%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:22:00 PM UTC 2026
% Result : Theorem 0.14s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n003.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Mon Sep 21 06:00:01 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.14/0.59 % Drodi V4.1.1
% 0.14/0.62 % Refutation found
% 0.14/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.62 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.62 fof(f3,axiom,(
% 0.14/0.62 (! [A] :( empty(A)=> function(A) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f4,axiom,(
% 0.14/0.62 (! [A] :( empty(A)=> relation(A) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f8,axiom,(
% 0.14/0.62 (! [A,B] :( relation(B)=> ( B = identity_relation(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> ( in(C,A)& C = D ) ) )) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f27,axiom,(
% 0.14/0.62 (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( ( in(B,relation_dom(A))=> ( C = apply(A,B)<=> in(ordered_pair(B,C),A) ) )& ( ~ in(B,relation_dom(A))=> ( C = apply(A,B)<=> C = empty_set ) ) ) )) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f28,axiom,(
% 0.14/0.62 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f72,axiom,(
% 0.14/0.62 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f84,axiom,(
% 0.14/0.62 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_dom(A)) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f86,axiom,(
% 0.14/0.62 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f107,axiom,(
% 0.14/0.62 (? [A] :( relation(A)& function(A) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f108,axiom,(
% 0.14/0.62 (? [A] :( empty(A)& relation(A) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f110,axiom,(
% 0.14/0.62 (? [A] : empty(A) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f149,lemma,(
% 0.14/0.62 (! [A] :( relation(A)=> (! [B] :( relation(B)=> ( subset(A,B)=> ( subset(relation_dom(A),relation_dom(B))& subset(relation_rng(A),relation_rng(B)) ) ) ) )) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f155,lemma,(
% 0.14/0.62 (! [A] : subset(empty_set,A) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f189,lemma,(
% 0.14/0.62 ( relation_dom(empty_set) = empty_set& relation_rng(empty_set) = empty_set ) ),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f192,lemma,(
% 0.14/0.62 (! [A] :( relation(A)=> ( ( relation_dom(A) = empty_set| relation_rng(A) = empty_set )=> A = empty_set ) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f193,lemma,(
% 0.14/0.62 (! [A] :( relation(A)=> ( relation_dom(A) = empty_set<=> relation_rng(A) = empty_set ) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f206,conjecture,(
% 0.14/0.62 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(ordered_pair(A,B),C)<=> ( in(A,relation_dom(C))& B = apply(C,A) ) ) ) )),
% 0.14/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.62 fof(f207,negated_conjecture,(
% 0.14/0.62 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(ordered_pair(A,B),C)<=> ( in(A,relation_dom(C))& B = apply(C,A) ) ) ) ))),
% 0.14/0.62 inference(negated_conjecture,[status(cth)],[f206])).
% 0.14/0.62 fof(f221,plain,(
% 0.14/0.62 ![A]: (~empty(A)|function(A))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.14/0.62 fof(f222,plain,(
% 0.14/0.62 ![X0]: (~empty(X0)|function(X0))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f221])).
% 0.14/0.62 fof(f223,plain,(
% 0.14/0.62 ![A]: (~empty(A)|relation(A))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/0.62 fof(f224,plain,(
% 0.14/0.62 ![X0]: (~empty(X0)|relation(X0))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f223])).
% 0.14/0.62 fof(f228,plain,(
% 0.14/0.62 ![A,B]: (~relation(B)|(B=identity_relation(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>(in(C,A)&C=D)))))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.14/0.62 fof(f229,plain,(
% 0.14/0.62 ![A,B]: (~relation(B)|((~B=identity_relation(A)|(![C,D]: ((~in(ordered_pair(C,D),B)|(in(C,A)&C=D))&(in(ordered_pair(C,D),B)|(~in(C,A)|~C=D)))))&(B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D)))))))),
% 0.14/0.62 inference(NNF_transformation,[status(thm)],[f228])).
% 0.14/0.62 fof(f230,plain,(
% 0.14/0.62 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D))))))))),
% 0.14/0.62 inference(miniscoping,[status(thm)],[f229])).
% 0.14/0.62 fof(f231,plain,(
% 0.14/0.62 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|((~in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(~in(sK0_skl(A,B),A)|~sK0_skl(A,B)=sK1_skl(A,B)))&(in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(in(sK0_skl(A,B),A)&sK0_skl(A,B)=sK1_skl(A,B))))))))),
% 0.14/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f230])).
% 0.14/0.62 fof(f235,plain,(
% 0.14/0.62 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|~in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|~in(sK0_skl(X1,X0),X1)|~sK0_skl(X1,X0)=sK1_skl(X1,X0))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f231])).
% 0.14/0.62 fof(f385,plain,(
% 0.14/0.62 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|(C=apply(A,B)<=>in(ordered_pair(B,C),A)))&(in(B,relation_dom(A))|(C=apply(A,B)<=>C=empty_set)))))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.14/0.62 fof(f386,plain,(
% 0.14/0.62 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|((~C=apply(A,B)|in(ordered_pair(B,C),A))&(C=apply(A,B)|~in(ordered_pair(B,C),A))))&(in(B,relation_dom(A))|((~C=apply(A,B)|C=empty_set)&(C=apply(A,B)|~C=empty_set))))))),
% 0.14/0.62 inference(NNF_transformation,[status(thm)],[f385])).
