%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET887+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 : n012.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 02:12:49 PM UTC 2026
% Result : Theorem 0.03s 0.33s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 05:42:52 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.03/0.33 % Refutation found
% 0.03/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.33 % SZS output start CNFRefutation for theBenchmark
% 0.03/0.33 fof(f2,axiom,(
% 0.03/0.33 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.03/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.33 fof(f3,axiom,(
% 0.03/0.33 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.03/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.33 fof(f4,axiom,(
% 0.03/0.33 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.03/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.33 fof(f6,axiom,(
% 0.03/0.33 (! [A,B,C] :( subset(A,unordered_pair(B,C))<=> ~ ( A != empty_set& A != singleton(B)& A != singleton(C)& A != unordered_pair(B,C) ) ) )),
% 0.03/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.33 fof(f10,axiom,(
% 0.03/0.33 (! [A,B,C,D] :~ ( unordered_pair(A,B) = unordered_pair(C,D)& A != C& A != D ) )),
% 0.03/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.33 fof(f11,conjecture,(
% 0.03/0.33 (! [A,B,C,D] :~ ( subset(unordered_pair(A,B),unordered_pair(C,D))& A != C& A != D ) )),
% 0.03/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.33 fof(f12,negated_conjecture,(
% 0.03/0.33 ~((! [A,B,C,D] :~ ( subset(unordered_pair(A,B),unordered_pair(C,D))& A != C& A != D ) ))),
% 0.03/0.33 inference(negated_conjecture,[status(cth)],[f11])).
% 0.03/0.33 fof(f13,axiom,(
% 0.03/0.33 (! [A,B,C] :( singleton(A) = unordered_pair(B,C)=> A = B ) )),
% 0.03/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/0.33 fof(f16,plain,(
% 0.03/0.33 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f2])).
% 0.03/0.33 fof(f17,plain,(
% 0.03/0.33 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.03/0.33 inference(NNF_transformation,[status(thm)],[f3])).
% 0.03/0.33 fof(f18,plain,(
% 0.03/0.33 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.03/0.33 inference(miniscoping,[status(thm)],[f17])).
% 0.03/0.33 fof(f19,plain,(
% 0.03/0.33 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK0_skl(A),A)))),
% 0.03/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f18])).
% 0.03/0.33 fof(f20,plain,(
% 0.03/0.33 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f19])).
% 0.03/0.33 fof(f22,plain,(
% 0.03/0.33 ![A,B,C]: ((~C=unordered_pair(A,B)|(![D]: ((~in(D,C)|(D=A|D=B))&(in(D,C)|(~D=A&~D=B)))))&(C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 0.03/0.33 inference(NNF_transformation,[status(thm)],[f4])).
% 0.03/0.33 fof(f23,plain,(
% 0.03/0.33 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 0.03/0.33 inference(miniscoping,[status(thm)],[f22])).
% 0.03/0.33 fof(f24,plain,(
% 0.03/0.33 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|((~in(sK1_skl(C,B,A),C)|(~sK1_skl(C,B,A)=A&~sK1_skl(C,B,A)=B))&(in(sK1_skl(C,B,A),C)|(sK1_skl(C,B,A)=A|sK1_skl(C,B,A)=B)))))),
% 0.03/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f23])).
% 0.03/0.33 fof(f26,plain,(
% 0.03/0.33 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X1)),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f24])).
% 0.03/0.33 fof(f32,plain,(
% 0.03/0.33 ![A,B,C]: (subset(A,unordered_pair(B,C))<=>(((A=empty_set|A=singleton(B))|A=singleton(C))|A=unordered_pair(B,C)))),
% 0.03/0.33 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.03/0.33 fof(f33,plain,(
% 0.03/0.33 ![A,B,C]: ((~subset(A,unordered_pair(B,C))|(((A=empty_set|A=singleton(B))|A=singleton(C))|A=unordered_pair(B,C)))&(subset(A,unordered_pair(B,C))|(((~A=empty_set&~A=singleton(B))&~A=singleton(C))&~A=unordered_pair(B,C))))),
% 0.03/0.33 inference(NNF_transformation,[status(thm)],[f32])).
