).
% 57.79/7.99 fof(f86,plain,(
% 57.79/7.99 (empty(sK4_skl)&relation(sK4_skl))),
% 57.79/7.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f19])).
% 57.79/7.99 fof(f87,plain,(
% 57.79/7.99 empty(sK4_skl)),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f86])).
% 57.79/7.99 fof(f93,plain,(
% 57.79/7.99 empty(sK6_skl)),
% 57.79/7.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f21])).
% 57.79/7.99 fof(f94,plain,(
% 57.79/7.99 empty(sK6_skl)),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f93])).
% 57.79/7.99 fof(f95,plain,(
% 57.79/7.99 (~empty(sK7_skl)&relation(sK7_skl))),
% 57.79/7.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f22])).
% 57.79/7.99 fof(f97,plain,(
% 57.79/7.99 relation(sK7_skl)),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f95])).
% 57.79/7.99 fof(f98,plain,(
% 57.79/7.99 ![A]: (element(sK8_skl(A),powerset(A))&empty(sK8_skl(A)))),
% 57.79/7.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(B,sK8_skl(A))],[f23])).
% 57.79/7.99 fof(f99,plain,(
% 57.79/7.99 ![X0]: (element(sK8_skl(X0),powerset(X0)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f98])).
% 57.79/7.99 fof(f100,plain,(
% 57.79/7.99 ![X0]: (empty(sK8_skl(X0)))),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f98])).
% 57.79/7.99 fof(f103,plain,(
% 57.79/7.99 (relation(sK10_skl)&relation_empty_yielding(sK10_skl))),
% 57.79/7.99 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f25])).
% 57.79/7.99 fof(f104,plain,(
% 57.79/7.99 relation(sK10_skl)),
% 57.79/7.99 inference(cnf_transformation,[status(thm)],[f103])).
% 57.79/7.99 fof(f110,plain,(
% 57.79/7.99 ![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))))))),
% 57.79/7.99 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 57.79/7.99 fof(f111,plain,(
% 57.79/8.00 ![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)))))))),
% 57.79/8.00 inference(miniscoping,[status(thm)],[f110])).
% 57.79/8.00 fof(f112,plain,(
% 57.79/8.00 ![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)))),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f111])).
% 57.79/8.00 fof(f115,plain,(
% 57.79/8.00 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 57.79/8.00 inference(NNF_transformation,[status(thm)],[f30])).
% 57.79/8.00 fof(f116,plain,(
% 57.79/8.00 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 57.79/8.00 inference(miniscoping,[status(thm)],[f115])).
% 57.79/8.00 fof(f117,plain,(
% 57.79/8.00 ![X0,X1]: (~element(X0,powerset(X1))|subset(X0,X1))),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f116])).
% 57.79/8.00 fof(f119,plain,(
% 57.79/8.00 ![A]: (~relation(A)|(![B]: (~relation(B)|(~subset(relation_rng(A),relation_dom(B))|relation_dom(relation_composition(A,B))=relation_dom(A)))))),
% 57.79/8.00 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 57.79/8.00 fof(f120,plain,(
% 57.79/8.00 ![X0,X1]: (~relation(X0)|~relation(X1)|~subset(relation_rng(X0),relation_dom(X1))|relation_dom(relation_composition(X0,X1))=relation_dom(X0))),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f119])).
% 57.79/8.00 fof(f121,plain,(
% 57.79/8.00 (?[A]: ((relation(A)&function(A))&(?[B]: ((relation(B)&function(B))&((one_to_one(relation_composition(B,A))&subset(relation_rng(B),relation_dom(A)))&~one_to_one(B))))))),
% 57.79/8.00 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 57.79/8.00 fof(f122,plain,(
% 57.79/8.00 ((relation(sK11_skl)&function(sK11_skl))&((relation(sK12_skl)&function(sK12_skl))&((one_to_one(relation_composition(sK12_skl,sK11_skl))&subset(relation_rng(sK12_skl),relation_dom(sK11_skl)))&~one_to_one(sK12_skl))))),
% 57.79/8.00 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f121])).
% 57.79/8.00 fof(f123,plain,(
% 57.79/8.00 relation(sK11_skl)),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f122])).
% 57.79/8.00 fof(f124,plain,(
% 57.79/8.00 function(sK11_skl)),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f122])).
% 57.79/8.00 fof(f125,plain,(
% 57.79/8.00 relation(sK12_skl)),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f122])).
% 57.79/8.00 fof(f126,plain,(
% 57.79/8.00 function(sK12_skl)),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f122])).
% 57.79/8.00 fof(f127,plain,(
% 57.79/8.00 one_to_one(relation_composition(sK12_skl,sK11_skl))),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f122])).