% 0.14/0.62 fof(f387,plain,(
% 0.14/0.62 ![A]: ((~relation(A)|~function(A))|((![B]: (~in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|in(ordered_pair(B,C),A)))&(![C]: (C=apply(A,B)|~in(ordered_pair(B,C),A))))))&(![B]: (in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|C=empty_set))&(![C]: (C=apply(A,B)|~C=empty_set)))))))),
% 0.14/0.62 inference(miniscoping,[status(thm)],[f386])).
% 0.14/0.62 fof(f388,plain,(
% 0.14/0.62 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|~X2=apply(X0,X1)|in(ordered_pair(X1,X2),X0))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f387])).
% 0.14/0.62 fof(f389,plain,(
% 0.14/0.62 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X2=apply(X0,X1)|~in(ordered_pair(X1,X2),X0))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f387])).
% 0.14/0.62 fof(f390,plain,(
% 0.14/0.62 ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_dom(X0))|~X2=apply(X0,X1)|X2=empty_set)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f387])).
% 0.14/0.62 fof(f392,plain,(
% 0.14/0.62 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.14/0.62 fof(f393,plain,(
% 0.14/0.62 ![A]: (~relation(A)|(![B]: ((~B=relation_dom(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(C,D),A)))&(in(C,B)|(![D]: ~in(ordered_pair(C,D),A))))))&(B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 0.14/0.62 inference(NNF_transformation,[status(thm)],[f392])).
% 0.14/0.62 fof(f394,plain,(
% 0.14/0.62 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(C,D),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 0.14/0.62 inference(miniscoping,[status(thm)],[f393])).
% 0.14/0.62 fof(f395,plain,(
% 0.14/0.62 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sK34_skl(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sK35_skl(B,A),B)|(![D]: ~in(ordered_pair(sK35_skl(B,A),D),A)))&(in(sK35_skl(B,A),B)|in(ordered_pair(sK35_skl(B,A),sK36_skl(B,A)),A)))))))),
% 0.14/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl]),skolemize(D,sK34_skl(C,B,A)),skolemize(C,sK35_skl(B,A)),skolemize(D,sK36_skl(B,A))],[f394])).
% 0.14/0.62 fof(f397,plain,(
% 0.14/0.62 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f395])).
% 0.14/0.62 fof(f494,plain,(
% 0.14/0.62 empty(empty_set)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f72])).
% 0.14/0.62 fof(f516,plain,(
% 0.14/0.62 ![A]: ((empty(A)|~relation(A))|~empty(relation_dom(A)))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 0.14/0.62 fof(f517,plain,(
% 0.14/0.62 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_dom(X0)))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f516])).
% 0.14/0.62 fof(f520,plain,(
% 0.14/0.62 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f86])).
% 0.14/0.62 fof(f521,plain,(
% 0.14/0.62 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f520])).
% 0.14/0.62 fof(f522,plain,(
% 0.14/0.62 ![X0]: (~empty(X0)|relation(relation_dom(X0)))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f520])).
% 0.14/0.62 fof(f577,plain,(
% 0.14/0.62 (relation(sK53_skl)&function(sK53_skl))),
% 0.14/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl]),skolemize(A,sK53_skl)],[f107])).
% 0.14/0.62 fof(f578,plain,(
% 0.14/0.62 relation(sK53_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f577])).
% 0.14/0.62 fof(f579,plain,(
% 0.14/0.62 function(sK53_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f577])).
% 0.14/0.62 fof(f580,plain,(
% 0.14/0.62 (empty(sK54_skl)&relation(sK54_skl))),
% 0.14/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK54_skl]),skolemize(A,sK54_skl)],[f108])).
% 0.14/0.62 fof(f581,plain,(
% 0.14/0.62 empty(sK54_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f580])).
% 0.14/0.62 fof(f582,plain,(
% 0.14/0.62 relation(sK54_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f580])).
% 0.14/0.62 fof(f587,plain,(
% 0.14/0.62 empty(sK56_skl)),
% 0.14/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl]),skolemize(A,sK56_skl)],[f110])).
% 0.14/0.62 fof(f588,plain,(
% 0.14/0.62 empty(sK56_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f587])).
% 0.14/0.62 fof(f705,plain,(
% 0.14/0.62 ![A]: (~relation(A)|(![B]: (~relation(B)|(~subset(A,B)|(subset(relation_dom(A),relation_dom(B))&subset(relation_rng(A),relation_rng(B)))))))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f149])).
% 0.14/0.62 fof(f706,plain,(
% 0.14/0.62 ![X0,X1]: (~relation(X0)|~relation(X1)|~subset(X0,X1)|subset(relation_dom(X0),relation_dom(X1)))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f705])).
% 0.14/0.62 fof(f721,plain,(
% 0.14/0.62 ![X0]: (subset(empty_set,X0))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f155])).
% 0.14/0.62 fof(f812,plain,(
% 0.14/0.62 relation_dom(empty_set)=empty_set),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f189])).
% 0.14/0.62 fof(f819,plain,(
% 0.14/0.62 ![A]: (~relation(A)|((~relation_dom(A)=empty_set&~relation_rng(A)=empty_set)|A=empty_set))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f192])).
