%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET996+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 : n018.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 02:12:58 PM UTC 2026
% Result : Theorem 21.40s 3.14s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET996+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
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:48:29 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 21.40/3.14 % Refutation found
% 21.40/3.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 21.40/3.14 % SZS output start CNFRefutation for theBenchmark
% 21.40/3.14 fof(f2,axiom,(
% 21.40/3.14 (! [A] :( empty(A)=> function(A) ) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f4,axiom,(
% 21.40/3.14 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f5,axiom,(
% 21.40/3.14 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(D,relation_dom(A))& C = apply(A,D) ) )) )) )) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f7,axiom,(
% 21.40/3.14 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f13,axiom,(
% 21.40/3.14 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f14,axiom,(
% 21.40/3.14 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f23,axiom,(
% 21.40/3.14 (! [A,B] : subset(A,A) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f24,axiom,(
% 21.40/3.14 (! [A,B,C] :( element(C,A)=> (? [D] :( relation(D)& function(D)& relation_dom(D) = B& (! [E] :( in(E,B)=> apply(D,E) = C ) )) )) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f25,conjecture,(
% 21.40/3.14 (! [A,B] :~ ( ~ ( A = empty_set& B != empty_set )& (! [C] :( ( relation(C)& function(C) )=> ~ ( B = relation_dom(C)& subset(relation_rng(C),A) ) ) )) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f26,negated_conjecture,(
% 21.40/3.14 ~((! [A,B] :~ ( ~ ( A = empty_set& B != empty_set )& (! [C] :( ( relation(C)& function(C) )=> ~ ( B = relation_dom(C)& subset(relation_rng(C),A) ) ) )) ))),
% 21.40/3.14 inference(negated_conjecture,[status(cth)],[f25])).
% 21.40/3.14 fof(f29,axiom,(
% 21.40/3.14 (! [A] : subset(empty_set,A) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f30,axiom,(
% 21.40/3.14 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f33,axiom,(
% 21.40/3.14 (! [A] :( empty(A)=> A = empty_set ) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f34,axiom,(
% 21.40/3.14 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 21.40/3.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 21.40/3.14 fof(f38,plain,(
% 21.40/3.14 ![A]: (~empty(A)|function(A))),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 21.40/3.14 fof(f39,plain,(
% 21.40/3.14 ![X0]: (~empty(X0)|function(X0))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f38])).
% 21.40/3.14 fof(f42,plain,(
% 21.40/3.14 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 21.40/3.14 fof(f43,plain,(
% 21.40/3.14 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 21.40/3.14 inference(NNF_transformation,[status(thm)],[f42])).
% 21.40/3.14 fof(f44,plain,(
% 21.40/3.14 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 21.40/3.14 inference(miniscoping,[status(thm)],[f43])).
% 21.40/3.14 fof(f45,plain,(
% 21.40/3.14 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK0_skl(B,A),A)&~in(sK0_skl(B,A),B))))),
% 21.40/3.14 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f44])).
% 21.40/3.14 fof(f47,plain,(
% 21.40/3.14 ![X0,X1]: (subset(X0,X1)|in(sK0_skl(X1,X0),X0))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f45])).
% 21.40/3.14 fof(f48,plain,(
% 21.40/3.14 ![X0,X1]: (subset(X0,X1)|~in(sK0_skl(X1,X0),X1))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f45])).
% 21.40/3.14 fof(f49,plain,(
% 21.40/3.14 ![A]: ((~relation(A)|~function(A))|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 21.40/3.14 fof(f50,plain,(
% 21.40/3.14 ![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))))))))))),
% 21.40/3.14 inference(NNF_transformation,[status(thm)],[f49])).
% 21.40/3.14 fof(f51,plain,(
% 21.40/3.14 ![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))))))))))),
% 21.40/3.14 inference(miniscoping,[status(thm)],[f50])).
% 21.40/3.14 fof(f52,plain,(
% 21.40/3.14 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(in(sK1_skl(C,B,A),relation_dom(A))&C=apply(A,sK1_skl(C,B,A)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|((~in(sK2_skl(B,A),B)|(![D]: (~in(D,relation_dom(A))|~sK2_skl(B,A)=apply(A,D))))&(in(sK2_skl(B,A),B)|(in(sK3_skl(B,A),relation_dom(A))&sK2_skl(B,A)=apply(A,sK3_skl(B,A)))))))))),
% 21.40/3.14 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f51])).
% 21.40/3.14 fof(f53,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(sK1_skl(X2,X1,X0),relation_dom(X0)))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f52])).