% 57.79/8.00 fof(f128,plain,(
% 57.79/8.00 subset(relation_rng(sK12_skl),relation_dom(sK11_skl))),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f122])).
% 57.79/8.00 fof(f129,plain,(
% 57.79/8.00 ~one_to_one(sK12_skl)),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f122])).
% 57.79/8.00 fof(f136,plain,(
% 57.79/8.00 ![A]: (~empty(A)|A=empty_set)),
% 57.79/8.00 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 57.79/8.00 fof(f137,plain,(
% 57.79/8.00 ![X0]: (~empty(X0)|X0=empty_set)),
% 57.79/8.00 inference(cnf_transformation,[status(thm)],[f136])).
% 57.79/8.00 fof(f144,plain,(
% 57.79/8.00 ![X0]: (~relation(X0)|relation(relation_composition(sK12_skl,X0)))),
% 57.79/8.00 inference(resolution,[status(thm)],[f54,f125])).
% 57.79/8.00 fof(f150,plain,(
% 57.79/8.00 ~function(sK12_skl)|one_to_one(sK12_skl)|in(sK0_skl(sK12_skl),relation_dom(sK12_skl))),
% 57.79/8.00 inference(resolution,[status(thm)],[f49,f125])).
% 57.79/8.00 fof(f162,definition,(
% 57.79/8.00 sQ3_spl <=> (function(sK12_skl))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f164,plain,(
% 57.79/8.00 ~function(sK12_skl)|sQ3_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f162])).
% 57.79/8.00 fof(f165,definition,(
% 57.79/8.00 sQ4_spl <=> (one_to_one(sK12_skl))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f166,plain,(
% 57.79/8.00 one_to_one(sK12_skl)|~sQ4_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f165])).
% 57.79/8.00 fof(f168,definition,(
% 57.79/8.00 sQ5_spl <=> (in(sK0_skl(sK12_skl),relation_dom(sK12_skl)))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f169,plain,(
% 57.79/8.00 in(sK0_skl(sK12_skl),relation_dom(sK12_skl))|~sQ5_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f168])).
% 57.79/8.00 fof(f171,plain,(
% 57.79/8.00 ~sQ3_spl|sQ4_spl|sQ5_spl),
% 57.79/8.00 inference(split_clause,[status(thm)],[f150,f162,f165,f168])).
% 57.79/8.00 fof(f172,definition,(
% 57.79/8.00 sQ6_spl <=> (function(sK11_skl))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f174,plain,(
% 57.79/8.00 ~function(sK11_skl)|sQ6_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f172])).
% 57.79/8.00 fof(f182,plain,(
% 57.79/8.00 $false|sQ6_spl),
% 57.79/8.00 inference(forward_subsumption_resolution,[status(thm)],[f174,f124])).
% 57.79/8.00 fof(f183,plain,(
% 57.79/8.00 sQ6_spl),
% 57.79/8.00 inference(contradiction_clause,[status(thm)],[f182])).
% 57.79/8.00 fof(f184,plain,(
% 57.79/8.00 $false|sQ3_spl),
% 57.79/8.00 inference(forward_subsumption_resolution,[status(thm)],[f164,f126])).
% 57.79/8.00 fof(f185,plain,(
% 57.79/8.00 sQ3_spl),
% 57.79/8.00 inference(contradiction_clause,[status(thm)],[f184])).
% 57.79/8.00 fof(f187,plain,(
% 57.79/8.00 ~function(sK12_skl)|one_to_one(sK12_skl)|in(sK1_skl(sK12_skl),relation_dom(sK12_skl))),
% 57.79/8.00 inference(resolution,[status(thm)],[f50,f125])).
% 57.79/8.00 fof(f193,definition,(
% 57.79/8.00 sQ10_spl <=> (in(sK1_skl(sK12_skl),relation_dom(sK12_skl)))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f194,plain,(
% 57.79/8.00 in(sK1_skl(sK12_skl),relation_dom(sK12_skl))|~sQ10_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f193])).
% 57.79/8.00 fof(f196,plain,(
% 57.79/8.00 ~sQ3_spl|sQ4_spl|sQ10_spl),
% 57.79/8.00 inference(split_clause,[status(thm)],[f187,f162,f165,f193])).
% 57.79/8.00 fof(f202,plain,(
% 57.79/8.00 ~function(sK12_skl)|one_to_one(sK12_skl)|apply(sK12_skl,sK0_skl(sK12_skl))=apply(sK12_skl,sK1_skl(sK12_skl))),
% 57.79/8.00 inference(resolution,[status(thm)],[f51,f125])).