% 0.14/0.62 fof(f820,plain,(
% 0.14/0.62 ![X0]: (~relation(X0)|~relation_dom(X0)=empty_set|X0=empty_set)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f819])).
% 0.14/0.62 fof(f822,plain,(
% 0.14/0.62 ![A]: (~relation(A)|(relation_dom(A)=empty_set<=>relation_rng(A)=empty_set))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f193])).
% 0.14/0.62 fof(f823,plain,(
% 0.14/0.62 ![A]: (~relation(A)|((~relation_dom(A)=empty_set|relation_rng(A)=empty_set)&(relation_dom(A)=empty_set|~relation_rng(A)=empty_set)))),
% 0.14/0.62 inference(NNF_transformation,[status(thm)],[f822])).
% 0.14/0.62 fof(f824,plain,(
% 0.14/0.62 ![X0]: (~relation(X0)|~relation_dom(X0)=empty_set|relation_rng(X0)=empty_set)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f823])).
% 0.14/0.62 fof(f864,plain,(
% 0.14/0.62 (?[A,B,C]: ((relation(C)&function(C))&(in(ordered_pair(A,B),C)<~>(in(A,relation_dom(C))&B=apply(C,A)))))),
% 0.14/0.62 inference(pre_NNF_transformation,[status(thm)],[f207])).
% 0.14/0.62 fof(f865,plain,(
% 0.14/0.62 ?[A,B,C]: ((relation(C)&function(C))&((in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A)))&(~in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A)))))),
% 0.14/0.62 inference(NNF_transformation,[status(thm)],[f864])).
% 0.14/0.62 fof(f866,plain,(
% 0.14/0.62 ?[C]: ((relation(C)&function(C))&(?[A,B]: ((in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A)))&(~in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A))))))),
% 0.14/0.62 inference(miniscoping,[status(thm)],[f865])).
% 0.14/0.62 fof(f867,plain,(
% 0.14/0.62 ((relation(sK69_skl)&function(sK69_skl))&((in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)|(in(sK70_skl,relation_dom(sK69_skl))&sK71_skl=apply(sK69_skl,sK70_skl)))&(~in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)|(~in(sK70_skl,relation_dom(sK69_skl))|~sK71_skl=apply(sK69_skl,sK70_skl)))))),
% 0.14/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK69_skl,sK70_skl,sK71_skl]),skolemize(C,sK69_skl),skolemize(A,sK70_skl),skolemize(B,sK71_skl)],[f866])).
% 0.14/0.62 fof(f868,plain,(
% 0.14/0.62 relation(sK69_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f867])).
% 0.14/0.62 fof(f869,plain,(
% 0.14/0.62 function(sK69_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f867])).
% 0.14/0.62 fof(f870,plain,(
% 0.14/0.62 in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)|in(sK70_skl,relation_dom(sK69_skl))),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f867])).
% 0.14/0.62 fof(f871,plain,(
% 0.14/0.62 in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)|sK71_skl=apply(sK69_skl,sK70_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f867])).
% 0.14/0.62 fof(f872,plain,(
% 0.14/0.62 ~in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)|~in(sK70_skl,relation_dom(sK69_skl))|~sK71_skl=apply(sK69_skl,sK70_skl)),
% 0.14/0.62 inference(cnf_transformation,[status(thm)],[f867])).
% 0.14/0.62 fof(f907,definition,(
% 0.14/0.62 sQ0_spl <=> (in(ordered_pair(sK70_skl,sK71_skl),sK69_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f908,plain,(
% 0.14/0.62 in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)|~sQ0_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f907])).
% 0.14/0.62 fof(f909,plain,(
% 0.14/0.62 ~in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)|sQ0_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f907])).
% 0.14/0.62 fof(f910,definition,(
% 0.14/0.62 sQ1_spl <=> (in(sK70_skl,relation_dom(sK69_skl)))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f911,plain,(
% 0.14/0.62 in(sK70_skl,relation_dom(sK69_skl))|~sQ1_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f910])).
% 0.14/0.62 fof(f913,plain,(
% 0.14/0.62 sQ0_spl|sQ1_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f870,f907,f910])).
% 0.14/0.62 fof(f914,definition,(
% 0.14/0.62 sQ2_spl <=> (sK71_skl=apply(sK69_skl,sK70_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f915,plain,(
% 0.14/0.62 sK71_skl=apply(sK69_skl,sK70_skl)|~sQ2_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f914])).
% 0.14/0.62 fof(f917,plain,(
% 0.14/0.62 sQ0_spl|sQ2_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f871,f907,f914])).
% 0.14/0.62 fof(f918,plain,(
% 0.14/0.62 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f872,f907,f910,f914])).
% 0.14/0.62 fof(f957,plain,(
% 0.14/0.62 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,apply(X0,X1)),X0))),
% 0.14/0.62 inference(destructive_equality_resolution,[status(thm)],[f388])).
% 0.14/0.62 fof(f958,plain,(
% 0.14/0.62 ![X0,X1]: (~relation(X0)|~function(X0)|in(X1,relation_dom(X0))|apply(X0,X1)=empty_set)),
% 0.14/0.62 inference(destructive_equality_resolution,[status(thm)],[f390])).