% 0.03/0.33 fof(f34,plain,(
% 0.03/0.33 (![A,B,C]: (~subset(A,unordered_pair(B,C))|(((A=empty_set|A=singleton(B))|A=singleton(C))|A=unordered_pair(B,C))))&(![A,B,C]: (subset(A,unordered_pair(B,C))|(((~A=empty_set&~A=singleton(B))&~A=singleton(C))&~A=unordered_pair(B,C))))),
% 0.03/0.33 inference(miniscoping,[status(thm)],[f33])).
% 0.03/0.33 fof(f35,plain,(
% 0.03/0.33 ![X0,X1,X2]: (~subset(X0,unordered_pair(X1,X2))|X0=empty_set|X0=singleton(X1)|X0=singleton(X2)|X0=unordered_pair(X1,X2))),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f34])).
% 0.03/0.33 fof(f46,plain,(
% 0.03/0.33 ![A,B,C,D]: ((~unordered_pair(A,B)=unordered_pair(C,D)|A=C)|A=D)),
% 0.03/0.33 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.03/0.33 fof(f47,plain,(
% 0.03/0.33 ![A,D]: ((![C]: ((![B]: ~unordered_pair(A,B)=unordered_pair(C,D))|A=C))|A=D)),
% 0.03/0.33 inference(miniscoping,[status(thm)],[f46])).
% 0.03/0.33 fof(f48,plain,(
% 0.03/0.33 ![X0,X1,X2,X3]: (~unordered_pair(X0,X1)=unordered_pair(X2,X3)|X0=X2|X0=X3)),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f47])).
% 0.03/0.33 fof(f49,plain,(
% 0.03/0.33 (?[A,B,C,D]: ((subset(unordered_pair(A,B),unordered_pair(C,D))&~A=C)&~A=D))),
% 0.03/0.33 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.03/0.33 fof(f50,plain,(
% 0.03/0.33 ?[A,D]: ((?[C]: ((?[B]: subset(unordered_pair(A,B),unordered_pair(C,D)))&~A=C))&~A=D)),
% 0.03/0.33 inference(miniscoping,[status(thm)],[f49])).
% 0.03/0.33 fof(f51,plain,(
% 0.03/0.33 ((subset(unordered_pair(sK4_skl,sK7_skl),unordered_pair(sK6_skl,sK5_skl))&~sK4_skl=sK6_skl)&~sK4_skl=sK5_skl)),
% 0.03/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK4_skl),skolemize(D,sK5_skl),skolemize(C,sK6_skl),skolemize(B,sK7_skl)],[f50])).
% 0.03/0.33 fof(f52,plain,(
% 0.03/0.33 subset(unordered_pair(sK4_skl,sK7_skl),unordered_pair(sK6_skl,sK5_skl))),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f51])).
% 0.03/0.33 fof(f53,plain,(
% 0.03/0.33 ~sK4_skl=sK6_skl),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f51])).
% 0.03/0.33 fof(f54,plain,(
% 0.03/0.33 ~sK4_skl=sK5_skl),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f51])).
% 0.03/0.33 fof(f55,plain,(
% 0.03/0.33 ![A,B,C]: (~singleton(A)=unordered_pair(B,C)|A=B)),
% 0.03/0.33 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.03/0.33 fof(f56,plain,(
% 0.03/0.33 ![A,B]: ((![C]: ~singleton(A)=unordered_pair(B,C))|A=B)),
% 0.03/0.33 inference(miniscoping,[status(thm)],[f55])).
% 0.03/0.33 fof(f57,plain,(
% 0.03/0.33 ![X0,X1,X2]: (~singleton(X0)=unordered_pair(X1,X2)|X0=X1)),
% 0.03/0.33 inference(cnf_transformation,[status(thm)],[f56])).
