%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET662+3 : 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 : 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 02:12:25 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n003.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 05:33:31 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 0.18/0.51 % Refutation found
% 0.18/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.51 fof(f2,axiom,(
% 0.18/0.51 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ( (! [D] :( ilf_type(D,subset_type(cross_product(B,C)))=> ilf_type(D,relation_type(B,C)) ))& (! [E] :( ilf_type(E,relation_type(B,C))=> ilf_type(E,subset_type(cross_product(B,C))) ) )) ) )) )),
% 0.18/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.51 fof(f4,axiom,(
% 0.18/0.51 (! [B] :( ilf_type(B,set_type)=> ~ member(B,empty_set) ) )),
% 0.18/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.51 fof(f8,axiom,(
% 0.18/0.51 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ( ilf_type(C,subset_type(B))<=> ilf_type(C,member_type(power_set(B))) ) ) )) )),
% 0.18/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.51 fof(f12,axiom,(
% 0.18/0.51 (! [B] :( ilf_type(B,set_type)=> ( empty(B)<=> (! [C] :( ilf_type(C,set_type)=> ~ member(C,B) ) )) ) )),
% 0.18/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.51 fof(f13,axiom,(
% 0.18/0.51 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ( member(B,power_set(C))<=> (! [D] :( ilf_type(D,set_type)=> ( member(D,B)=> member(D,C) ) ) )) ) )) )),
% 0.18/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.51 fof(f15,axiom,(
% 0.18/0.51 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ( ~ empty(C)& ilf_type(C,set_type) )=> ( ilf_type(B,member_type(C))<=> member(B,C) ) ) )) )),
% 0.18/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.51 fof(f21,axiom,(
% 0.18/0.51 (! [B] : ilf_type(B,set_type) )),
% 0.18/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.51 fof(f22,conjecture,(
% 0.18/0.51 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ilf_type(empty_set,relation_type(B,C)) ) )) )),
% 0.18/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.51 fof(f23,negated_conjecture,(
% 0.18/0.51 ~((! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ilf_type(empty_set,relation_type(B,C)) ) )) ))),
% 0.18/0.51 inference(negated_conjecture,[status(cth)],[f22])).
% 0.18/0.51 fof(f26,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|((![D]: (~ilf_type(D,subset_type(cross_product(B,C)))|ilf_type(D,relation_type(B,C))))&(![E]: (~ilf_type(E,relation_type(B,C))|ilf_type(E,subset_type(cross_product(B,C)))))))))),
% 0.18/0.51 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.18/0.51 fof(f27,plain,(
% 0.18/0.51 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,subset_type(cross_product(X0,X1)))|ilf_type(X2,relation_type(X0,X1)))),
% 0.18/0.51 inference(cnf_transformation,[status(thm)],[f26])).
% 0.18/0.51 fof(f32,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|~member(B,empty_set))),
% 0.18/0.51 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.18/0.51 fof(f33,plain,(
% 0.18/0.51 ![X0]: (~ilf_type(X0,set_type)|~member(X0,empty_set))),
% 0.18/0.51 inference(cnf_transformation,[status(thm)],[f32])).
% 0.18/0.51 fof(f38,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(ilf_type(C,subset_type(B))<=>ilf_type(C,member_type(power_set(B)))))))),
% 0.18/0.51 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.18/0.51 fof(f39,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|((~ilf_type(C,subset_type(B))|ilf_type(C,member_type(power_set(B))))&(ilf_type(C,subset_type(B))|~ilf_type(C,member_type(power_set(B))))))))),
% 0.18/0.51 inference(NNF_transformation,[status(thm)],[f38])).
% 0.18/0.51 fof(f41,plain,(
% 0.18/0.51 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|ilf_type(X1,subset_type(X0))|~ilf_type(X1,member_type(power_set(X0))))),
% 0.18/0.51 inference(cnf_transformation,[status(thm)],[f39])).
% 0.18/0.51 fof(f54,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(empty(B)<=>(![C]: (~ilf_type(C,set_type)|~member(C,B)))))),
% 0.18/0.51 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.18/0.51 fof(f55,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|((~empty(B)|(![C]: (~ilf_type(C,set_type)|~member(C,B))))&(empty(B)|(?[C]: (ilf_type(C,set_type)&member(C,B))))))),
% 0.18/0.51 inference(NNF_transformation,[status(thm)],[f54])).