% 21.40/3.14 fof(f54,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|~in(X2,X1)|X2=apply(X0,sK1_skl(X2,X1,X0)))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f52])).
% 21.40/3.14 fof(f57,plain,(
% 21.40/3.14 ![X0,X1]: (~relation(X0)|~function(X0)|X1=relation_rng(X0)|in(sK2_skl(X1,X0),X1)|in(sK3_skl(X1,X0),relation_dom(X0)))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f52])).
% 21.40/3.14 fof(f61,plain,(
% 21.40/3.14 empty(empty_set)),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f7])).
% 21.40/3.14 fof(f62,plain,(
% 21.40/3.14 relation(empty_set)),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f7])).
% 21.40/3.14 fof(f72,plain,(
% 21.40/3.14 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 21.40/3.14 fof(f73,plain,(
% 21.40/3.14 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f72])).
% 21.40/3.14 fof(f75,plain,(
% 21.40/3.14 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 21.40/3.14 fof(f76,plain,(
% 21.40/3.14 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f75])).
% 21.40/3.14 fof(f101,plain,(
% 21.40/3.14 ![A]: subset(A,A)),
% 21.40/3.14 inference(miniscoping,[status(thm)],[f23])).
% 21.40/3.14 fof(f102,plain,(
% 21.40/3.14 ![X0]: (subset(X0,X0))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f101])).
% 21.40/3.14 fof(f103,plain,(
% 21.40/3.14 ![A,B,C]: (~element(C,A)|(?[D]: (((relation(D)&function(D))&relation_dom(D)=B)&(![E]: (~in(E,B)|apply(D,E)=C)))))),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 21.40/3.14 fof(f104,plain,(
% 21.40/3.14 ![C]: ((![A]: ~element(C,A))|(![B]: ?[D]: (((relation(D)&function(D))&relation_dom(D)=B)&(![E]: (~in(E,B)|apply(D,E)=C)))))),
% 21.40/3.14 inference(miniscoping,[status(thm)],[f103])).
% 21.40/3.14 fof(f105,plain,(
% 21.40/3.14 ![C]: ((![A]: ~element(C,A))|(![B]: (((relation(sK13_skl(B,C))&function(sK13_skl(B,C)))&relation_dom(sK13_skl(B,C))=B)&(![E]: (~in(E,B)|apply(sK13_skl(B,C),E)=C)))))),
% 21.40/3.14 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(D,sK13_skl(B,C))],[f104])).
% 21.40/3.14 fof(f106,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~element(X0,X1)|relation(sK13_skl(X2,X0)))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f105])).
% 21.40/3.14 fof(f107,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~element(X0,X1)|function(sK13_skl(X2,X0)))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f105])).
% 21.40/3.14 fof(f108,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~element(X0,X1)|relation_dom(sK13_skl(X2,X0))=X2)),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f105])).
% 21.40/3.14 fof(f109,plain,(
% 21.40/3.14 ![X0,X1,X2,X3]: (~element(X0,X1)|~in(X2,X3)|apply(sK13_skl(X3,X0),X2)=X0)),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f105])).
% 21.40/3.14 fof(f110,plain,(
% 21.40/3.14 (?[A,B]: ((~A=empty_set|B=empty_set)&(![C]: ((~relation(C)|~function(C))|(~B=relation_dom(C)|~subset(relation_rng(C),A))))))),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 21.40/3.14 fof(f111,plain,(
% 21.40/3.14 ((~sK14_skl=empty_set|sK15_skl=empty_set)&(![C]: ((~relation(C)|~function(C))|(~sK15_skl=relation_dom(C)|~subset(relation_rng(C),sK14_skl)))))),
% 21.40/3.14 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(A,sK14_skl),skolemize(B,sK15_skl)],[f110])).
% 21.40/3.14 fof(f112,plain,(
% 21.40/3.14 ~sK14_skl=empty_set|sK15_skl=empty_set),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f111])).
% 21.40/3.14 fof(f113,plain,(
% 21.40/3.14 ![X0]: (~relation(X0)|~function(X0)|~sK15_skl=relation_dom(X0)|~subset(relation_rng(X0),sK14_skl))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f111])).
% 21.40/3.14 fof(f118,plain,(
% 21.40/3.14 ![X0]: (subset(empty_set,X0))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f29])).
% 21.40/3.14 fof(f119,plain,(
% 21.40/3.14 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 21.40/3.14 inference(NNF_transformation,[status(thm)],[f30])).
