%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:12:36 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 05:38:12 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.38 fof(f1,conjecture,(
% 0.13/0.38 ( (! [X,Y] :( equalish(X,Y)<=> (! [Z] :( a_member_of(Z,X)<=> a_member_of(Z,Y) ) )))=> (! [X,Y] :( equalish(X,Y)<=> equalish(Y,X) ) )) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f2,negated_conjecture,(
% 0.13/0.38 ~(( (! [X,Y] :( equalish(X,Y)<=> (! [Z] :( a_member_of(Z,X)<=> a_member_of(Z,Y) ) )))=> (! [X,Y] :( equalish(X,Y)<=> equalish(Y,X) ) )) )),
% 0.13/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.13/0.38 fof(f3,plain,(
% 0.13/0.38 ((![X,Y]: (equalish(X,Y)<=>(![Z]: (a_member_of(Z,X)<=>a_member_of(Z,Y)))))&(?[X,Y]: (equalish(X,Y)<~>equalish(Y,X))))),
% 0.13/0.38 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.13/0.38 fof(f4,plain,(
% 0.13/0.38 (![X,Y]: ((~equalish(X,Y)|(![Z]: ((~a_member_of(Z,X)|a_member_of(Z,Y))&(a_member_of(Z,X)|~a_member_of(Z,Y)))))&(equalish(X,Y)|(?[Z]: ((~a_member_of(Z,X)|~a_member_of(Z,Y))&(a_member_of(Z,X)|a_member_of(Z,Y)))))))&(?[X,Y]: ((equalish(X,Y)|equalish(Y,X))&(~equalish(X,Y)|~equalish(Y,X))))),
% 0.13/0.38 inference(NNF_transformation,[status(thm)],[f3])).
% 0.13/0.38 fof(f5,plain,(
% 0.13/0.38 ((![X,Y]: (~equalish(X,Y)|((![Z]: (~a_member_of(Z,X)|a_member_of(Z,Y)))&(![Z]: (a_member_of(Z,X)|~a_member_of(Z,Y))))))&(![X,Y]: (equalish(X,Y)|(?[Z]: ((~a_member_of(Z,X)|~a_member_of(Z,Y))&(a_member_of(Z,X)|a_member_of(Z,Y)))))))&(?[X,Y]: ((equalish(X,Y)|equalish(Y,X))&(~equalish(X,Y)|~equalish(Y,X))))),
% 0.13/0.38 inference(miniscoping,[status(thm)],[f4])).
% 0.13/0.38 fof(f6,plain,(
% 0.13/0.38 ((![X,Y]: (~equalish(X,Y)|((![Z]: (~a_member_of(Z,X)|a_member_of(Z,Y)))&(![Z]: (a_member_of(Z,X)|~a_member_of(Z,Y))))))&(![X,Y]: (equalish(X,Y)|((~a_member_of(sK0_skl(Y,X),X)|~a_member_of(sK0_skl(Y,X),Y))&(a_member_of(sK0_skl(Y,X),X)|a_member_of(sK0_skl(Y,X),Y))))))&((equalish(sK1_skl,sK2_skl)|equalish(sK2_skl,sK1_skl))&(~equalish(sK1_skl,sK2_skl)|~equalish(sK2_skl,sK1_skl)))),
% 0.13/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Z,sK0_skl(Y,X)),skolemize(X,sK1_skl),skolemize(Y,sK2_skl)],[f5])).
% 0.13/0.38 fof(f7,plain,(
% 0.13/0.38 ![X0,X1,X2]: (~equalish(X0,X1)|~a_member_of(X2,X0)|a_member_of(X2,X1))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f8,plain,(
% 0.13/0.38 ![X0,X1,X2]: (~equalish(X0,X1)|a_member_of(X2,X0)|~a_member_of(X2,X1))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f9,plain,(
% 0.13/0.38 ![X0,X1]: (equalish(X0,X1)|~a_member_of(sK0_skl(X1,X0),X0)|~a_member_of(sK0_skl(X1,X0),X1))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f10,plain,(
% 0.13/0.38 ![X0,X1]: (equalish(X0,X1)|a_member_of(sK0_skl(X1,X0),X0)|a_member_of(sK0_skl(X1,X0),X1))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f11,plain,(
% 0.13/0.38 equalish(sK1_skl,sK2_skl)|equalish(sK2_skl,sK1_skl)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f12,plain,(
% 0.13/0.38 ~equalish(sK1_skl,sK2_skl)|~equalish(sK2_skl,sK1_skl)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f13,definition,(
% 0.13/0.38 sQ0_spl <=> (equalish(sK1_skl,sK2_skl))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f14,plain,(
% 0.13/0.38 equalish(sK1_skl,sK2_skl)|~sQ0_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f13])).
% 0.13/0.38 fof(f16,definition,(
% 0.13/0.38 sQ1_spl <=> (equalish(sK2_skl,sK1_skl))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f17,plain,(
% 0.13/0.38 equalish(sK2_skl,sK1_skl)|~sQ1_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f16])).