% 0.14/0.62 fof(f961,plain,(
% 0.14/0.62 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.14/0.62 inference(destructive_equality_resolution,[status(thm)],[f397])).
% 0.14/0.62 fof(f990,definition,(
% 0.14/0.62 sQ4_spl <=> (relation(empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f992,plain,(
% 0.14/0.62 ~relation(empty_set)|sQ4_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f990])).
% 0.14/0.62 fof(f994,plain,(
% 0.14/0.62 ~relation(empty_set)|empty_set=empty_set),
% 0.14/0.62 inference(resolution,[status(thm)],[f820,f812])).
% 0.14/0.62 fof(f996,definition,(
% 0.14/0.62 sQ5_spl <=> (empty_set=empty_set)),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f999,plain,(
% 0.14/0.62 ~sQ4_spl|sQ5_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f994,f990,f996])).
% 0.14/0.62 fof(f1001,plain,(
% 0.14/0.62 ~relation(empty_set)|relation_rng(empty_set)=empty_set),
% 0.14/0.62 inference(resolution,[status(thm)],[f824,f812])).
% 0.14/0.62 fof(f1003,definition,(
% 0.14/0.62 sQ6_spl <=> (relation_rng(empty_set)=empty_set)),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1006,plain,(
% 0.14/0.62 ~sQ4_spl|sQ6_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1001,f990,f1003])).
% 0.14/0.62 fof(f1008,plain,(
% 0.14/0.62 ![X0]: (~relation(empty_set)|~function(empty_set)|~in(X0,empty_set)|in(ordered_pair(X0,apply(empty_set,X0)),empty_set))),
% 0.14/0.62 inference(paramodulation,[status(thm)],[f812,f957])).
% 0.14/0.62 fof(f1009,definition,(
% 0.14/0.62 sQ7_spl <=> (function(empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1011,plain,(
% 0.14/0.62 ~function(empty_set)|sQ7_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1009])).
% 0.14/0.62 fof(f1012,definition,(
% 0.14/0.62 ![X0]: (sQ8_spl <=> (~in(X0,empty_set)|in(ordered_pair(X0,apply(empty_set,X0)),empty_set)))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1015,plain,(
% 0.14/0.62 ~sQ4_spl|~sQ7_spl|sQ8_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1008,f990,f1009,f1012])).
% 0.14/0.62 fof(f1016,plain,(
% 0.14/0.62 ~relation(sK69_skl)|~function(sK69_skl)|~in(sK70_skl,relation_dom(sK69_skl))|sK71_skl=apply(sK69_skl,sK70_skl)|~sQ0_spl),
% 0.14/0.62 inference(resolution,[status(thm)],[f389,f908])).
% 0.14/0.62 fof(f1017,definition,(
% 0.14/0.62 sQ9_spl <=> (relation(sK69_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1019,plain,(
% 0.14/0.62 ~relation(sK69_skl)|sQ9_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1017])).
% 0.14/0.62 fof(f1020,definition,(
% 0.14/0.62 sQ10_spl <=> (function(sK69_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1022,plain,(
% 0.14/0.62 ~function(sK69_skl)|sQ10_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1020])).
% 0.14/0.62 fof(f1023,plain,(
% 0.14/0.62 ~sQ9_spl|~sQ10_spl|~sQ1_spl|sQ2_spl|~sQ0_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1016,f1017,f1020,f910,f914,f907])).
% 0.14/0.62 fof(f1024,plain,(
% 0.14/0.62 $false|sQ9_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1019,f868])).
% 0.14/0.62 fof(f1025,plain,(
% 0.14/0.62 sQ9_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1024])).
% 0.14/0.62 fof(f1026,plain,(
% 0.14/0.62 $false|sQ10_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1022,f869])).
% 0.14/0.62 fof(f1027,plain,(
% 0.14/0.62 sQ10_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1026])).
% 0.14/0.62 fof(f1028,plain,(
% 0.14/0.62 relation(relation_dom(empty_set))),
% 0.14/0.62 inference(resolution,[status(thm)],[f494,f522])).
% 0.14/0.62 fof(f1030,plain,(
% 0.14/0.62 function(empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f494,f222])).
% 0.14/0.62 fof(f1031,plain,(
% 0.14/0.62 relation(empty_set)),
% 0.14/0.62 inference(forward_demodulation,[status(thm)],[f812,f1028])).
% 0.14/0.62 fof(f1032,plain,(
% 0.14/0.62 $false|sQ4_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1031,f992])).
% 0.14/0.62 fof(f1033,plain,(
% 0.14/0.62 sQ4_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1032])).
% 0.14/0.62 fof(f1035,plain,(
% 0.14/0.62 relation(relation_dom(sK54_skl))),
% 0.14/0.62 inference(resolution,[status(thm)],[f581,f522])).
% 0.14/0.62 fof(f1036,plain,(
% 0.14/0.62 empty(relation_dom(sK54_skl))),
% 0.14/0.62 inference(resolution,[status(thm)],[f581,f521])).
% 0.14/0.62 fof(f1037,plain,(
% 0.14/0.62 function(sK54_skl)),
% 0.14/0.62 inference(resolution,[status(thm)],[f581,f222])).
