%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET656+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:12:24 PM UTC 2026
% Result : Theorem 0.17s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET656+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n007.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 05:29:06 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.17/0.43 % Drodi V4.1.1
% 0.17/0.62 % Refutation found
% 0.17/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.62 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.62 fof(f1,axiom,(
% 0.17/0.62 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ( subset(B,C)=> intersection(B,C) = B ) ) )) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f6,axiom,(
% 0.17/0.62 (! [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))) ) )) ) )) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f13,axiom,(
% 0.17/0.62 (! [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))) ) ) )) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f17,axiom,(
% 0.17/0.62 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ( subset(B,C)<=> (! [D] :( ilf_type(D,set_type)=> ( member(D,B)=> member(D,C) ) ) )) ) )) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f19,axiom,(
% 0.17/0.62 (! [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) ) ) )) ) )) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f20,axiom,(
% 0.17/0.62 (! [B] :( ilf_type(B,set_type)=> ( ~ empty(power_set(B))& ilf_type(power_set(B),set_type) ) ) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f21,axiom,(
% 0.17/0.62 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ( ~ empty(C)& ilf_type(C,set_type) )=> ( ilf_type(B,member_type(C))<=> member(B,C) ) ) )) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f30,axiom,(
% 0.17/0.62 (! [B] : ilf_type(B,set_type) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f31,conjecture,(
% 0.17/0.62 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(B,C))=> intersection(D,cross_product(B,C)) = D ) )) )) )),
% 0.17/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f32,negated_conjecture,(
% 0.17/0.62 ~((! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(B,C))=> intersection(D,cross_product(B,C)) = D ) )) )) ))),
% 0.17/0.62 inference(negated_conjecture,[status(cth)],[f31])).
% 0.17/0.62 fof(f33,plain,(
% 0.17/0.62 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(~subset(B,C)|intersection(B,C)=B))))),
% 0.17/0.62 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.17/0.62 fof(f34,plain,(
% 0.17/0.62 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~subset(X0,X1)|intersection(X0,X1)=X0)),
% 0.17/0.62 inference(cnf_transformation,[status(thm)],[f33])).
% 0.17/0.62 fof(f53,plain,(
% 0.17/0.62 ![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)))))))))),
% 0.17/0.62 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.17/0.62 fof(f55,plain,(
% 0.17/0.62 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|ilf_type(X2,subset_type(cross_product(X0,X1))))),
% 0.17/0.62 inference(cnf_transformation,[status(thm)],[f53])).
% 0.17/0.62 fof(f79,plain,(
% 0.17/0.62 ![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)))))))),
% 0.17/0.62 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.17/0.62 fof(f80,plain,(
% 0.17/0.62 ![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))))))))),
% 0.17/0.62 inference(NNF_transformation,[status(thm)],[f79])).
% 0.17/0.62 fof(f81,plain,(
% 0.17/0.62 ![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))))),
% 0.17/0.62 inference(cnf_transformation,[status(thm)],[f80])).
% 0.17/0.62 fof(f90,plain,(
% 0.17/0.62 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(subset(B,C)<=>(![D]: (~ilf_type(D,set_type)|(~member(D,B)|member(D,C))))))))),
% 0.17/0.62 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.17/0.63 fof(f91,plain,(
% 0.17/0.63 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|((~subset(B,C)|(![D]: (~ilf_type(D,set_type)|(~member(D,B)|member(D,C)))))&(subset(B,C)|(?[D]: (ilf_type(D,set_type)&(member(D,B)&~member(D,C)))))))))),
% 0.17/0.63 inference(NNF_transformation,[status(thm)],[f90])).
% 0.17/0.63 fof(f92,plain,(
% 0.17/0.63 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|((~subset(B,C)|(![D]: (~ilf_type(D,set_type)|(~member(D,B)|member(D,C)))))&(subset(B,C)|(ilf_type(sK7_skl(C,B),set_type)&(member(sK7_skl(C,B),B)&~member(sK7_skl(C,B),C))))))))),
% 0.17/0.63 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(D,sK7_skl(C,B))],[f91])).
% 0.17/0.63 fof(f95,plain,(
% 0.17/0.63 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|subset(X0,X1)|member(sK7_skl(X1,X0),X0))),
% 0.17/0.63 inference(cnf_transformation,[status(thm)],[f92])).