% 0.13/0.38 fof(f19,plain,(
% 0.13/0.38 sQ0_spl|sQ1_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f11,f13,f16])).
% 0.13/0.38 fof(f20,plain,(
% 0.13/0.38 ~sQ0_spl|~sQ1_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f12,f13,f16])).
% 0.13/0.38 fof(f21,plain,(
% 0.13/0.38 ![X0]: (a_member_of(X0,sK2_skl)|~a_member_of(X0,sK1_skl)|~sQ1_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f17,f8])).
% 0.13/0.38 fof(f22,plain,(
% 0.13/0.38 ![X0]: (~a_member_of(X0,sK2_skl)|a_member_of(X0,sK1_skl)|~sQ1_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f17,f7])).
% 0.13/0.38 fof(f28,plain,(
% 0.13/0.38 ![X0]: (equalish(sK1_skl,X0)|a_member_of(sK0_skl(X0,sK1_skl),X0)|a_member_of(sK0_skl(X0,sK1_skl),sK2_skl)|~sQ1_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f10,f21])).
% 0.13/0.38 fof(f30,plain,(
% 0.13/0.38 ![X0]: (equalish(X0,sK2_skl)|a_member_of(sK0_skl(sK2_skl,X0),X0)|a_member_of(sK0_skl(sK2_skl,X0),sK1_skl)|~sQ1_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f10,f22])).
% 0.13/0.38 fof(f73,definition,(
% 0.13/0.38 sQ8_spl <=> (a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f78,plain,(
% 0.13/0.38 equalish(sK1_skl,sK2_skl)|a_member_of(sK0_skl(sK2_skl,sK1_skl),sK1_skl)|~sQ1_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f28,f22])).
% 0.13/0.38 fof(f86,definition,(
% 0.13/0.38 sQ10_spl <=> (a_member_of(sK0_skl(sK2_skl,sK1_skl),sK1_skl))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f87,plain,(
% 0.13/0.38 a_member_of(sK0_skl(sK2_skl,sK1_skl),sK1_skl)|~sQ10_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f86])).
% 0.13/0.38 fof(f89,plain,(
% 0.13/0.38 sQ0_spl|sQ10_spl|~sQ1_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f78,f13,f86,f16])).
% 0.13/0.38 fof(f90,definition,(
% 0.13/0.38 sQ11_spl <=> (a_member_of(sK0_skl(sK2_skl,sK1_skl),sK2_skl))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f95,plain,(
% 0.13/0.38 equalish(sK1_skl,sK2_skl)|~a_member_of(sK0_skl(sK2_skl,sK1_skl),sK2_skl)|~sQ10_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f87,f9])).
% 0.13/0.38 fof(f97,plain,(
% 0.13/0.38 sQ0_spl|~sQ11_spl|~sQ10_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f95,f13,f90,f86])).
% 0.13/0.38 fof(f101,plain,(
% 0.13/0.38 equalish(sK1_skl,sK2_skl)|a_member_of(sK0_skl(sK2_skl,sK1_skl),sK2_skl)|~sQ1_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f30,f21])).
% 0.13/0.38 fof(f108,plain,(
% 0.13/0.38 sQ0_spl|sQ11_spl|~sQ1_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f101,f13,f90,f16])).
% 0.13/0.38 fof(f111,plain,(
% 0.13/0.38 ![X0]: (a_member_of(X0,sK1_skl)|~a_member_of(X0,sK2_skl)|~sQ0_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f14,f8])).
% 0.13/0.38 fof(f112,plain,(
% 0.13/0.38 ![X0]: (~a_member_of(X0,sK1_skl)|a_member_of(X0,sK2_skl)|~sQ0_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f14,f7])).
% 0.13/0.38 fof(f140,plain,(
% 0.13/0.38 ![X0]: (a_member_of(sK0_skl(sK1_skl,X0),sK2_skl)|equalish(X0,sK1_skl)|a_member_of(sK0_skl(sK1_skl,X0),X0)|~sQ0_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f112,f10])).
% 0.13/0.38 fof(f151,plain,(
% 0.13/0.38 equalish(sK2_skl,sK1_skl)|equalish(sK2_skl,sK1_skl)|~a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|~sQ0_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f140,f9])).
% 0.13/0.38 fof(f153,plain,(
% 0.13/0.38 equalish(sK2_skl,sK1_skl)|a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|~sQ0_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f140,f111])).
% 0.13/0.38 fof(f158,plain,(
% 0.13/0.38 sQ1_spl|~sQ8_spl|~sQ0_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f151,f16,f73,f13])).
% 0.13/0.38 fof(f160,plain,(
% 0.13/0.38 sQ1_spl|sQ8_spl|~sQ0_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f153,f16,f73,f13])).
% 0.13/0.38 fof(f164,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(sat_refutation,[status(thm)],[f19,f20,f89,f97,f108,f158,f160])).
% 0.13/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.048286 seconds
% 0.13/0.42 % CPU time: 0.140136 seconds
% 0.13/0.42 % Total memory used: 17.042 MB
% 0.13/0.42 % Net memory used: 16.511 MB
%------------------------------------------------------------------------------