%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 02:12:47 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:44:58 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f2,axiom,(
% 0.13/0.39 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f3,axiom,(
% 0.13/0.39 (! [A,B] :( B = union(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(C,D)& in(D,A) ) )) )) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f7,conjecture,(
% 0.13/0.39 union(empty_set) = empty_set ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f8,negated_conjecture,(
% 0.13/0.39 ~(union(empty_set) = empty_set )),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f7])).
% 0.13/0.39 fof(f11,plain,(
% 0.13/0.39 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f2])).
% 0.13/0.39 fof(f12,plain,(
% 0.13/0.39 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f11])).
% 0.13/0.39 fof(f13,plain,(
% 0.13/0.39 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK0_skl(A),A)))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f12])).
% 0.13/0.39 fof(f14,plain,(
% 0.13/0.39 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.39 fof(f15,plain,(
% 0.13/0.39 ![X0]: (X0=empty_set|in(sK0_skl(X0),X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.39 fof(f16,plain,(
% 0.13/0.39 ![A,B]: ((~B=union(A)|(![C]: ((~in(C,B)|(?[D]: (in(C,D)&in(D,A))))&(in(C,B)|(![D]: (~in(C,D)|~in(D,A)))))))&(B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f17,plain,(
% 0.13/0.39 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(?[D]: (in(C,D)&in(D,A)))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f16])).
% 0.13/0.39 fof(f18,plain,(
% 0.13/0.39 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(in(C,sK1_skl(C,B,A))&in(sK1_skl(C,B,A),A))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|((~in(sK2_skl(B,A),B)|(![D]: (~in(sK2_skl(B,A),D)|~in(D,A))))&(in(sK2_skl(B,A),B)|(in(sK2_skl(B,A),sK3_skl(B,A))&in(sK3_skl(B,A),A))))))),
% 0.13/0.39 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))],[f17])).
% 0.13/0.39 fof(f20,plain,(
% 0.13/0.39 ![X0,X1,X2]: (~X0=union(X1)|~in(X2,X0)|in(sK1_skl(X2,X0,X1),X1))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.39 fof(f30,plain,(
% 0.13/0.39 ~union(empty_set)=empty_set),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.39 fof(f31,plain,(
% 0.13/0.39 ![X0]: (~in(X0,empty_set))),
% 0.13/0.39 inference(destructive_equality_resolution,[status(thm)],[f14])).
% 0.13/0.39 fof(f33,plain,(
% 0.13/0.39 ![X0,X1]: (~in(X0,union(X1))|in(sK1_skl(X0,union(X1),X1),X1))),
% 0.13/0.39 inference(destructive_equality_resolution,[status(thm)],[f20])).
% 0.13/0.39 fof(f44,plain,(
% 0.13/0.39 ![X0]: (in(sK1_skl(sK0_skl(union(X0)),union(X0),X0),X0)|union(X0)=empty_set)),
% 0.13/0.39 inference(resolution,[status(thm)],[f33,f15])).
% 0.13/0.39 fof(f68,plain,(
% 0.13/0.39 union(empty_set)=empty_set),
% 0.13/0.39 inference(resolution,[status(thm)],[f44,f31])).
% 0.13/0.39 fof(f71,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f68,f30])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.054862 seconds
% 0.13/0.42 % CPU time: 0.155558 seconds
% 0.13/0.42 % Total memory used: 80.376 MB
% 0.13/0.42 % Net memory used: 79.820 MB
%------------------------------------------------------------------------------