% 0.17/0.63 fof(f96,plain,(
% 0.17/0.63 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|subset(X0,X1)|~member(sK7_skl(X1,X0),X1))),
% 0.17/0.63 inference(cnf_transformation,[status(thm)],[f92])).
% 0.17/0.63 fof(f99,plain,(
% 0.17/0.63 ![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))))))))),
% 0.17/0.63 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.17/0.63 fof(f100,plain,(
% 0.17/0.63 ![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)))))))))),
% 0.17/0.63 inference(NNF_transformation,[status(thm)],[f99])).
% 0.17/0.63 fof(f101,plain,(
% 0.17/0.63 ![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(sK8_skl(C,B),set_type)&(member(sK8_skl(C,B),B)&~member(sK8_skl(C,B),C))))))))),
% 0.17/0.63 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(D,sK8_skl(C,B))],[f100])).
% 0.17/0.63 fof(f102,plain,(
% 0.17/0.63 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~member(X0,power_set(X1))|~ilf_type(X2,set_type)|~member(X2,X0)|member(X2,X1))),
% 0.17/0.63 inference(cnf_transformation,[status(thm)],[f101])).
% 0.17/0.63 fof(f106,plain,(
% 0.17/0.63 ![B]: (~ilf_type(B,set_type)|(~empty(power_set(B))&ilf_type(power_set(B),set_type)))),
% 0.17/0.63 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.17/0.63 fof(f107,plain,(
% 0.17/0.63 ![X0]: (~ilf_type(X0,set_type)|~empty(power_set(X0)))),
% 0.17/0.63 inference(cnf_transformation,[status(thm)],[f106])).
% 0.17/0.63 fof(f109,plain,(
% 0.17/0.63 ![B]: (~ilf_type(B,set_type)|(![C]: ((empty(C)|~ilf_type(C,set_type))|(ilf_type(B,member_type(C))<=>member(B,C)))))),
% 0.17/0.63 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.17/0.63 fof(f110,plain,(
% 0.17/0.63 ![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))))))),
% 0.17/0.63 inference(NNF_transformation,[status(thm)],[f109])).
% 0.17/0.63 fof(f111,plain,(
% 0.17/0.63 ![X0,X1]: (~ilf_type(X0,set_type)|empty(X1)|~ilf_type(X1,set_type)|~ilf_type(X0,member_type(X1))|member(X0,X1))),
% 0.17/0.63 inference(cnf_transformation,[status(thm)],[f110])).
% 0.17/0.63 fof(f147,plain,(
% 0.17/0.63 ![X0]: (ilf_type(X0,set_type))),
% 0.17/0.63 inference(cnf_transformation,[status(thm)],[f30])).
% 0.17/0.63 fof(f148,plain,(
% 0.17/0.63 (?[B]: (ilf_type(B,set_type)&(?[C]: (ilf_type(C,set_type)&(?[D]: (ilf_type(D,relation_type(B,C))&~intersection(D,cross_product(B,C))=D))))))),
% 0.17/0.63 inference(pre_NNF_transformation,[status(thm)],[f32])).
% 0.17/0.63 fof(f149,plain,(
% 0.17/0.63 (ilf_type(sK15_skl,set_type)&(ilf_type(sK16_skl,set_type)&(ilf_type(sK17_skl,relation_type(sK15_skl,sK16_skl))&~intersection(sK17_skl,cross_product(sK15_skl,sK16_skl))=sK17_skl)))),
% 0.17/0.63 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl,sK17_skl]),skolemize(B,sK15_skl),skolemize(C,sK16_skl),skolemize(D,sK17_skl)],[f148])).
% 0.17/0.63 fof(f152,plain,(
% 0.17/0.63 ilf_type(sK17_skl,relation_type(sK15_skl,sK16_skl))),
% 0.17/0.63 inference(cnf_transformation,[status(thm)],[f149])).
% 0.17/0.63 fof(f153,plain,(
% 0.17/0.63 ~intersection(sK17_skl,cross_product(sK15_skl,sK16_skl))=sK17_skl),
% 0.17/0.63 inference(cnf_transformation,[status(thm)],[f149])).
% 0.17/0.63 fof(f170,plain,(
% 0.17/0.63 ![X0]: (~empty(power_set(X0)))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f107,f147])).
% 0.17/0.63 fof(f172,plain,(
% 0.17/0.63 ![X0,X1]: (~ilf_type(X0,set_type)|~subset(X1,X0)|intersection(X1,X0)=X1)),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f34,f147])).