% 0.14/0.62 fof(f1044,plain,(
% 0.14/0.62 ~relation(sK69_skl)|~function(sK69_skl)|in(ordered_pair(sK70_skl,apply(sK69_skl,sK70_skl)),sK69_skl)|~sQ1_spl),
% 0.14/0.62 inference(resolution,[status(thm)],[f911,f957])).
% 0.14/0.62 fof(f1046,definition,(
% 0.14/0.62 sQ11_spl <=> (in(ordered_pair(sK70_skl,apply(sK69_skl,sK70_skl)),sK69_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1047,plain,(
% 0.14/0.62 in(ordered_pair(sK70_skl,apply(sK69_skl,sK70_skl)),sK69_skl)|~sQ11_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1046])).
% 0.14/0.62 fof(f1049,plain,(
% 0.14/0.62 ~sQ9_spl|~sQ10_spl|sQ11_spl|~sQ1_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1044,f1017,f1020,f1046,f910])).
% 0.14/0.62 fof(f1053,plain,(
% 0.14/0.62 ![X0]: (~relation(sK53_skl)|in(X0,relation_dom(sK53_skl))|apply(sK53_skl,X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f958,f579])).
% 0.14/0.62 fof(f1054,plain,(
% 0.14/0.62 ![X0]: (~relation(sK69_skl)|in(X0,relation_dom(sK69_skl))|apply(sK69_skl,X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f958,f869])).
% 0.14/0.62 fof(f1055,definition,(
% 0.14/0.62 sQ12_spl <=> (relation(sK53_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1057,plain,(
% 0.14/0.62 ~relation(sK53_skl)|sQ12_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1055])).
% 0.14/0.62 fof(f1058,definition,(
% 0.14/0.62 ![X0]: (sQ13_spl <=> (in(X0,relation_dom(sK53_skl))|apply(sK53_skl,X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1061,plain,(
% 0.14/0.62 ~sQ12_spl|sQ13_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1053,f1055,f1058])).
% 0.14/0.62 fof(f1062,definition,(
% 0.14/0.62 ![X0]: (sQ14_spl <=> (in(X0,relation_dom(sK69_skl))|apply(sK69_skl,X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1063,plain,(
% 0.14/0.62 ![X0]: (in(X0,relation_dom(sK69_skl))|apply(sK69_skl,X0)=empty_set|~sQ14_spl)),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1062])).
% 0.14/0.62 fof(f1065,plain,(
% 0.14/0.62 ~sQ9_spl|sQ14_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1054,f1017,f1062])).
% 0.14/0.62 fof(f1066,plain,(
% 0.14/0.62 $false|sQ12_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1057,f578])).
% 0.14/0.62 fof(f1067,plain,(
% 0.14/0.62 sQ12_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1066])).
% 0.14/0.62 fof(f1068,plain,(
% 0.14/0.62 ![X0]: (~relation(empty_set)|in(X0,relation_dom(empty_set))|apply(empty_set,X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1030,f958])).
% 0.14/0.62 fof(f1069,definition,(
% 0.14/0.62 ![X0]: (sQ15_spl <=> (in(X0,relation_dom(empty_set))|apply(empty_set,X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1072,plain,(
% 0.14/0.62 ~sQ4_spl|sQ15_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1068,f990,f1069])).
% 0.14/0.62 fof(f1074,plain,(
% 0.14/0.62 $false|sQ7_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1011,f1030])).
% 0.14/0.62 fof(f1075,plain,(
% 0.14/0.62 sQ7_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1074])).
% 0.14/0.62 fof(f1076,plain,(
% 0.14/0.62 ![X0]: (~relation(sK54_skl)|in(X0,relation_dom(sK54_skl))|apply(sK54_skl,X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1037,f958])).
% 0.14/0.62 fof(f1077,definition,(
% 0.14/0.62 sQ16_spl <=> (relation(sK54_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1079,plain,(
% 0.14/0.62 ~relation(sK54_skl)|sQ16_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1077])).
% 0.14/0.62 fof(f1080,definition,(
% 0.14/0.62 ![X0]: (sQ17_spl <=> (in(X0,relation_dom(sK54_skl))|apply(sK54_skl,X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1083,plain,(
% 0.14/0.62 ~sQ16_spl|sQ17_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1076,f1077,f1080])).
% 0.14/0.62 fof(f1084,plain,(
% 0.14/0.62 $false|sQ16_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1079,f582])).
% 0.14/0.62 fof(f1085,plain,(
% 0.14/0.62 sQ16_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1084])).
% 0.14/0.62 fof(f1086,plain,(
% 0.14/0.62 empty(sK54_skl)|~relation(sK54_skl)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1036,f517])).
% 0.14/0.62 fof(f1088,plain,(
% 0.14/0.62 relation(relation_dom(relation_dom(sK54_skl)))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1036,f522])).
% 0.14/0.62 fof(f1089,plain,(
% 0.14/0.62 empty(relation_dom(relation_dom(sK54_skl)))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1036,f521])).
% 0.14/0.62 fof(f1090,plain,(
% 0.14/0.62 function(relation_dom(sK54_skl))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1036,f222])).
