%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET994+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 : 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 02:12:57 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:48:01 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.48 % Refutation found
% 0.16/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.48 fof(f4,axiom,(
% 0.16/0.48 (! [A] :(? [B] : element(B,A) ))),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f5,axiom,(
% 0.16/0.48 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f20,axiom,(
% 0.16/0.48 (! [A] :(? [B] :( relation(B)& function(B)& relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = n0 ) )) ))),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f21,axiom,(
% 0.16/0.48 (! [A] :(? [B] :( relation(B)& function(B)& relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = n1 ) )) ))),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f22,axiom,(
% 0.16/0.48 empty(n0) ),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f23,axiom,(
% 0.16/0.48 ~ empty(n1) ),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f24,conjecture,(
% 0.16/0.48 (! [A] :( (! [B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( ( relation_dom(B) = A& relation_dom(C) = A )=> B = C ) ) )))=> A = empty_set ) )),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f25,negated_conjecture,(
% 0.16/0.48 ~((! [A] :( (! [B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( ( relation_dom(B) = A& relation_dom(C) = A )=> B = C ) ) )))=> A = empty_set ) ))),
% 0.16/0.48 inference(negated_conjecture,[status(cth)],[f24])).
% 0.16/0.48 fof(f27,axiom,(
% 0.16/0.48 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f31,axiom,(
% 0.16/0.48 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.16/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.48 fof(f40,plain,(
% 0.16/0.48 ![A]: element(sK0_skl(A),A)),
% 0.16/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f4])).
% 0.16/0.48 fof(f41,plain,(
% 0.16/0.48 ![X0]: (element(sK0_skl(X0),X0))),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f40])).
% 0.16/0.48 fof(f42,plain,(
% 0.16/0.48 empty(empty_set)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f5])).
% 0.16/0.48 fof(f79,plain,(
% 0.16/0.48 ![A]: (?[B]: (((relation(B)&function(B))&relation_dom(B)=A)&(![C]: (~in(C,A)|apply(B,C)=n0))))),
% 0.16/0.48 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.16/0.48 fof(f80,plain,(
% 0.16/0.48 ![A]: (((relation(sK9_skl(A))&function(sK9_skl(A)))&relation_dom(sK9_skl(A))=A)&(![C]: (~in(C,A)|apply(sK9_skl(A),C)=n0)))),
% 0.16/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(B,sK9_skl(A))],[f79])).
% 0.16/0.48 fof(f81,plain,(
% 0.16/0.48 ![X0]: (relation(sK9_skl(X0)))),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f80])).
% 0.16/0.48 fof(f82,plain,(
% 0.16/0.48 ![X0]: (function(sK9_skl(X0)))),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f80])).
% 0.16/0.48 fof(f83,plain,(
% 0.16/0.48 ![X0]: (relation_dom(sK9_skl(X0))=X0)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f80])).
% 0.16/0.48 fof(f84,plain,(
% 0.16/0.48 ![X0,X1]: (~in(X0,X1)|apply(sK9_skl(X1),X0)=n0)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f80])).
% 0.16/0.48 fof(f85,plain,(
% 0.16/0.48 ![A]: (?[B]: (((relation(B)&function(B))&relation_dom(B)=A)&(![C]: (~in(C,A)|apply(B,C)=n1))))),
% 0.16/0.48 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.16/0.48 fof(f86,plain,(
% 0.16/0.48 ![A]: (((relation(sK10_skl(A))&function(sK10_skl(A)))&relation_dom(sK10_skl(A))=A)&(![C]: (~in(C,A)|apply(sK10_skl(A),C)=n1)))),
% 0.16/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(B,sK10_skl(A))],[f85])).
% 0.16/0.48 fof(f87,plain,(
% 0.16/0.48 ![X0]: (relation(sK10_skl(X0)))),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f86])).
% 0.16/0.48 fof(f88,plain,(
% 0.16/0.48 ![X0]: (function(sK10_skl(X0)))),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f86])).