% 0.18/0.51 fof(f56,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|((~empty(B)|(![C]: (~ilf_type(C,set_type)|~member(C,B))))&(empty(B)|(ilf_type(sK3_skl(B),set_type)&member(sK3_skl(B),B)))))),
% 0.18/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B))],[f55])).
% 0.18/0.51 fof(f57,plain,(
% 0.18/0.51 ![X0,X1]: (~ilf_type(X0,set_type)|~empty(X0)|~ilf_type(X1,set_type)|~member(X1,X0))),
% 0.18/0.51 inference(cnf_transformation,[status(thm)],[f56])).
% 0.18/0.51 fof(f60,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(member(B,power_set(C))<=>(![D]: (~ilf_type(D,set_type)|(~member(D,B)|member(D,C))))))))),
% 0.18/0.51 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.18/0.51 fof(f61,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|((~member(B,power_set(C))|(![D]: (~ilf_type(D,set_type)|(~member(D,B)|member(D,C)))))&(member(B,power_set(C))|(?[D]: (ilf_type(D,set_type)&(member(D,B)&~member(D,C)))))))))),
% 0.18/0.51 inference(NNF_transformation,[status(thm)],[f60])).
% 0.18/0.51 fof(f62,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|((~member(B,power_set(C))|(![D]: (~ilf_type(D,set_type)|(~member(D,B)|member(D,C)))))&(member(B,power_set(C))|(ilf_type(sK4_skl(C,B),set_type)&(member(sK4_skl(C,B),B)&~member(sK4_skl(C,B),C))))))))),
% 0.18/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B))],[f61])).
% 0.18/0.51 fof(f65,plain,(
% 0.18/0.51 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|member(X0,power_set(X1))|member(sK4_skl(X1,X0),X0))),
% 0.18/0.51 inference(cnf_transformation,[status(thm)],[f62])).
% 0.18/0.51 fof(f70,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(![C]: ((empty(C)|~ilf_type(C,set_type))|(ilf_type(B,member_type(C))<=>member(B,C)))))),
% 0.18/0.51 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.18/0.51 fof(f71,plain,(
% 0.18/0.51 ![B]: (~ilf_type(B,set_type)|(![C]: ((empty(C)|~ilf_type(C,set_type))|((~ilf_type(B,member_type(C))|member(B,C))&(ilf_type(B,member_type(C))|~member(B,C))))))),
% 0.18/0.51 inference(NNF_transformation,[status(thm)],[f70])).
% 0.18/0.51 fof(f73,plain,(
% 0.18/0.51 ![X0,X1]: (~ilf_type(X0,set_type)|empty(X1)|~ilf_type(X1,set_type)|ilf_type(X0,member_type(X1))|~member(X0,X1))),
% 0.18/0.51 inference(cnf_transformation,[status(thm)],[f71])).
% 0.18/0.51 fof(f92,plain,(
% 0.18/0.51 ![X0]: (ilf_type(X0,set_type))),
% 0.18/0.51 inference(cnf_transformation,[status(thm)],[f21])).
% 0.18/0.51 fof(f93,plain,(
% 0.18/0.51 (?[B]: (ilf_type(B,set_type)&(?[C]: (ilf_type(C,set_type)&~ilf_type(empty_set,relation_type(B,C))))))),
% 0.18/0.51 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.18/0.51 fof(f94,plain,(
% 0.18/0.51 (ilf_type(sK9_skl,set_type)&(ilf_type(sK10_skl,set_type)&~ilf_type(empty_set,relation_type(sK9_skl,sK10_skl))))),
% 0.18/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(B,sK9_skl),skolemize(C,sK10_skl)],[f93])).
% 0.18/0.51 fof(f97,plain,(
% 0.18/0.51 ~ilf_type(empty_set,relation_type(sK9_skl,sK10_skl))),
% 0.18/0.51 inference(cnf_transformation,[status(thm)],[f94])).
% 0.18/0.51 fof(f98,plain,(
% 0.18/0.51 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|ilf_type(X0,member_type(X1))|~member(X0,X1))),
% 0.18/0.51 inference(forward_subsumption_resolution,[status(thm)],[f73,f57])).