% 57.79/8.00 fof(f208,definition,(
% 57.79/8.00 sQ13_spl <=> (apply(sK12_skl,sK0_skl(sK12_skl))=apply(sK12_skl,sK1_skl(sK12_skl)))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f209,plain,(
% 57.79/8.00 apply(sK12_skl,sK0_skl(sK12_skl))=apply(sK12_skl,sK1_skl(sK12_skl))|~sQ13_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f208])).
% 57.79/8.00 fof(f211,plain,(
% 57.79/8.00 ~sQ3_spl|sQ4_spl|sQ13_spl),
% 57.79/8.00 inference(split_clause,[status(thm)],[f202,f162,f165,f208])).
% 57.79/8.00 fof(f217,plain,(
% 57.79/8.00 ~function(sK12_skl)|one_to_one(sK12_skl)|~sK0_skl(sK12_skl)=sK1_skl(sK12_skl)),
% 57.79/8.00 inference(resolution,[status(thm)],[f52,f125])).
% 57.79/8.00 fof(f223,definition,(
% 57.79/8.00 sQ16_spl <=> (sK0_skl(sK12_skl)=sK1_skl(sK12_skl))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f226,plain,(
% 57.79/8.00 ~sQ3_spl|sQ4_spl|~sQ16_spl),
% 57.79/8.00 inference(split_clause,[status(thm)],[f217,f162,f165,f223])).
% 57.79/8.00 fof(f231,plain,(
% 57.79/8.00 ![X0]: (~relation(X0)|empty(relation_composition(X0,empty_set)))),
% 57.79/8.00 inference(resolution,[status(thm)],[f58,f60])).
% 57.79/8.00 fof(f234,plain,(
% 57.79/8.00 ![X0]: (~function(sK12_skl)|~relation(X0)|~function(X0)|function(relation_composition(sK12_skl,X0)))),
% 57.79/8.00 inference(resolution,[status(thm)],[f65,f125])).
% 57.79/8.00 fof(f240,definition,(
% 57.79/8.00 ![X0]: (sQ19_spl <=> (~relation(X0)|~function(X0)|function(relation_composition(sK12_skl,X0))))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f241,plain,(
% 57.79/8.00 ![X0]: (~relation(X0)|~function(X0)|function(relation_composition(sK12_skl,X0))|~sQ19_spl)),
% 57.79/8.00 inference(component_clause,[status(thm)],[f240])).
% 57.79/8.00 fof(f243,plain,(
% 57.79/8.00 ~sQ3_spl|sQ19_spl),
% 57.79/8.00 inference(split_clause,[status(thm)],[f234,f162,f240])).
% 57.79/8.00 fof(f255,plain,(
% 57.79/8.00 relation(relation_composition(sK12_skl,sK11_skl))),
% 57.79/8.00 inference(resolution,[status(thm)],[f144,f123])).
% 57.79/8.00 fof(f259,plain,(
% 57.79/8.00 $false|~sQ4_spl),
% 57.79/8.00 inference(forward_subsumption_resolution,[status(thm)],[f166,f129])).
% 57.79/8.00 fof(f260,plain,(
% 57.79/8.00 ~sQ4_spl),
% 57.79/8.00 inference(contradiction_clause,[status(thm)],[f259])).
% 57.79/8.00 fof(f279,plain,(
% 57.79/8.00 ![X0]: (~relation(X0)|empty(relation_composition(empty_set,X0)))),
% 57.79/8.00 inference(resolution,[status(thm)],[f81,f60])).
% 57.79/8.00 fof(f284,plain,(
% 57.79/8.00 relation(relation_composition(sK12_skl,sK3_skl))),
% 57.79/8.00 inference(resolution,[status(thm)],[f84,f144])).
% 57.79/8.00 fof(f317,plain,(
% 57.79/8.00 ![X0]: (~relation(X0)|relation(relation_composition(sK4_skl,X0)))),
% 57.79/8.00 inference(resolution,[status(thm)],[f87,f82])).
% 57.79/8.00 fof(f326,plain,(
% 57.79/8.00 function(sK4_skl)),
% 57.79/8.00 inference(resolution,[status(thm)],[f87,f42])).
% 57.79/8.00 fof(f481,plain,(
% 57.79/8.00 ~function(sK11_skl)|function(relation_composition(sK12_skl,sK11_skl))|~sQ19_spl),
% 57.79/8.00 inference(resolution,[status(thm)],[f241,f123])).
% 57.79/8.00 fof(f503,definition,(
% 57.79/8.00 sQ63_spl <=> (function(relation_composition(sK12_skl,sK11_skl)))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f506,plain,(
% 57.79/8.00 ~sQ6_spl|sQ63_spl|~sQ19_spl),
% 57.79/8.00 inference(split_clause,[status(thm)],[f481,f172,f503,f240])).