% 0.16/0.48 fof(f89,plain,(
% 0.16/0.48 ![X0]: (relation_dom(sK10_skl(X0))=X0)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f86])).
% 0.16/0.48 fof(f90,plain,(
% 0.16/0.48 ![X0,X1]: (~in(X0,X1)|apply(sK10_skl(X1),X0)=n1)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f86])).
% 0.16/0.48 fof(f91,plain,(
% 0.16/0.48 empty(n0)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f22])).
% 0.16/0.48 fof(f92,plain,(
% 0.16/0.48 ~empty(n1)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f23])).
% 0.16/0.48 fof(f93,plain,(
% 0.16/0.48 (?[A]: ((![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~relation_dom(B)=A|~relation_dom(C)=A)|B=C)))))&~A=empty_set))),
% 0.16/0.48 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.16/0.48 fof(f94,plain,(
% 0.16/0.48 ((![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~relation_dom(B)=sK11_skl|~relation_dom(C)=sK11_skl)|B=C)))))&~sK11_skl=empty_set)),
% 0.16/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(A,sK11_skl)],[f93])).
% 0.16/0.48 fof(f95,plain,(
% 0.16/0.48 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation_dom(X0)=sK11_skl|~relation_dom(X1)=sK11_skl|X0=X1)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f94])).
% 0.16/0.48 fof(f96,plain,(
% 0.16/0.48 ~sK11_skl=empty_set),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f94])).
% 0.16/0.48 fof(f99,plain,(
% 0.16/0.48 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 0.16/0.48 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.16/0.48 fof(f100,plain,(
% 0.16/0.48 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f99])).
% 0.16/0.48 fof(f111,plain,(
% 0.16/0.48 ![A]: (~empty(A)|A=empty_set)),
% 0.16/0.48 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 0.16/0.48 fof(f112,plain,(
% 0.16/0.48 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.16/0.48 inference(cnf_transformation,[status(thm)],[f111])).
% 0.16/0.48 fof(f155,plain,(
% 0.16/0.48 n0=empty_set),
% 0.16/0.48 inference(resolution,[status(thm)],[f91,f112])).
% 0.16/0.48 fof(f160,plain,(
% 0.16/0.48 ![X0,X1]: (~in(X0,X1)|apply(sK9_skl(X1),X0)=empty_set)),
% 0.16/0.48 inference(backward_demodulation,[status(thm)],[f155,f84])).
% 0.16/0.48 fof(f180,plain,(
% 0.16/0.48 ![X0,X1]: (~relation(X0)|~function(X0)|~function(sK9_skl(X1))|~relation_dom(X0)=sK11_skl|~relation_dom(sK9_skl(X1))=sK11_skl|X0=sK9_skl(X1))),
% 0.16/0.48 inference(resolution,[status(thm)],[f81,f95])).
% 0.16/0.48 fof(f181,plain,(
% 0.16/0.48 ![X0,X1]: (~relation(X0)|~function(X0)|~function(sK9_skl(X1))|~relation_dom(X0)=sK11_skl|~X1=sK11_skl|X0=sK9_skl(X1))),
% 0.16/0.48 inference(forward_demodulation,[status(thm)],[f83,f180])).
% 0.16/0.48 fof(f182,plain,(
% 0.16/0.48 ![X0]: (~relation(X0)|~function(X0)|~function(sK9_skl(sK11_skl))|~relation_dom(X0)=sK11_skl|X0=sK9_skl(sK11_skl))),
% 0.16/0.48 inference(destructive_equality_resolution,[status(thm)],[f181])).
% 0.16/0.48 fof(f183,plain,(
% 0.16/0.48 ![X0]: (~relation(X0)|~function(X0)|~relation_dom(X0)=sK11_skl|X0=sK9_skl(sK11_skl))),
% 0.16/0.48 inference(forward_subsumption_resolution,[status(thm)],[f182,f82])).
% 0.16/0.48 fof(f193,plain,(
% 0.16/0.48 ![X0]: (~relation(sK10_skl(X0))|~relation_dom(sK10_skl(X0))=sK11_skl|sK10_skl(X0)=sK9_skl(sK11_skl))),
% 0.16/0.48 inference(resolution,[status(thm)],[f88,f183])).