% 21.40/3.14 fof(f120,plain,(
% 21.40/3.14 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 21.40/3.14 inference(miniscoping,[status(thm)],[f119])).
% 21.40/3.14 fof(f122,plain,(
% 21.40/3.14 ![X0,X1]: (element(X0,powerset(X1))|~subset(X0,X1))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f120])).
% 21.40/3.14 fof(f129,plain,(
% 21.40/3.14 ![A]: (~empty(A)|A=empty_set)),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 21.40/3.14 fof(f130,plain,(
% 21.40/3.14 ![X0]: (~empty(X0)|X0=empty_set)),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f129])).
% 21.40/3.14 fof(f131,plain,(
% 21.40/3.14 ![A,B]: (~in(A,B)|~empty(B))),
% 21.40/3.14 inference(pre_NNF_transformation,[status(thm)],[f34])).
% 21.40/3.14 fof(f132,plain,(
% 21.40/3.14 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 21.40/3.14 inference(miniscoping,[status(thm)],[f131])).
% 21.40/3.14 fof(f133,plain,(
% 21.40/3.14 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 21.40/3.14 inference(cnf_transformation,[status(thm)],[f132])).
% 21.40/3.14 fof(f137,plain,(
% 21.40/3.14 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|in(sK1_skl(X1,relation_rng(X0),X0),relation_dom(X0)))),
% 21.40/3.14 inference(destructive_equality_resolution,[status(thm)],[f53])).
% 21.40/3.14 fof(f138,plain,(
% 21.40/3.14 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|X1=apply(X0,sK1_skl(X1,relation_rng(X0),X0)))),
% 21.40/3.14 inference(destructive_equality_resolution,[status(thm)],[f54])).
% 21.40/3.14 fof(f140,plain,(
% 21.40/3.14 function(empty_set)),
% 21.40/3.14 inference(resolution,[status(thm)],[f61,f39])).
% 21.40/3.14 fof(f145,plain,(
% 21.40/3.14 ![X0,X1]: (~relation(X0)|~function(X0)|in(sK1_skl(sK0_skl(X1,relation_rng(X0)),relation_rng(X0),X0),relation_dom(X0))|subset(relation_rng(X0),X1))),
% 21.40/3.14 inference(resolution,[status(thm)],[f137,f47])).
% 21.40/3.14 fof(f151,plain,(
% 21.40/3.14 empty(relation_dom(empty_set))),
% 21.40/3.14 inference(resolution,[status(thm)],[f73,f61])).
% 21.40/3.14 fof(f153,plain,(
% 21.40/3.14 empty(relation_rng(empty_set))),
% 21.40/3.14 inference(resolution,[status(thm)],[f76,f61])).
% 21.40/3.14 fof(f164,plain,(
% 21.40/3.14 ![X0]: (~relation(empty_set)|X0=relation_rng(empty_set)|in(sK2_skl(X0,empty_set),X0)|in(sK3_skl(X0,empty_set),relation_dom(empty_set)))),
% 21.40/3.14 inference(resolution,[status(thm)],[f57,f140])).
% 21.40/3.14 fof(f166,plain,(
% 21.40/3.14 ![X0]: (X0=relation_rng(empty_set)|in(sK2_skl(X0,empty_set),X0)|in(sK3_skl(X0,empty_set),relation_dom(empty_set)))),
% 21.40/3.14 inference(forward_subsumption_resolution,[status(thm)],[f164,f62])).
% 21.40/3.14 fof(f184,plain,(
% 21.40/3.14 relation_dom(empty_set)=empty_set),
% 21.40/3.14 inference(resolution,[status(thm)],[f151,f130])).
% 21.40/3.14 fof(f192,plain,(
% 21.40/3.14 relation_rng(empty_set)=empty_set),
% 21.40/3.14 inference(resolution,[status(thm)],[f153,f130])).
% 21.40/3.14 fof(f262,plain,(
% 21.40/3.14 ~relation(empty_set)|~function(empty_set)|~sK15_skl=relation_dom(empty_set)|~subset(empty_set,sK14_skl)),
% 21.40/3.14 inference(paramodulation,[status(thm)],[f192,f113])).
% 21.40/3.14 fof(f266,plain,(
% 21.40/3.14 ~relation(empty_set)|~function(empty_set)|~sK15_skl=empty_set|~subset(empty_set,sK14_skl)),
% 21.40/3.14 inference(forward_demodulation,[status(thm)],[f184,f262])).