% 57.79/8.00 fof(f511,plain,(
% 57.79/8.00 ~relation(sK12_skl)|~relation(sK11_skl)|relation_dom(relation_composition(sK12_skl,sK11_skl))=relation_dom(sK12_skl)),
% 57.79/8.00 inference(resolution,[status(thm)],[f120,f128])).
% 57.79/8.00 fof(f512,definition,(
% 57.79/8.00 sQ64_spl <=> (relation(sK12_skl))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f514,plain,(
% 57.79/8.00 ~relation(sK12_skl)|sQ64_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f512])).
% 57.79/8.00 fof(f515,definition,(
% 57.79/8.00 sQ65_spl <=> (relation(sK11_skl))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f517,plain,(
% 57.79/8.00 ~relation(sK11_skl)|sQ65_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f515])).
% 57.79/8.00 fof(f518,definition,(
% 57.79/8.00 sQ66_spl <=> (relation_dom(relation_composition(sK12_skl,sK11_skl))=relation_dom(sK12_skl))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f519,plain,(
% 57.79/8.00 relation_dom(relation_composition(sK12_skl,sK11_skl))=relation_dom(sK12_skl)|~sQ66_spl),
% 57.79/8.00 inference(component_clause,[status(thm)],[f518])).
% 57.79/8.00 fof(f521,plain,(
% 57.79/8.00 ~sQ64_spl|~sQ65_spl|sQ66_spl),
% 57.79/8.00 inference(split_clause,[status(thm)],[f511,f512,f515,f518])).
% 57.79/8.00 fof(f530,plain,(
% 57.79/8.00 empty(relation_composition(sK7_skl,empty_set))),
% 57.79/8.00 inference(resolution,[status(thm)],[f231,f97])).
% 57.79/8.00 fof(f536,plain,(
% 57.79/8.00 empty(relation_composition(sK10_skl,empty_set))),
% 57.79/8.00 inference(resolution,[status(thm)],[f104,f231])).
% 57.79/8.00 fof(f600,plain,(
% 57.79/8.00 ![X0,X1]: (~relation(X0)|~function(X0)|~function(sK11_skl)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sK11_skl),X1)=apply(sK11_skl,apply(X0,X1)))),
% 57.79/8.00 inference(resolution,[status(thm)],[f112,f123])).
% 57.79/8.00 fof(f629,definition,(
% 57.79/8.00 ![X0,X1]: (sQ83_spl <=> (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sK11_skl),X1)=apply(sK11_skl,apply(X0,X1))))),
% 57.79/8.00 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 57.79/8.00 fof(f630,plain,(
% 57.79/8.00 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sK11_skl),X1)=apply(sK11_skl,apply(X0,X1))|~sQ83_spl)),
% 57.79/8.00 inference(component_clause,[status(thm)],[f629])).
% 57.79/8.00 fof(f632,plain,(
% 57.79/8.00 sQ83_spl|~sQ6_spl),
% 57.79/8.00 inference(split_clause,[status(thm)],[f600,f629,f172])).
% 57.79/8.00 fof(f646,plain,(
% 57.79/8.00 $false|sQ64_spl),
% 57.79/8.00 inference(forward_subsumption_resolution,[status(thm)],[f514,f125])).
% 57.79/8.00 fof(f647,plain,(
% 57.79/8.00 sQ64_spl),
% 57.79/8.00 inference(contradiction_clause,[status(thm)],[f646])).
% 57.79/8.00 fof(f648,plain,(
% 57.79/8.00 $false|sQ65_spl),
% 57.79/8.00 inference(forward_subsumption_resolution,[status(thm)],[f517,f123])).
% 57.79/8.00 fof(f649,plain,(
% 57.79/8.00 sQ65_spl),
% 57.79/8.00 inference(contradiction_clause,[status(thm)],[f648])).
% 57.79/8.00 fof(f837,plain,(
% 57.79/8.00 ![X0]: (sK8_skl(X0)=empty_set)),
% 57.79/8.00 inference(resolution,[status(thm)],[f137,f100])).
% 57.79/8.00 fof(f838,plain,(
% 57.79/8.00 sK6_skl=empty_set),
% 57.79/8.00 inference(resolution,[status(thm)],[f137,f94])).
% 57.79/8.01 fof(f839,plain,(
% 57.79/8.01 sK4_skl=empty_set),
% 57.79/8.01 inference(resolution,[status(thm)],[f137,f87])).
