%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:11:57 PM UTC 2026
% Result : Theorem 0.15s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n009.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 05:10:12 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.15/0.57 % Refutation found
% 0.15/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.57 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.57 fof(f1,axiom,(
% 0.15/0.57 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 0.15/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.57 fof(f2,axiom,(
% 0.15/0.57 (! [A,B] :( equal_set(A,B)<=> ( subset(A,B)& subset(B,A) ) ) )),
% 0.15/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.57 fof(f8,axiom,(
% 0.15/0.57 (! [X,A] :( member(X,singleton(A))<=> X = A ) )),
% 0.15/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.57 fof(f10,axiom,(
% 0.15/0.57 (! [X,A] :( member(X,sum(A))<=> (? [Y] :( member(Y,A)& member(X,Y) ) )) )),
% 0.15/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.57 fof(f12,conjecture,(
% 0.15/0.57 (! [A] : equal_set(sum(singleton(A)),A) )),
% 0.15/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.57 fof(f13,negated_conjecture,(
% 0.15/0.57 ~((! [A] : equal_set(sum(singleton(A)),A) ))),
% 0.15/0.57 inference(negated_conjecture,[status(cth)],[f12])).
% 0.15/0.57 fof(f14,plain,(
% 0.15/0.57 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 0.15/0.57 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.15/0.57 fof(f15,plain,(
% 0.15/0.57 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.15/0.57 inference(NNF_transformation,[status(thm)],[f14])).
% 0.15/0.57 fof(f16,plain,(
% 0.15/0.57 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.15/0.57 inference(miniscoping,[status(thm)],[f15])).
% 0.15/0.57 fof(f17,plain,(
% 0.15/0.57 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(member(sK0_skl(B,A),A)&~member(sK0_skl(B,A),B))))),
% 0.15/0.57 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16])).
% 0.15/0.57 fof(f19,plain,(
% 0.15/0.57 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 0.15/0.57 inference(cnf_transformation,[status(thm)],[f17])).
% 0.15/0.57 fof(f20,plain,(
% 0.15/0.57 ![X0,X1]: (subset(X0,X1)|~member(sK0_skl(X1,X0),X1))),
% 0.15/0.57 inference(cnf_transformation,[status(thm)],[f17])).
% 0.15/0.57 fof(f21,plain,(
% 0.15/0.57 ![A,B]: ((~equal_set(A,B)|(subset(A,B)&subset(B,A)))&(equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 0.15/0.57 inference(NNF_transformation,[status(thm)],[f2])).
% 0.15/0.57 fof(f22,plain,(
% 0.15/0.57 (![A,B]: (~equal_set(A,B)|(subset(A,B)&subset(B,A))))&(![A,B]: (equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 0.15/0.57 inference(miniscoping,[status(thm)],[f21])).
% 0.15/0.57 fof(f25,plain,(
% 0.15/0.57 ![X0,X1]: (equal_set(X0,X1)|~subset(X0,X1)|~subset(X1,X0))),
% 0.15/0.57 inference(cnf_transformation,[status(thm)],[f22])).
% 0.15/0.57 fof(f46,plain,(
% 0.15/0.57 ![X,A]: ((~member(X,singleton(A))|X=A)&(member(X,singleton(A))|~X=A))),
% 0.15/0.57 inference(NNF_transformation,[status(thm)],[f8])).
% 0.15/0.57 fof(f47,plain,(
% 0.15/0.57 (![X,A]: (~member(X,singleton(A))|X=A))&(![X,A]: (member(X,singleton(A))|~X=A))),
% 0.15/0.57 inference(miniscoping,[status(thm)],[f46])).
% 0.15/0.57 fof(f48,plain,(
% 0.15/0.57 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 0.15/0.57 inference(cnf_transformation,[status(thm)],[f47])).
% 0.15/0.57 fof(f49,plain,(
% 0.15/0.57 ![X0,X1]: (member(X0,singleton(X1))|~X0=X1)),
% 0.15/0.57 inference(cnf_transformation,[status(thm)],[f47])).
% 0.15/0.57 fof(f55,plain,(
% 0.15/0.57 ![X,A]: ((~member(X,sum(A))|(?[Y]: (member(Y,A)&member(X,Y))))&(member(X,sum(A))|(![Y]: (~member(Y,A)|~member(X,Y)))))),
% 0.15/0.57 inference(NNF_transformation,[status(thm)],[f10])).
% 0.15/0.57 fof(f56,plain,(
% 0.15/0.57 (![X,A]: (~member(X,sum(A))|(?[Y]: (member(Y,A)&member(X,Y)))))&(![X,A]: (member(X,sum(A))|(![Y]: (~member(Y,A)|~member(X,Y)))))),
% 0.15/0.57 inference(miniscoping,[status(thm)],[f55])).
% 0.15/0.57 fof(f57,plain,(
% 0.15/0.57 (![X,A]: (~member(X,sum(A))|(member(sK1_skl(A,X),A)&member(X,sK1_skl(A,X)))))&(![X,A]: (member(X,sum(A))|(![Y]: (~member(Y,A)|~member(X,Y)))))),
% 0.15/0.57 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(A,X))],[f56])).
% 0.15/0.57 fof(f58,plain,(
% 0.15/0.57 ![X0,X1]: (~member(X0,sum(X1))|member(sK1_skl(X1,X0),X1))),
% 0.15/0.57 inference(cnf_transformation,[status(thm)],[f57])).