% 0.03/0.33 fof(f58,plain,(
% 0.03/0.33 ![X0]: (~in(X0,empty_set))),
% 0.03/0.33 inference(destructive_equality_resolution,[status(thm)],[f20])).
% 0.03/0.33 fof(f60,plain,(
% 0.03/0.33 ![X0,X1]: (in(X0,unordered_pair(X0,X1)))),
% 0.03/0.33 inference(destructive_equality_resolution,[status(thm)],[f26])).
% 0.03/0.33 fof(f86,plain,(
% 0.03/0.33 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.03/0.33 inference(paramodulation,[status(thm)],[f16,f60])).
% 0.03/0.33 fof(f161,plain,(
% 0.03/0.33 unordered_pair(sK4_skl,sK7_skl)=empty_set|unordered_pair(sK4_skl,sK7_skl)=singleton(sK6_skl)|unordered_pair(sK4_skl,sK7_skl)=singleton(sK5_skl)|unordered_pair(sK4_skl,sK7_skl)=unordered_pair(sK6_skl,sK5_skl)),
% 0.03/0.33 inference(resolution,[status(thm)],[f35,f52])).
% 0.03/0.33 fof(f185,definition,(
% 0.03/0.33 sQ6_spl <=> (unordered_pair(sK4_skl,sK7_skl)=empty_set)),
% 0.03/0.33 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.03/0.33 fof(f186,plain,(
% 0.03/0.33 unordered_pair(sK4_skl,sK7_skl)=empty_set|~sQ6_spl),
% 0.03/0.33 inference(component_clause,[status(thm)],[f185])).
% 0.03/0.33 fof(f188,definition,(
% 0.03/0.33 sQ7_spl <=> (unordered_pair(sK4_skl,sK7_skl)=singleton(sK6_skl))),
% 0.03/0.33 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.03/0.33 fof(f189,plain,(
% 0.03/0.33 unordered_pair(sK4_skl,sK7_skl)=singleton(sK6_skl)|~sQ7_spl),
% 0.03/0.33 inference(component_clause,[status(thm)],[f188])).
% 0.03/0.33 fof(f191,definition,(
% 0.03/0.33 sQ8_spl <=> (unordered_pair(sK4_skl,sK7_skl)=singleton(sK5_skl))),
% 0.03/0.33 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.03/0.33 fof(f192,plain,(
% 0.03/0.33 unordered_pair(sK4_skl,sK7_skl)=singleton(sK5_skl)|~sQ8_spl),
% 0.03/0.33 inference(component_clause,[status(thm)],[f191])).
% 0.03/0.33 fof(f194,definition,(
% 0.03/0.33 sQ9_spl <=> (unordered_pair(sK4_skl,sK7_skl)=unordered_pair(sK6_skl,sK5_skl))),
% 0.03/0.33 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.03/0.33 fof(f195,plain,(
% 0.03/0.33 unordered_pair(sK4_skl,sK7_skl)=unordered_pair(sK6_skl,sK5_skl)|~sQ9_spl),
% 0.03/0.33 inference(component_clause,[status(thm)],[f194])).
% 0.03/0.33 fof(f197,plain,(
% 0.03/0.33 sQ6_spl|sQ7_spl|sQ8_spl|sQ9_spl),
% 0.03/0.33 inference(split_clause,[status(thm)],[f161,f185,f188,f191,f194])).
% 0.03/0.33 fof(f212,plain,(
% 0.03/0.33 in(sK7_skl,empty_set)|~sQ6_spl),
% 0.03/0.33 inference(paramodulation,[status(thm)],[f186,f86])).
% 0.03/0.33 fof(f236,plain,(
% 0.03/0.33 $false|~sQ6_spl),
% 0.03/0.33 inference(forward_subsumption_resolution,[status(thm)],[f212,f58])).
% 0.03/0.33 fof(f237,plain,(
% 0.03/0.33 ~sQ6_spl),
% 0.03/0.33 inference(contradiction_clause,[status(thm)],[f236])).