% 57.79/8.01 fof(f861,plain,(
% 57.79/8.01 ~relation(sK12_skl)|~function(sK12_skl)|apply(relation_composition(sK12_skl,sK11_skl),sK1_skl(sK12_skl))=apply(sK11_skl,apply(sK12_skl,sK1_skl(sK12_skl)))|~sQ83_spl|~sQ10_spl),
% 57.79/8.01 inference(resolution,[status(thm)],[f630,f194])).
% 57.79/8.01 fof(f862,plain,(
% 57.79/8.01 ~relation(sK12_skl)|~function(sK12_skl)|apply(relation_composition(sK12_skl,sK11_skl),sK0_skl(sK12_skl))=apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))|~sQ83_spl|~sQ5_spl),
% 57.79/8.01 inference(resolution,[status(thm)],[f630,f169])).
% 57.79/8.01 fof(f863,definition,(
% 57.79/8.01 sQ118_spl <=> (apply(relation_composition(sK12_skl,sK11_skl),sK1_skl(sK12_skl))=apply(sK11_skl,apply(sK12_skl,sK1_skl(sK12_skl))))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f864,plain,(
% 57.79/8.01 apply(relation_composition(sK12_skl,sK11_skl),sK1_skl(sK12_skl))=apply(sK11_skl,apply(sK12_skl,sK1_skl(sK12_skl)))|~sQ118_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f863])).
% 57.79/8.01 fof(f866,plain,(
% 57.79/8.01 ~sQ64_spl|~sQ3_spl|sQ118_spl|~sQ83_spl|~sQ10_spl),
% 57.79/8.01 inference(split_clause,[status(thm)],[f861,f512,f162,f863,f629,f193])).
% 57.79/8.01 fof(f867,definition,(
% 57.79/8.01 sQ119_spl <=> (apply(relation_composition(sK12_skl,sK11_skl),sK0_skl(sK12_skl))=apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl))))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f870,plain,(
% 57.79/8.01 ~sQ64_spl|~sQ3_spl|sQ119_spl|~sQ83_spl|~sQ5_spl),
% 57.79/8.01 inference(split_clause,[status(thm)],[f862,f512,f162,f867,f629,f168])).
% 57.79/8.01 fof(f871,plain,(
% 57.79/8.01 apply(relation_composition(sK12_skl,sK11_skl),sK1_skl(sK12_skl))=apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))|~sQ13_spl|~sQ118_spl),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f209,f864])).
% 57.79/8.01 fof(f934,plain,(
% 57.79/8.01 empty(relation_composition(empty_set,sK10_skl))),
% 57.79/8.01 inference(resolution,[status(thm)],[f279,f104])).
% 57.79/8.01 fof(f936,plain,(
% 57.79/8.01 empty(relation_composition(empty_set,sK7_skl))),
% 57.79/8.01 inference(resolution,[status(thm)],[f279,f97])).
% 57.79/8.01 fof(f945,plain,(
% 57.79/8.01 ![X0]: (~empty(X0)|X0=sK6_skl)),
% 57.79/8.01 inference(backward_demodulation,[status(thm)],[f838,f137])).
% 57.79/8.01 fof(f961,plain,(
% 57.79/8.01 sK4_skl=sK6_skl),
% 57.79/8.01 inference(resolution,[status(thm)],[f945,f87])).
% 57.79/8.01 fof(f1050,plain,(
% 57.79/8.01 ![X0,X1]: (~relation(relation_composition(sK12_skl,sK11_skl))|~function(relation_composition(sK12_skl,sK11_skl))|~one_to_one(relation_composition(sK12_skl,sK11_skl))|~in(X0,relation_dom(sK12_skl))|~in(X1,relation_dom(relation_composition(sK12_skl,sK11_skl)))|~apply(relation_composition(sK12_skl,sK11_skl),X0)=apply(relation_composition(sK12_skl,sK11_skl),X1)|X0=X1|~sQ66_spl)),
% 57.79/8.01 inference(paramodulation,[status(thm)],[f519,f48])).
% 57.79/8.01 fof(f1051,definition,(
% 57.79/8.01 sQ143_spl <=> (relation(relation_composition(sK12_skl,sK11_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f1053,plain,(
% 57.79/8.01 ~relation(relation_composition(sK12_skl,sK11_skl))|sQ143_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f1051])).
% 57.79/8.01 fof(f1073,definition,(
% 57.79/8.01 sQ149_spl <=> (one_to_one(relation_composition(sK12_skl,sK11_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f1075,plain,(
% 57.79/8.01 ~one_to_one(relation_composition(sK12_skl,sK11_skl))|sQ149_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f1073])).