% 0.15/0.57 fof(f59,plain,(
% 0.15/0.57 ![X0,X1]: (~member(X0,sum(X1))|member(X0,sK1_skl(X1,X0)))),
% 0.15/0.57 inference(cnf_transformation,[status(thm)],[f57])).
% 0.15/0.57 fof(f60,plain,(
% 0.15/0.57 ![X0,X1,X2]: (member(X0,sum(X1))|~member(X2,X1)|~member(X0,X2))),
% 0.15/0.57 inference(cnf_transformation,[status(thm)],[f57])).
% 0.15/0.57 fof(f68,plain,(
% 0.15/0.57 (?[A]: ~equal_set(sum(singleton(A)),A))),
% 0.15/0.58 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.15/0.58 fof(f69,plain,(
% 0.15/0.58 ~equal_set(sum(singleton(sK3_skl)),sK3_skl)),
% 0.15/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f68])).
% 0.15/0.58 fof(f70,plain,(
% 0.15/0.58 ~equal_set(sum(singleton(sK3_skl)),sK3_skl)),
% 0.15/0.58 inference(cnf_transformation,[status(thm)],[f69])).
% 0.15/0.58 fof(f71,plain,(
% 0.15/0.58 ![X0]: (member(X0,singleton(X0)))),
% 0.15/0.58 inference(destructive_equality_resolution,[status(thm)],[f49])).
% 0.15/0.58 fof(f77,plain,(
% 0.15/0.58 ![X0,X1,X2]: (subset(X0,sum(X1))|~member(X2,X1)|~member(sK0_skl(sum(X1),X0),X2))),
% 0.15/0.58 inference(resolution,[status(thm)],[f20,f60])).
% 0.15/0.58 fof(f84,plain,(
% 0.15/0.58 ![X0,X1]: (~member(X0,sum(singleton(X1)))|sK1_skl(singleton(X1),X0)=X1)),
% 0.15/0.58 inference(resolution,[status(thm)],[f58,f48])).
% 0.15/0.58 fof(f94,plain,(
% 0.15/0.58 ![X0,X1]: (sK1_skl(singleton(X0),sK0_skl(X1,sum(singleton(X0))))=X0|subset(sum(singleton(X0)),X1))),
% 0.15/0.58 inference(resolution,[status(thm)],[f84,f19])).
% 0.15/0.58 fof(f98,plain,(
% 0.15/0.58 ![X0,X1]: (subset(X0,sum(X1))|~member(X0,X1)|subset(X0,sum(X1)))),
% 0.15/0.58 inference(resolution,[status(thm)],[f77,f19])).
% 0.15/0.58 fof(f103,plain,(
% 0.15/0.58 ![X0,X1]: (subset(X0,sum(X1))|~member(X0,X1))),
% 0.15/0.58 inference(duplicate_literals_removal,[status(thm)],[f98])).
% 0.15/0.58 fof(f105,plain,(
% 0.15/0.58 ![X0,X1]: (~member(X0,X1)|equal_set(sum(X1),X0)|~subset(sum(X1),X0))),
% 0.15/0.58 inference(resolution,[status(thm)],[f103,f25])).
% 0.15/0.58 fof(f106,plain,(
% 0.15/0.58 ~member(sK3_skl,singleton(sK3_skl))|~subset(sum(singleton(sK3_skl)),sK3_skl)),
% 0.15/0.58 inference(resolution,[status(thm)],[f105,f70])).
% 0.15/0.58 fof(f109,plain,(
% 0.15/0.58 ~subset(sum(singleton(sK3_skl)),sK3_skl)),
% 0.15/0.58 inference(forward_subsumption_resolution,[status(thm)],[f106,f71])).
% 0.15/0.58 fof(f145,plain,(
% 0.15/0.58 sK1_skl(singleton(sK3_skl),sK0_skl(sK3_skl,sum(singleton(sK3_skl))))=sK3_skl),
% 0.15/0.58 inference(resolution,[status(thm)],[f109,f94])).
% 0.15/0.58 fof(f146,plain,(
% 0.15/0.58 ~member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sum(singleton(sK3_skl)))|member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sK3_skl)),
% 0.15/0.58 inference(paramodulation,[status(thm)],[f145,f59])).
% 0.15/0.58 fof(f148,plain,(
% 0.15/0.58 member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sK3_skl)|subset(sum(singleton(sK3_skl)),sK3_skl)),
% 0.62/0.58 inference(resolution,[status(thm)],[f146,f19])).
% 0.62/0.58 fof(f151,plain,(
% 0.62/0.58 subset(sum(singleton(sK3_skl)),sK3_skl)),
% 0.62/0.58 inference(forward_subsumption_resolution,[status(thm)],[f148,f20])).
% 0.62/0.58 fof(f152,plain,(
% 0.62/0.58 $false),
% 0.62/0.58 inference(backward_subsumption_resolution,[status(thm)],[f109,f151])).
% 0.62/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 0.62/0.60 % Elapsed time: 0.152931 seconds
% 0.62/0.60 % CPU time: 0.863958 seconds
% 0.62/0.60 % Total memory used: 91.001 MB
% 0.62/0.60 % Net memory used: 89.731 MB
%------------------------------------------------------------------------------