% 0.08/0.34 fof(f354,plain,(
% 0.08/0.34 sK5_skl=sK4_skl|~sQ8_spl),
% 0.08/0.34 inference(resolution,[status(thm)],[f192,f57])).
% 0.08/0.34 fof(f377,plain,(
% 0.08/0.34 $false|~sQ8_spl),
% 0.08/0.34 inference(forward_subsumption_resolution,[status(thm)],[f354,f54])).
% 0.08/0.34 fof(f378,plain,(
% 0.08/0.34 ~sQ8_spl),
% 0.08/0.34 inference(contradiction_clause,[status(thm)],[f377])).
% 0.08/0.34 fof(f383,plain,(
% 0.08/0.34 sK6_skl=sK4_skl|~sQ7_spl),
% 0.08/0.34 inference(resolution,[status(thm)],[f189,f57])).
% 0.08/0.34 fof(f406,plain,(
% 0.08/0.34 $false|~sQ7_spl),
% 0.08/0.34 inference(forward_subsumption_resolution,[status(thm)],[f383,f53])).
% 0.08/0.34 fof(f407,plain,(
% 0.08/0.34 ~sQ7_spl),
% 0.08/0.34 inference(contradiction_clause,[status(thm)],[f406])).
% 0.08/0.34 fof(f445,plain,(
% 0.08/0.34 sK4_skl=sK6_skl|sK4_skl=sK5_skl|~sQ9_spl),
% 0.08/0.34 inference(resolution,[status(thm)],[f195,f48])).
% 0.08/0.34 fof(f478,definition,(
% 0.08/0.34 sQ28_spl <=> (sK4_skl=sK6_skl)),
% 0.08/0.34 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.08/0.34 fof(f479,plain,(
% 0.08/0.34 sK4_skl=sK6_skl|~sQ28_spl),
% 0.08/0.34 inference(component_clause,[status(thm)],[f478])).
% 0.08/0.34 fof(f481,definition,(
% 0.08/0.34 sQ29_spl <=> (sK4_skl=sK5_skl)),
% 0.08/0.34 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.08/0.34 fof(f482,plain,(
% 0.08/0.34 sK4_skl=sK5_skl|~sQ29_spl),
% 0.08/0.34 inference(component_clause,[status(thm)],[f481])).
% 0.08/0.34 fof(f484,plain,(
% 0.08/0.34 sQ28_spl|sQ29_spl|~sQ9_spl),
% 0.08/0.34 inference(split_clause,[status(thm)],[f445,f478,f481,f194])).
% 0.08/0.34 fof(f500,plain,(
% 0.08/0.34 $false|~sQ28_spl),
% 0.08/0.34 inference(forward_subsumption_resolution,[status(thm)],[f479,f53])).
% 0.08/0.34 fof(f501,plain,(
% 0.08/0.34 ~sQ28_spl),
% 0.08/0.34 inference(contradiction_clause,[status(thm)],[f500])).
% 0.08/0.34 fof(f502,plain,(
% 0.08/0.34 $false|~sQ29_spl),
% 0.08/0.34 inference(forward_subsumption_resolution,[status(thm)],[f482,f54])).
% 0.08/0.34 fof(f503,plain,(
% 0.08/0.34 ~sQ29_spl),
% 0.08/0.34 inference(contradiction_clause,[status(thm)],[f502])).
% 0.08/0.34 fof(f504,plain,(
% 0.08/0.34 $false),
% 0.08/0.34 inference(sat_refutation,[status(thm)],[f197,f237,f378,f407,f484,f501,f503])).
% 0.08/0.34 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.35 % Elapsed time: 0.041913 seconds
% 0.08/0.35 % CPU time: 0.110627 seconds
% 0.08/0.35 % Total memory used: 102.816 MB
% 0.08/0.35 % Net memory used: 102.439 MB
%------------------------------------------------------------------------------