% 57.79/8.01 fof(f1076,definition,(
% 57.79/8.01 ![X0,X1]: (sQ150_spl <=> (~in(X0,relation_dom(sK12_skl))|~in(X1,relation_dom(relation_composition(sK12_skl,sK11_skl)))|~apply(relation_composition(sK12_skl,sK11_skl),X0)=apply(relation_composition(sK12_skl,sK11_skl),X1)|X0=X1))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f1077,plain,(
% 57.79/8.01 ![X0,X1]: (~in(X0,relation_dom(sK12_skl))|~in(X1,relation_dom(relation_composition(sK12_skl,sK11_skl)))|~apply(relation_composition(sK12_skl,sK11_skl),X0)=apply(relation_composition(sK12_skl,sK11_skl),X1)|X0=X1|~sQ150_spl)),
% 57.79/8.01 inference(component_clause,[status(thm)],[f1076])).
% 57.79/8.01 fof(f1079,plain,(
% 57.79/8.01 ~sQ143_spl|~sQ63_spl|~sQ149_spl|sQ150_spl|~sQ66_spl),
% 57.79/8.01 inference(split_clause,[status(thm)],[f1050,f1051,f503,f1073,f1076,f518])).
% 57.79/8.01 fof(f1193,plain,(
% 57.79/8.01 ![X0]: (~empty(X0)|X0=sK4_skl)),
% 57.79/8.01 inference(backward_demodulation,[status(thm)],[f961,f945])).
% 57.79/8.01 fof(f1266,plain,(
% 57.79/8.01 relation(relation_composition(sK4_skl,relation_composition(sK12_skl,sK11_skl)))),
% 57.79/8.01 inference(resolution,[status(thm)],[f255,f317])).
% 57.79/8.01 fof(f1371,plain,(
% 57.79/8.01 ![X0]: (element(sK4_skl,powerset(X0)))),
% 57.79/8.01 inference(backward_demodulation,[status(thm)],[f1372,f99])).
% 57.79/8.01 fof(f1372,plain,(
% 57.79/8.01 ![X0]: (sK8_skl(X0)=sK4_skl)),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f839,f837])).
% 57.79/8.01 fof(f1841,definition,(
% 57.79/8.01 sQ260_spl <=> (function(relation_composition(sK4_skl,sK10_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f1843,plain,(
% 57.79/8.01 ~function(relation_composition(sK4_skl,sK10_skl))|sQ260_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f1841])).
% 57.79/8.01 fof(f1845,definition,(
% 57.79/8.01 sQ261_spl <=> (function(relation_composition(sK4_skl,sK7_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f1847,plain,(
% 57.79/8.01 ~function(relation_composition(sK4_skl,sK7_skl))|sQ261_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f1845])).
% 57.79/8.01 fof(f2497,plain,(
% 57.79/8.01 empty(relation_composition(sK7_skl,sK4_skl))),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f839,f530])).
% 57.79/8.01 fof(f2498,plain,(
% 57.79/8.01 relation_composition(sK7_skl,sK4_skl)=sK4_skl),
% 57.79/8.01 inference(resolution,[status(thm)],[f2497,f1193])).
% 57.79/8.01 fof(f2565,plain,(
% 57.79/8.01 empty(relation_composition(sK10_skl,sK4_skl))),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f839,f536])).
% 57.79/8.01 fof(f2566,plain,(
% 57.79/8.01 relation_composition(sK10_skl,sK4_skl)=sK4_skl),
% 57.79/8.01 inference(resolution,[status(thm)],[f2565,f1193])).
% 57.79/8.01 fof(f2794,definition,(
% 57.79/8.01 sQ388_spl <=> (function(relation_composition(sK10_skl,sK4_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f2796,plain,(
% 57.79/8.01 ~function(relation_composition(sK10_skl,sK4_skl))|sQ388_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f2794])).
% 57.79/8.01 fof(f2861,definition,(
% 57.79/8.01 sQ400_spl <=> (function(relation_composition(sK7_skl,sK4_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f2863,plain,(
% 57.79/8.01 ~function(relation_composition(sK7_skl,sK4_skl))|sQ400_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f2861])).
% 57.79/8.01 fof(f3063,plain,(
% 57.79/8.01 empty(relation_composition(sK4_skl,sK10_skl))),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f839,f934])).
% 57.79/8.01 fof(f3064,plain,(
% 57.79/8.01 relation_composition(sK4_skl,sK10_skl)=sK4_skl),
% 57.79/8.01 inference(resolution,[status(thm)],[f3063,f1193])).
% 57.79/8.01 fof(f3087,plain,(
% 57.79/8.01 empty(relation_composition(sK4_skl,sK7_skl))),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f839,f936])).
% 57.79/8.01 fof(f3088,plain,(
% 57.79/8.01 relation_composition(sK4_skl,sK7_skl)=sK4_skl),
% 57.79/8.01 inference(resolution,[status(thm)],[f3087,f1193])).