% 0.14/0.62 fof(f1091,definition,(
% 0.14/0.62 sQ18_spl <=> (empty(sK54_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1094,plain,(
% 0.14/0.62 sQ18_spl|~sQ16_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1086,f1091,f1077])).
% 0.14/0.62 fof(f1095,plain,(
% 0.14/0.62 ![X0]: (~relation(relation_dom(sK54_skl))|in(X0,relation_dom(relation_dom(sK54_skl)))|apply(relation_dom(sK54_skl),X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1090,f958])).
% 0.14/0.62 fof(f1096,definition,(
% 0.14/0.62 sQ19_spl <=> (relation(relation_dom(sK54_skl)))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1098,plain,(
% 0.14/0.62 ~relation(relation_dom(sK54_skl))|sQ19_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1096])).
% 0.14/0.62 fof(f1099,definition,(
% 0.14/0.62 ![X0]: (sQ20_spl <=> (in(X0,relation_dom(relation_dom(sK54_skl)))|apply(relation_dom(sK54_skl),X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1102,plain,(
% 0.14/0.62 ~sQ19_spl|sQ20_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1095,f1096,f1099])).
% 0.14/0.62 fof(f1103,plain,(
% 0.14/0.62 $false|sQ19_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1098,f1035])).
% 0.14/0.62 fof(f1104,plain,(
% 0.14/0.62 sQ19_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1103])).
% 0.14/0.62 fof(f1106,plain,(
% 0.14/0.62 ~relation(sK69_skl)|in(sK70_skl,relation_dom(sK69_skl))|~sQ0_spl),
% 0.14/0.62 inference(resolution,[status(thm)],[f961,f908])).
% 0.14/0.62 fof(f1107,plain,(
% 0.14/0.62 ~sQ9_spl|sQ1_spl|~sQ0_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1106,f1017,f910,f907])).
% 0.14/0.62 fof(f1108,plain,(
% 0.14/0.62 relation(sK56_skl)),
% 0.14/0.62 inference(resolution,[status(thm)],[f588,f224])).
% 0.14/0.62 fof(f1109,plain,(
% 0.14/0.62 relation(relation_dom(sK56_skl))),
% 0.14/0.62 inference(resolution,[status(thm)],[f588,f522])).
% 0.14/0.62 fof(f1110,plain,(
% 0.14/0.62 empty(relation_dom(sK56_skl))),
% 0.14/0.62 inference(resolution,[status(thm)],[f588,f521])).
% 0.14/0.62 fof(f1111,plain,(
% 0.14/0.62 function(sK56_skl)),
% 0.14/0.62 inference(resolution,[status(thm)],[f588,f222])).
% 0.14/0.62 fof(f1112,plain,(
% 0.14/0.62 ![X0]: (~relation(sK56_skl)|in(X0,relation_dom(sK56_skl))|apply(sK56_skl,X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1111,f958])).
% 0.14/0.62 fof(f1113,definition,(
% 0.14/0.62 sQ21_spl <=> (relation(sK56_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1115,plain,(
% 0.14/0.62 ~relation(sK56_skl)|sQ21_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1113])).
% 0.14/0.62 fof(f1116,definition,(
% 0.14/0.62 ![X0]: (sQ22_spl <=> (in(X0,relation_dom(sK56_skl))|apply(sK56_skl,X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1119,plain,(
% 0.14/0.62 ~sQ21_spl|sQ22_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1112,f1113,f1116])).
% 0.14/0.62 fof(f1120,plain,(
% 0.14/0.62 $false|sQ21_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1115,f1108])).
% 0.14/0.62 fof(f1121,plain,(
% 0.14/0.62 sQ21_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1120])).
% 0.14/0.62 fof(f1134,plain,(
% 0.14/0.62 ![X0,X1]: (apply(sK69_skl,ordered_pair(X0,X1))=empty_set|~relation(relation_dom(sK69_skl))|in(X0,relation_dom(relation_dom(sK69_skl)))|~sQ14_spl)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1063,f961])).
% 0.14/0.62 fof(f1135,plain,(
% 0.14/0.62 ![X0]: (apply(sK69_skl,X0)=empty_set|~relation(sK69_skl)|~function(sK69_skl)|in(ordered_pair(X0,apply(sK69_skl,X0)),sK69_skl)|~sQ14_spl)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1063,f957])).
% 0.14/0.62 fof(f1137,definition,(
% 0.14/0.62 ![X0,X1]: (sQ23_spl <=> (apply(sK69_skl,ordered_pair(X0,X1))=empty_set|in(X0,relation_dom(relation_dom(sK69_skl)))))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1140,definition,(
% 0.14/0.62 sQ24_spl <=> (relation(relation_dom(sK69_skl)))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1143,plain,(
% 0.14/0.62 sQ23_spl|~sQ24_spl|~sQ14_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1134,f1137,f1140,f1062])).
% 0.14/0.62 fof(f1144,definition,(
% 0.14/0.62 ![X0]: (sQ25_spl <=> (apply(sK69_skl,X0)=empty_set|in(ordered_pair(X0,apply(sK69_skl,X0)),sK69_skl)))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1147,plain,(
% 0.14/0.62 sQ25_spl|~sQ9_spl|~sQ10_spl|~sQ14_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1135,f1144,f1017,f1020,f1062])).