% 21.40/3.14 fof(f267,plain,(
% 21.40/3.14 ~function(empty_set)|~sK15_skl=empty_set|~subset(empty_set,sK14_skl)),
% 21.40/3.14 inference(forward_subsumption_resolution,[status(thm)],[f266,f62])).
% 21.40/3.14 fof(f273,plain,(
% 21.40/3.14 ![X0]: (element(X0,powerset(X0)))),
% 21.40/3.14 inference(resolution,[status(thm)],[f122,f102])).
% 21.40/3.14 fof(f278,plain,(
% 21.40/3.14 ![X0]: (~in(X0,empty_set))),
% 21.40/3.14 inference(resolution,[status(thm)],[f133,f61])).
% 21.40/3.14 fof(f280,plain,(
% 21.40/3.14 ~sK15_skl=empty_set|~subset(empty_set,sK14_skl)),
% 21.40/3.14 inference(forward_subsumption_resolution,[status(thm)],[f267,f140])).
% 21.40/3.14 fof(f281,plain,(
% 21.40/3.14 ~sK15_skl=empty_set),
% 21.40/3.14 inference(resolution,[status(thm)],[f280,f118])).
% 21.40/3.14 fof(f282,plain,(
% 21.40/3.14 ~sK14_skl=empty_set),
% 21.40/3.14 inference(backward_subsumption_resolution,[status(thm)],[f112,f281])).
% 21.40/3.14 fof(f296,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~in(X0,X1)|apply(sK13_skl(X1,X2),X0)=X2)),
% 21.40/3.14 inference(resolution,[status(thm)],[f273,f109])).
% 21.40/3.14 fof(f297,plain,(
% 21.40/3.14 ![X0,X1]: (relation_dom(sK13_skl(X0,X1))=X0)),
% 21.40/3.14 inference(resolution,[status(thm)],[f273,f108])).
% 21.40/3.14 fof(f298,plain,(
% 21.40/3.14 ![X0,X1]: (function(sK13_skl(X0,X1)))),
% 21.40/3.14 inference(resolution,[status(thm)],[f273,f107])).
% 21.40/3.14 fof(f299,plain,(
% 21.40/3.14 ![X0,X1]: (relation(sK13_skl(X0,X1)))),
% 21.40/3.14 inference(resolution,[status(thm)],[f273,f106])).
% 21.40/3.14 fof(f306,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~relation(sK13_skl(X0,X1))|~in(X2,relation_rng(sK13_skl(X0,X1)))|X2=apply(sK13_skl(X0,X1),sK1_skl(X2,relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1))))),
% 21.40/3.14 inference(resolution,[status(thm)],[f298,f138])).
% 21.40/3.14 fof(f307,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~relation(sK13_skl(X0,X1))|in(sK1_skl(sK0_skl(X2,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1)),relation_dom(sK13_skl(X0,X1)))|subset(relation_rng(sK13_skl(X0,X1)),X2))),
% 21.40/3.14 inference(resolution,[status(thm)],[f145,f298])).
% 21.40/3.14 fof(f354,plain,(
% 21.40/3.14 ![X0]: (X0=empty_set|in(sK2_skl(X0,empty_set),X0)|in(sK3_skl(X0,empty_set),relation_dom(empty_set)))),
% 21.40/3.14 inference(forward_demodulation,[status(thm)],[f192,f166])).
% 21.40/3.14 fof(f355,plain,(
% 21.40/3.14 ![X0]: (X0=empty_set|in(sK2_skl(X0,empty_set),X0)|in(sK3_skl(X0,empty_set),empty_set))),
% 21.40/3.14 inference(forward_demodulation,[status(thm)],[f184,f354])).
% 21.40/3.14 fof(f356,plain,(
% 21.40/3.14 ![X0]: (X0=empty_set|in(sK2_skl(X0,empty_set),X0))),
% 21.40/3.14 inference(forward_subsumption_resolution,[status(thm)],[f355,f278])).
% 21.40/3.14 fof(f1040,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~in(X0,relation_rng(sK13_skl(X1,X2)))|X0=apply(sK13_skl(X1,X2),sK1_skl(X0,relation_rng(sK13_skl(X1,X2)),sK13_skl(X1,X2))))),
% 21.40/3.14 inference(forward_subsumption_resolution,[status(thm)],[f306,f299])).