% 57.79/8.01 fof(f3455,plain,(
% 57.79/8.01 $false|sQ143_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f1053,f255])).
% 57.79/8.01 fof(f3456,plain,(
% 57.79/8.01 sQ143_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f3455])).
% 57.79/8.01 fof(f3459,plain,(
% 57.79/8.01 $false|sQ149_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f1075,f127])).
% 57.79/8.01 fof(f3460,plain,(
% 57.79/8.01 sQ149_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f3459])).
% 57.79/8.01 fof(f3461,plain,(
% 57.79/8.01 ![X0,X1]: (~in(X0,relation_dom(sK12_skl))|~in(X1,relation_dom(sK12_skl))|~apply(relation_composition(sK12_skl,sK11_skl),X0)=apply(relation_composition(sK12_skl,sK11_skl),X1)|X0=X1|~sQ66_spl|~sQ150_spl)),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f519,f1077])).
% 57.79/8.01 fof(f4781,definition,(
% 57.79/8.01 sQ724_spl <=> (relation(sK3_skl))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ724_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f4783,plain,(
% 57.79/8.01 ~relation(sK3_skl)|sQ724_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f4781])).
% 57.79/8.01 fof(f5093,plain,(
% 57.79/8.01 $false|sQ724_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f4783,f84])).
% 57.79/8.01 fof(f5094,plain,(
% 57.79/8.01 sQ724_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f5093])).
% 57.79/8.01 fof(f5139,plain,(
% 57.79/8.01 ![X0]: (subset(sK4_skl,X0))),
% 57.79/8.01 inference(resolution,[status(thm)],[f1371,f117])).
% 57.79/8.01 fof(f5411,definition,(
% 57.79/8.01 sQ740_spl <=> (relation(relation_composition(sK12_skl,sK3_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ740_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f5413,plain,(
% 57.79/8.01 ~relation(relation_composition(sK12_skl,sK3_skl))|sQ740_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f5411])).
% 57.79/8.01 fof(f6294,definition,(
% 57.79/8.01 sQ817_spl <=> (empty(powerset(sK4_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ817_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f6295,plain,(
% 57.79/8.01 empty(powerset(sK4_skl))|~sQ817_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f6294])).
% 57.79/8.01 fof(f6301,plain,(
% 57.79/8.01 $false|~sQ817_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f6295,f66])).
% 57.79/8.01 fof(f6302,plain,(
% 57.79/8.01 ~sQ817_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f6301])).
% 57.79/8.01 fof(f7120,definition,(
% 57.79/8.01 sQ847_spl <=> (subset(sK4_skl,relation_dom(sK12_skl)))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ847_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f7122,plain,(
% 57.79/8.01 ~subset(sK4_skl,relation_dom(sK12_skl))|sQ847_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f7120])).
% 57.79/8.01 fof(f7129,plain,(
% 57.79/8.01 $false|sQ847_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f7122,f5139])).
% 57.79/8.01 fof(f7130,plain,(
% 57.79/8.01 sQ847_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f7129])).
% 57.79/8.01 fof(f7173,plain,(
% 57.79/8.01 ![X0]: (~in(X0,relation_dom(sK12_skl))|~apply(relation_composition(sK12_skl,sK11_skl),sK1_skl(sK12_skl))=apply(relation_composition(sK12_skl,sK11_skl),X0)|sK1_skl(sK12_skl)=X0|~sQ66_spl|~sQ150_spl|~sQ10_spl)),
% 57.79/8.01 inference(resolution,[status(thm)],[f3461,f194])).
% 57.79/8.01 fof(f8102,plain,(
% 57.79/8.01 ~function(sK4_skl)|sQ388_spl),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f2566,f2796])).
% 57.79/8.01 fof(f8103,plain,(
% 57.79/8.01 $false|sQ388_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f8102,f326])).
% 57.79/8.01 fof(f8104,plain,(
% 57.79/8.01 sQ388_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f8103])).
% 57.79/8.01 fof(f8124,plain,(
% 57.79/8.01 ~function(sK4_skl)|sQ400_spl),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f2498,f2863])).
% 57.79/8.01 fof(f8125,plain,(
% 57.79/8.01 $false|sQ400_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f8124,f326])).
% 57.79/8.01 fof(f8126,plain,(
% 57.79/8.01 sQ400_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f8125])).
% 57.79/8.01 fof(f8160,plain,(
% 57.79/8.01 ~function(sK4_skl)|sQ260_spl),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f3064,f1843])).
% 57.79/8.01 fof(f8161,plain,(
% 57.79/8.01 $false|sQ260_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f8160,f326])).