% 0.14/0.62 fof(f1148,plain,(
% 0.14/0.62 empty(sK56_skl)|~relation(sK56_skl)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1110,f517])).
% 0.14/0.62 fof(f1150,plain,(
% 0.14/0.62 relation(relation_dom(relation_dom(sK56_skl)))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1110,f522])).
% 0.14/0.62 fof(f1151,plain,(
% 0.14/0.62 empty(relation_dom(relation_dom(sK56_skl)))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1110,f521])).
% 0.14/0.62 fof(f1152,plain,(
% 0.14/0.62 function(relation_dom(sK56_skl))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1110,f222])).
% 0.14/0.62 fof(f1153,definition,(
% 0.14/0.62 sQ26_spl <=> (empty(sK56_skl))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1156,plain,(
% 0.14/0.62 sQ26_spl|~sQ21_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1148,f1153,f1113])).
% 0.14/0.62 fof(f1157,plain,(
% 0.14/0.62 ![X0]: (~relation(relation_dom(sK56_skl))|in(X0,relation_dom(relation_dom(sK56_skl)))|apply(relation_dom(sK56_skl),X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1152,f958])).
% 0.14/0.62 fof(f1158,definition,(
% 0.14/0.62 sQ27_spl <=> (relation(relation_dom(sK56_skl)))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1160,plain,(
% 0.14/0.62 ~relation(relation_dom(sK56_skl))|sQ27_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1158])).
% 0.14/0.62 fof(f1161,definition,(
% 0.14/0.62 ![X0]: (sQ28_spl <=> (in(X0,relation_dom(relation_dom(sK56_skl)))|apply(relation_dom(sK56_skl),X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1164,plain,(
% 0.14/0.62 ~sQ27_spl|sQ28_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1157,f1158,f1161])).
% 0.14/0.62 fof(f1165,plain,(
% 0.14/0.62 $false|sQ27_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1160,f1109])).
% 0.14/0.62 fof(f1166,plain,(
% 0.14/0.62 sQ27_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1165])).
% 0.14/0.62 fof(f1167,plain,(
% 0.14/0.62 empty(relation_dom(sK54_skl))|~relation(relation_dom(sK54_skl))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1089,f517])).
% 0.14/0.62 fof(f1170,plain,(
% 0.14/0.62 empty(relation_dom(relation_dom(relation_dom(sK54_skl))))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1089,f521])).
% 0.14/0.62 fof(f1171,plain,(
% 0.14/0.62 function(relation_dom(relation_dom(sK54_skl)))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1089,f222])).
% 0.14/0.62 fof(f1172,definition,(
% 0.14/0.62 sQ29_spl <=> (empty(relation_dom(sK54_skl)))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1175,plain,(
% 0.14/0.62 sQ29_spl|~sQ19_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1167,f1172,f1096])).
% 0.14/0.62 fof(f1176,plain,(
% 0.14/0.62 empty(relation_dom(sK56_skl))|~relation(relation_dom(sK56_skl))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1151,f517])).
% 0.14/0.62 fof(f1180,plain,(
% 0.14/0.62 function(relation_dom(relation_dom(sK56_skl)))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1151,f222])).
% 0.14/0.62 fof(f1181,definition,(
% 0.14/0.62 sQ30_spl <=> (empty(relation_dom(sK56_skl)))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1184,plain,(
% 0.14/0.62 sQ30_spl|~sQ27_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1176,f1181,f1158])).
% 0.14/0.62 fof(f1185,plain,(
% 0.14/0.62 ![X0]: (~relation(relation_dom(relation_dom(sK54_skl)))|in(X0,relation_dom(relation_dom(relation_dom(sK54_skl))))|apply(relation_dom(relation_dom(sK54_skl)),X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1171,f958])).
% 0.14/0.62 fof(f1186,definition,(
% 0.14/0.62 sQ31_spl <=> (relation(relation_dom(relation_dom(sK54_skl))))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1188,plain,(
% 0.14/0.62 ~relation(relation_dom(relation_dom(sK54_skl)))|sQ31_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1186])).
% 0.14/0.62 fof(f1189,definition,(
% 0.14/0.62 ![X0]: (sQ32_spl <=> (in(X0,relation_dom(relation_dom(relation_dom(sK54_skl))))|apply(relation_dom(relation_dom(sK54_skl)),X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1192,plain,(
% 0.14/0.62 ~sQ31_spl|sQ32_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1185,f1186,f1189])).
% 0.14/0.62 fof(f1193,plain,(
% 0.14/0.62 $false|sQ31_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1188,f1088])).
% 0.14/0.62 fof(f1194,plain,(
% 0.14/0.62 sQ31_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1193])).
% 0.14/0.62 fof(f1195,plain,(
% 0.14/0.62 ![X0]: (~relation(relation_dom(relation_dom(sK56_skl)))|in(X0,relation_dom(relation_dom(relation_dom(sK56_skl))))|apply(relation_dom(relation_dom(sK56_skl)),X0)=empty_set)),
% 0.14/0.62 inference(resolution,[status(thm)],[f1180,f958])).