% 0.18/0.51 fof(f105,plain,(
% 0.18/0.51 ![X0,X1]: (~ilf_type(X0,set_type)|ilf_type(X0,member_type(X1))|~member(X0,X1))),
% 0.18/0.51 inference(backward_subsumption_resolution,[status(thm)],[f98,f92])).
% 0.18/0.51 fof(f109,plain,(
% 0.18/0.51 ![X0,X1]: (~ilf_type(X0,set_type)|member(X0,power_set(X1))|member(sK4_skl(X1,X0),X0))),
% 0.18/0.51 inference(backward_subsumption_resolution,[status(thm)],[f65,f92])).
% 0.18/0.51 fof(f118,plain,(
% 0.18/0.51 ![X0,X1]: (~ilf_type(X0,set_type)|ilf_type(X1,subset_type(X0))|~ilf_type(X1,member_type(power_set(X0))))),
% 0.18/0.51 inference(backward_subsumption_resolution,[status(thm)],[f41,f92])).
% 0.18/0.51 fof(f120,plain,(
% 0.18/0.51 ![X0]: (~member(X0,empty_set))),
% 0.18/0.51 inference(backward_subsumption_resolution,[status(thm)],[f33,f92])).
% 0.18/0.51 fof(f123,plain,(
% 0.18/0.51 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,subset_type(cross_product(X0,X2)))|ilf_type(X1,relation_type(X0,X2)))),
% 0.18/0.51 inference(backward_subsumption_resolution,[status(thm)],[f27,f92])).
% 0.18/0.51 fof(f128,plain,(
% 0.18/0.51 ![X0,X1]: (ilf_type(X0,member_type(X1))|~member(X0,X1))),
% 0.18/0.51 inference(forward_subsumption_resolution,[status(thm)],[f105,f92])).
% 0.18/0.51 fof(f131,plain,(
% 0.18/0.51 ![X0,X1]: (member(X0,power_set(X1))|member(sK4_skl(X1,X0),X0))),
% 0.18/0.51 inference(forward_subsumption_resolution,[status(thm)],[f109,f92])).
% 0.18/0.51 fof(f137,plain,(
% 0.18/0.51 ![X0,X1]: (ilf_type(X0,subset_type(X1))|~ilf_type(X0,member_type(power_set(X1))))),
% 0.18/0.51 inference(forward_subsumption_resolution,[status(thm)],[f118,f92])).
% 0.18/0.51 fof(f141,plain,(
% 0.18/0.51 ![X0,X1,X2]: (~ilf_type(X0,subset_type(cross_product(X1,X2)))|ilf_type(X0,relation_type(X1,X2)))),
% 0.18/0.51 inference(forward_subsumption_resolution,[status(thm)],[f123,f92])).
% 0.18/0.51 fof(f161,plain,(
% 0.18/0.51 ![X0]: (member(empty_set,power_set(X0)))),
% 0.18/0.51 inference(resolution,[status(thm)],[f131,f120])).
% 0.18/0.51 fof(f169,plain,(
% 0.18/0.51 ![X0,X1]: (ilf_type(X0,subset_type(X1))|~member(X0,power_set(X1)))),
% 0.18/0.51 inference(resolution,[status(thm)],[f137,f128])).
% 0.18/0.51 fof(f195,plain,(
% 0.18/0.51 ![X0,X1,X2]: (ilf_type(X0,relation_type(X1,X2))|~member(X0,power_set(cross_product(X1,X2))))),
% 0.18/0.51 inference(resolution,[status(thm)],[f141,f169])).
% 0.18/0.51 fof(f241,plain,(
% 0.18/0.51 ![X0,X1]: (ilf_type(empty_set,relation_type(X0,X1)))),
% 0.18/0.51 inference(resolution,[status(thm)],[f195,f161])).
% 0.18/0.51 fof(f251,plain,(
% 0.18/0.51 $false),
% 0.18/0.51 inference(backward_subsumption_resolution,[status(thm)],[f97,f241])).
% 0.18/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.58 % Elapsed time: 0.103273 seconds
% 0.18/0.58 % CPU time: 0.146846 seconds
% 0.18/0.58 % Total memory used: 18.307 MB
% 0.18/0.58 % Net memory used: 18.231 MB
%------------------------------------------------------------------------------