% 0.16/0.48 fof(f194,plain,(
% 0.16/0.48 ![X0]: (~relation(sK10_skl(X0))|~X0=sK11_skl|sK10_skl(X0)=sK9_skl(sK11_skl))),
% 0.16/0.48 inference(forward_demodulation,[status(thm)],[f89,f193])).
% 0.16/0.48 fof(f195,plain,(
% 0.16/0.48 ~relation(sK10_skl(sK11_skl))|sK10_skl(sK11_skl)=sK9_skl(sK11_skl)),
% 0.16/0.48 inference(destructive_equality_resolution,[status(thm)],[f194])).
% 0.16/0.48 fof(f197,plain,(
% 0.16/0.48 sK10_skl(sK11_skl)=sK9_skl(sK11_skl)),
% 0.16/0.48 inference(forward_subsumption_resolution,[status(thm)],[f195,f87])).
% 0.16/0.48 fof(f204,plain,(
% 0.16/0.48 ![X0]: (empty(X0)|in(sK0_skl(X0),X0))),
% 0.16/0.48 inference(resolution,[status(thm)],[f100,f41])).
% 0.16/0.48 fof(f257,plain,(
% 0.16/0.48 ![X0]: (empty(X0)|apply(sK10_skl(X0),sK0_skl(X0))=n1)),
% 0.16/0.48 inference(resolution,[status(thm)],[f204,f90])).
% 0.16/0.48 fof(f259,plain,(
% 0.16/0.48 ![X0]: (empty(X0)|apply(sK9_skl(X0),sK0_skl(X0))=empty_set)),
% 0.16/0.49 inference(resolution,[status(thm)],[f204,f160])).
% 0.16/0.49 fof(f283,plain,(
% 0.16/0.49 ![X0]: (apply(sK9_skl(X0),sK0_skl(X0))=empty_set|X0=empty_set)),
% 0.16/0.49 inference(resolution,[status(thm)],[f259,f112])).
% 0.16/0.49 fof(f438,plain,(
% 0.16/0.49 ![X0]: (apply(sK10_skl(X0),sK0_skl(X0))=n1|X0=empty_set)),
% 0.16/0.49 inference(resolution,[status(thm)],[f257,f112])).
% 0.16/0.49 fof(f481,plain,(
% 0.16/0.49 apply(sK9_skl(sK11_skl),sK0_skl(sK11_skl))=n1|sK11_skl=empty_set),
% 0.16/0.49 inference(paramodulation,[status(thm)],[f197,f438])).
% 0.16/0.49 fof(f485,plain,(
% 0.16/0.49 apply(sK9_skl(sK11_skl),sK0_skl(sK11_skl))=n1),
% 0.16/0.49 inference(forward_subsumption_resolution,[status(thm)],[f481,f96])).
% 0.16/0.49 fof(f486,plain,(
% 0.16/0.49 empty_set=n1|sK11_skl=empty_set),
% 0.16/0.49 inference(paramodulation,[status(thm)],[f283,f485])).
% 0.16/0.49 fof(f497,plain,(
% 0.16/0.49 ~empty(empty_set)),
% 0.16/0.49 inference(backward_demodulation,[status(thm)],[f528,f92])).
% 0.16/0.49 fof(f528,plain,(
% 0.16/0.49 empty_set=n1),
% 0.16/0.49 inference(forward_subsumption_resolution,[status(thm)],[f486,f96])).
% 0.16/0.49 fof(f531,plain,(
% 0.16/0.49 $false),
% 0.16/0.49 inference(forward_subsumption_resolution,[status(thm)],[f497,f42])).
% 0.16/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.48/0.53 % Elapsed time: 0.088446 seconds
% 0.48/0.53 % CPU time: 0.266501 seconds
% 0.48/0.53 % Total memory used: 69.422 MB
% 0.48/0.53 % Net memory used: 69.191 MB
%------------------------------------------------------------------------------