% 0.14/0.62 fof(f1196,definition,(
% 0.14/0.62 sQ33_spl <=> (relation(relation_dom(relation_dom(sK56_skl))))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1198,plain,(
% 0.14/0.62 ~relation(relation_dom(relation_dom(sK56_skl)))|sQ33_spl),
% 0.14/0.62 inference(component_clause,[status(thm)],[f1196])).
% 0.14/0.62 fof(f1199,definition,(
% 0.14/0.62 ![X0]: (sQ34_spl <=> (in(X0,relation_dom(relation_dom(relation_dom(sK56_skl))))|apply(relation_dom(relation_dom(sK56_skl)),X0)=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1202,plain,(
% 0.14/0.62 ~sQ33_spl|sQ34_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1195,f1196,f1199])).
% 0.14/0.62 fof(f1203,plain,(
% 0.14/0.62 $false|sQ33_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1198,f1150])).
% 0.14/0.62 fof(f1204,plain,(
% 0.14/0.62 sQ33_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1203])).
% 0.14/0.62 fof(f1205,plain,(
% 0.14/0.62 empty(relation_dom(relation_dom(sK54_skl)))|~relation(relation_dom(relation_dom(sK54_skl)))),
% 0.14/0.62 inference(resolution,[status(thm)],[f1170,f517])).
% 0.14/0.62 fof(f1210,definition,(
% 0.14/0.62 sQ35_spl <=> (empty(relation_dom(relation_dom(sK54_skl))))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1213,plain,(
% 0.14/0.62 sQ35_spl|~sQ31_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1205,f1210,f1186])).
% 0.14/0.62 fof(f1220,plain,(
% 0.14/0.62 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_dom(empty_set),relation_dom(X0)))),
% 0.14/0.62 inference(resolution,[status(thm)],[f721,f706])).
% 0.14/0.62 fof(f1221,definition,(
% 0.14/0.62 ![X0]: (sQ36_spl <=> (~relation(X0)|subset(relation_dom(empty_set),relation_dom(X0))))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1224,plain,(
% 0.14/0.62 ~sQ4_spl|sQ36_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1220,f990,f1221])).
% 0.14/0.62 fof(f1246,plain,(
% 0.14/0.62 ![X0]: (~relation(relation_dom(sK69_skl))|relation_dom(sK69_skl)=identity_relation(X0)|~in(sK0_skl(X0,relation_dom(sK69_skl)),X0)|~sK0_skl(X0,relation_dom(sK69_skl))=sK1_skl(X0,relation_dom(sK69_skl))|apply(sK69_skl,ordered_pair(sK0_skl(X0,relation_dom(sK69_skl)),sK1_skl(X0,relation_dom(sK69_skl))))=empty_set|~sQ14_spl)),
% 0.14/0.62 inference(resolution,[status(thm)],[f235,f1063])).
% 0.14/0.62 fof(f1247,definition,(
% 0.14/0.62 ![X0]: (sQ37_spl <=> (relation_dom(sK69_skl)=identity_relation(X0)|~in(sK0_skl(X0,relation_dom(sK69_skl)),X0)|~sK0_skl(X0,relation_dom(sK69_skl))=sK1_skl(X0,relation_dom(sK69_skl))|apply(sK69_skl,ordered_pair(sK0_skl(X0,relation_dom(sK69_skl)),sK1_skl(X0,relation_dom(sK69_skl))))=empty_set))),
% 0.14/0.62 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.14/0.62 fof(f1250,plain,(
% 0.14/0.62 ~sQ24_spl|sQ37_spl|~sQ14_spl),
% 0.14/0.62 inference(split_clause,[status(thm)],[f1246,f1140,f1247,f1062])).
% 0.14/0.62 fof(f1251,plain,(
% 0.14/0.62 in(ordered_pair(sK70_skl,sK71_skl),sK69_skl)|~sQ2_spl|~sQ11_spl),
% 0.14/0.62 inference(forward_demodulation,[status(thm)],[f915,f1047])).
% 0.14/0.62 fof(f1252,plain,(
% 0.14/0.62 $false|sQ0_spl|~sQ2_spl|~sQ11_spl),
% 0.14/0.62 inference(forward_subsumption_resolution,[status(thm)],[f1251,f909])).
% 0.14/0.62 fof(f1253,plain,(
% 0.14/0.62 sQ0_spl|~sQ2_spl|~sQ11_spl),
% 0.14/0.62 inference(contradiction_clause,[status(thm)],[f1252])).
% 0.14/0.62 fof(f1254,plain,(
% 0.14/0.62 $false),
% 0.14/0.62 inference(sat_refutation,[status(thm)],[f913,f917,f918,f999,f1006,f1015,f1023,f1025,f1027,f1033,f1049,f1061,f1065,f1067,f1072,f1075,f1083,f1085,f1094,f1102,f1104,f1107,f1119,f1121,f1143,f1147,f1156,f1164,f1166,f1175,f1184,f1192,f1194,f1202,f1204,f1213,f1224,f1250,f1253])).
% 0.14/0.62 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.64 % Elapsed time: 0.075781 seconds
% 0.14/0.64 % CPU time: 0.253491 seconds
% 0.14/0.64 % Total memory used: 120.141 MB
% 0.14/0.64 % Net memory used: 119.760 MB
%------------------------------------------------------------------------------