% 57.79/8.01 fof(f8162,plain,(
% 57.79/8.01 sQ260_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f8161])).
% 57.79/8.01 fof(f8178,plain,(
% 57.79/8.01 ~function(sK4_skl)|sQ261_spl),
% 57.79/8.01 inference(forward_demodulation,[status(thm)],[f3088,f1847])).
% 57.79/8.01 fof(f8179,plain,(
% 57.79/8.01 $false|sQ261_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f8178,f326])).
% 57.79/8.01 fof(f8180,plain,(
% 57.79/8.01 sQ261_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f8179])).
% 57.79/8.01 fof(f15318,definition,(
% 57.79/8.01 sQ2031_spl <=> (subset(sK4_skl,sK4_skl))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ2031_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f15320,plain,(
% 57.79/8.01 ~subset(sK4_skl,sK4_skl)|sQ2031_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f15318])).
% 57.79/8.01 fof(f15325,plain,(
% 57.79/8.01 $false|sQ2031_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f15320,f5139])).
% 57.79/8.01 fof(f15326,plain,(
% 57.79/8.01 sQ2031_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f15325])).
% 57.79/8.01 fof(f17736,plain,(
% 57.79/8.01 $false|sQ740_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f5413,f284])).
% 57.79/8.01 fof(f17737,plain,(
% 57.79/8.01 sQ740_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f17736])).
% 57.79/8.01 fof(f30442,definition,(
% 57.79/8.01 sQ4095_spl <=> (relation(relation_composition(sK4_skl,relation_composition(sK12_skl,sK11_skl))))),
% 57.79/8.01 introduced(definition,[new_symbols(definition,[sQ4095_spl])],[split_symbol_definition])).
% 57.79/8.01 fof(f30444,plain,(
% 57.79/8.01 ~relation(relation_composition(sK4_skl,relation_composition(sK12_skl,sK11_skl)))|sQ4095_spl),
% 57.79/8.01 inference(component_clause,[status(thm)],[f30442])).
% 57.79/8.01 fof(f30481,plain,(
% 57.79/8.01 $false|sQ4095_spl),
% 57.79/8.01 inference(forward_subsumption_resolution,[status(thm)],[f30444,f1266])).
% 57.79/8.01 fof(f30482,plain,(
% 57.79/8.01 sQ4095_spl),
% 57.79/8.01 inference(contradiction_clause,[status(thm)],[f30481])).
% 51.11/8.06 fof(f30500,plain,(
% 51.11/8.06 ![X0]: (~in(X0,relation_dom(sK12_skl))|~apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))=apply(relation_composition(sK12_skl,sK11_skl),X0)|sK1_skl(sK12_skl)=X0|~sQ13_spl|~sQ118_spl|~sQ66_spl|~sQ150_spl|~sQ10_spl)),
% 51.11/8.06 inference(forward_demodulation,[status(thm)],[f871,f7173])).
% 51.11/8.06 fof(f30504,plain,(
% 51.11/8.06 ~apply(sK11_skl,apply(sK12_skl,sK0_skl(sK12_skl)))=apply(relation_composition(sK12_skl,sK11_skl),sK0_skl(sK12_skl))|sK1_skl(sK12_skl)=sK0_skl(sK12_skl)|~sQ13_spl|~sQ118_spl|~sQ66_spl|~sQ150_spl|~sQ10_spl|~sQ5_spl),
% 51.11/8.06 inference(resolution,[status(thm)],[f30500,f169])).
% 51.11/8.06 fof(f30523,plain,(
% 51.11/8.06 ~sQ119_spl|sQ16_spl|~sQ13_spl|~sQ118_spl|~sQ66_spl|~sQ150_spl|~sQ10_spl|~sQ5_spl),
% 51.11/8.06 inference(split_clause,[status(thm)],[f30504,f867,f223,f208,f863,f518,f1076,f193,f168])).
% 51.11/8.06 fof(f30524,plain,(
% 51.11/8.06 $false),
% 51.11/8.06 inference(sat_refutation,[status(thm)],[f171,f183,f185,f196,f211,f226,f243,f260,f506,f521,f632,f647,f649,f866,f870,f1079,f3456,f3460,f5094,f6302,f7130,f8104,f8126,f8162,f8180,f15326,f17737,f30482,f30523])).
% 51.11/8.06 % SZS output end CNFRefutation for theBenchmark.p
% 4.12/8.13 % Elapsed time: 7.731069 seconds
% 4.12/8.13 % CPU time: 60.701056 seconds
% 4.12/8.13 % Total memory used: 586.436 MB
% 4.12/8.13 % Net memory used: 557.945 MB
%------------------------------------------------------------------------------