% 21.40/3.14 fof(f1052,plain,(
% 21.40/3.14 ![X0,X1,X2]: (sK0_skl(X0,relation_rng(sK13_skl(X1,X2)))=apply(sK13_skl(X1,X2),sK1_skl(sK0_skl(X0,relation_rng(sK13_skl(X1,X2))),relation_rng(sK13_skl(X1,X2)),sK13_skl(X1,X2)))|subset(relation_rng(sK13_skl(X1,X2)),X0))),
% 21.40/3.14 inference(resolution,[status(thm)],[f1040,f47])).
% 21.40/3.14 fof(f1059,plain,(
% 21.40/3.14 ![X0,X1,X2]: (~relation(sK13_skl(X0,X1))|in(sK1_skl(sK0_skl(X2,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1)),X0)|subset(relation_rng(sK13_skl(X0,X1)),X2))),
% 21.40/3.14 inference(forward_demodulation,[status(thm)],[f297,f307])).
% 21.40/3.14 fof(f1060,plain,(
% 21.40/3.14 ![X0,X1,X2]: (in(sK1_skl(sK0_skl(X0,relation_rng(sK13_skl(X1,X2))),relation_rng(sK13_skl(X1,X2)),sK13_skl(X1,X2)),X1)|subset(relation_rng(sK13_skl(X1,X2)),X0))),
% 21.40/3.14 inference(forward_subsumption_resolution,[status(thm)],[f1059,f299])).
% 21.40/3.14 fof(f1071,plain,(
% 21.40/3.14 ![X0,X1,X2,X3]: (subset(relation_rng(sK13_skl(X0,X1)),X2)|apply(sK13_skl(X0,X3),sK1_skl(sK0_skl(X2,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1)))=X3)),
% 21.40/3.14 inference(resolution,[status(thm)],[f1060,f296])).
% 21.40/3.14 fof(f12457,plain,(
% 21.40/3.14 ![X0,X1]: (sK0_skl(sK14_skl,relation_rng(sK13_skl(X0,X1)))=apply(sK13_skl(X0,X1),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1)))|~relation(sK13_skl(X0,X1))|~function(sK13_skl(X0,X1))|~sK15_skl=relation_dom(sK13_skl(X0,X1)))),
% 21.40/3.14 inference(resolution,[status(thm)],[f1052,f113])).
% 21.40/3.14 fof(f12461,plain,(
% 21.40/3.14 ![X0,X1]: (sK0_skl(sK14_skl,relation_rng(sK13_skl(X0,X1)))=apply(sK13_skl(X0,X1),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1)))|~relation(sK13_skl(X0,X1))|~function(sK13_skl(X0,X1))|~sK15_skl=X0)),
% 21.40/3.14 inference(forward_demodulation,[status(thm)],[f297,f12457])).
% 21.40/3.14 fof(f12462,plain,(
% 21.40/3.14 ![X1]: (sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X1)))=apply(sK13_skl(sK15_skl,X1),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X1))),relation_rng(sK13_skl(sK15_skl,X1)),sK13_skl(sK15_skl,X1)))|~relation(sK13_skl(sK15_skl,X1))|~function(sK13_skl(sK15_skl,X1)))),
% 21.40/3.14 inference(destructive_equality_resolution,[status(thm)],[f12461])).
% 21.40/3.14 fof(f12463,plain,(
% 21.40/3.14 ![X0]: (sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X0)))=apply(sK13_skl(sK15_skl,X0),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X0))),relation_rng(sK13_skl(sK15_skl,X0)),sK13_skl(sK15_skl,X0)))|~function(sK13_skl(sK15_skl,X0)))),
% 21.40/3.17 inference(forward_subsumption_resolution,[status(thm)],[f12462,f299])).
% 21.40/3.17 fof(f12756,plain,(
% 21.40/3.17 ![X0]: (sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X0)))=apply(sK13_skl(sK15_skl,X0),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X0))),relation_rng(sK13_skl(sK15_skl,X0)),sK13_skl(sK15_skl,X0))))),
% 21.40/3.17 inference(forward_subsumption_resolution,[status(thm)],[f12463,f298])).
% 21.40/3.17 fof(f12865,plain,(
% 21.40/3.17 ![X0,X1,X2]: (apply(sK13_skl(X0,X1),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(X0,X2))),relation_rng(sK13_skl(X0,X2)),sK13_skl(X0,X2)))=X1|~relation(sK13_skl(X0,X2))|~function(sK13_skl(X0,X2))|~sK15_skl=relation_dom(sK13_skl(X0,X2)))),
% 21.40/3.17 inference(resolution,[status(thm)],[f1071,f113])).
% 21.40/3.17 fof(f12869,plain,(
% 21.40/3.17 ![X0,X1,X2]: (apply(sK13_skl(X0,X1),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(X0,X2))),relation_rng(sK13_skl(X0,X2)),sK13_skl(X0,X2)))=X1|~relation(sK13_skl(X0,X2))|~function(sK13_skl(X0,X2))|~sK15_skl=X0)),
% 21.40/3.17 inference(forward_demodulation,[status(thm)],[f297,f12865])).
% 21.40/3.17 fof(f12870,plain,(
% 21.40/3.17 ![X1,X2]: (apply(sK13_skl(sK15_skl,X1),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X2))),relation_rng(sK13_skl(sK15_skl,X2)),sK13_skl(sK15_skl,X2)))=X1|~relation(sK13_skl(sK15_skl,X2))|~function(sK13_skl(sK15_skl,X2)))),
% 21.40/3.17 inference(destructive_equality_resolution,[status(thm)],[f12869])).
% 21.40/3.17 fof(f12871,plain,(
% 21.40/3.17 ![X0,X1]: (apply(sK13_skl(sK15_skl,X0),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X1))),relation_rng(sK13_skl(sK15_skl,X1)),sK13_skl(sK15_skl,X1)))=X0|~function(sK13_skl(sK15_skl,X1)))),
% 21.40/3.17 inference(forward_subsumption_resolution,[status(thm)],[f12870,f299])).
% 21.40/3.17 fof(f13662,plain,(
% 21.40/3.17 ![X0]: (sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X0)))=X0)),
% 21.40/3.17 inference(backward_demodulation,[status(thm)],[f13663,f12756])).
% 21.40/3.17 fof(f13663,plain,(
% 21.40/3.17 ![X0,X1]: (apply(sK13_skl(sK15_skl,X0),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X1))),relation_rng(sK13_skl(sK15_skl,X1)),sK13_skl(sK15_skl,X1)))=X0)),
% 21.40/3.17 inference(forward_subsumption_resolution,[status(thm)],[f12871,f298])).
% 21.40/3.17 fof(f13707,plain,(
% 21.40/3.17 ![X0]: (subset(relation_rng(sK13_skl(sK15_skl,X0)),sK14_skl)|~in(X0,sK14_skl))),
% 21.40/3.17 inference(paramodulation,[status(thm)],[f13662,f48])).
% 21.40/3.17 fof(f13836,plain,(
% 21.40/3.17 subset(relation_rng(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set))),sK14_skl)|sK14_skl=empty_set),
% 21.40/3.17 inference(resolution,[status(thm)],[f13707,f356])).
% 21.40/3.17 fof(f13851,plain,(
% 21.40/3.17 subset(relation_rng(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set))),sK14_skl)),
% 21.40/3.17 inference(forward_subsumption_resolution,[status(thm)],[f13836,f282])).
% 21.40/3.17 fof(f13852,plain,(
% 21.40/3.17 ~relation(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set)))|~function(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set)))|~sK15_skl=relation_dom(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set)))),
% 21.40/3.17 inference(resolution,[status(thm)],[f13851,f113])).
% 21.40/3.17 fof(f13855,plain,(
% 21.40/3.17 ~relation(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set)))|~function(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set)))|~sK15_skl=sK15_skl),
% 21.40/3.17 inference(forward_demodulation,[status(thm)],[f297,f13852])).
% 21.40/3.17 fof(f13856,plain,(
% 21.40/3.17 ~relation(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set)))|~function(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set)))),
% 21.40/3.17 inference(trivial_equality_resolution,[status(thm)],[f13855])).
% 21.40/3.17 fof(f13857,plain,(
% 21.40/3.17 ~function(sK13_skl(sK15_skl,sK2_skl(sK14_skl,empty_set)))),
% 21.40/3.17 inference(forward_subsumption_resolution,[status(thm)],[f13856,f299])).
% 21.40/3.17 fof(f13858,plain,(
% 21.40/3.17 $false),
% 21.40/3.17 inference(forward_subsumption_resolution,[status(thm)],[f13857,f298])).
% 21.40/3.17 % SZS output end CNFRefutation for theBenchmark.p
% 21.40/3.18 % Elapsed time: 2.793872 seconds
% 21.40/3.18 % CPU time: 21.904723 seconds
% 21.40/3.18 % Total memory used: 255.562 MB
% 21.40/3.18 % Net memory used: 223.674 MB
%------------------------------------------------------------------------------