% 0.17/0.63 fof(f173,plain,(
% 0.17/0.63 ![X0,X1]: (~subset(X0,X1)|intersection(X0,X1)=X0)),
% 0.17/0.63 inference(resolution,[status(thm)],[f172,f147])).
% 0.17/0.63 fof(f283,plain,(
% 0.17/0.63 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X2,X0))|ilf_type(X1,subset_type(cross_product(X2,X0))))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f55,f147])).
% 0.17/0.63 fof(f284,plain,(
% 0.17/0.63 ![X0,X1,X2]: (~ilf_type(X0,relation_type(X1,X2))|ilf_type(X0,subset_type(cross_product(X1,X2))))),
% 0.17/0.63 inference(resolution,[status(thm)],[f283,f147])).
% 0.17/0.63 fof(f317,plain,(
% 0.17/0.63 ilf_type(sK17_skl,subset_type(cross_product(sK15_skl,sK16_skl)))),
% 0.17/0.63 inference(resolution,[status(thm)],[f284,f152])).
% 0.17/0.63 fof(f394,plain,(
% 0.17/0.63 ![X0,X1]: (~ilf_type(X0,set_type)|subset(X1,X0)|member(sK7_skl(X0,X1),X1))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f95,f147])).
% 0.17/0.63 fof(f395,plain,(
% 0.17/0.63 ![X0,X1]: (subset(X0,X1)|member(sK7_skl(X1,X0),X0))),
% 0.17/0.63 inference(resolution,[status(thm)],[f394,f147])).
% 0.17/0.63 fof(f429,plain,(
% 0.17/0.63 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X0,subset_type(X1))|ilf_type(X0,member_type(power_set(X1))))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f81,f147])).
% 0.17/0.63 fof(f430,plain,(
% 0.17/0.63 ![X0,X1]: (~ilf_type(X0,subset_type(X1))|ilf_type(X0,member_type(power_set(X1))))),
% 0.17/0.63 inference(resolution,[status(thm)],[f429,f147])).
% 0.17/0.63 fof(f435,plain,(
% 0.17/0.63 ilf_type(sK17_skl,member_type(power_set(cross_product(sK15_skl,sK16_skl))))),
% 0.17/0.63 inference(resolution,[status(thm)],[f430,f317])).
% 0.17/0.63 fof(f473,plain,(
% 0.17/0.63 ![X0,X1]: (~ilf_type(X0,set_type)|subset(X1,X0)|~member(sK7_skl(X0,X1),X0))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f96,f147])).
% 0.17/0.63 fof(f474,plain,(
% 0.17/0.63 ![X0,X1]: (subset(X0,X1)|~member(sK7_skl(X1,X0),X1))),
% 0.17/0.63 inference(resolution,[status(thm)],[f473,f147])).
% 0.17/0.63 fof(f478,plain,(
% 0.17/0.63 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~member(X1,power_set(X0))|~ilf_type(X2,set_type)|~member(X2,X1)|member(X2,X0))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f102,f147])).
% 0.17/0.63 fof(f479,plain,(
% 0.17/0.63 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~member(X1,power_set(X0))|~member(X2,X1)|member(X2,X0))),
% 0.17/0.63 inference(resolution,[status(thm)],[f478,f147])).
% 0.17/0.63 fof(f480,plain,(
% 0.17/0.63 ![X0,X1,X2]: (~member(X0,power_set(X1))|~member(X2,X0)|member(X2,X1))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f479,f147])).
% 0.17/0.63 fof(f1076,plain,(
% 0.17/0.63 ![X0,X1]: (empty(X0)|~ilf_type(X0,set_type)|~ilf_type(X1,member_type(X0))|member(X1,X0))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f111,f147])).
% 0.17/0.63 fof(f1081,plain,(
% 0.17/0.63 empty(power_set(cross_product(sK15_skl,sK16_skl)))|~ilf_type(power_set(cross_product(sK15_skl,sK16_skl)),set_type)|member(sK17_skl,power_set(cross_product(sK15_skl,sK16_skl)))),
% 0.17/0.63 inference(resolution,[status(thm)],[f1076,f435])).
% 0.17/0.63 fof(f1087,plain,(
% 0.17/0.63 ~ilf_type(power_set(cross_product(sK15_skl,sK16_skl)),set_type)|member(sK17_skl,power_set(cross_product(sK15_skl,sK16_skl)))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f1081,f170])).
% 0.17/0.63 fof(f1138,plain,(
% 0.17/0.63 member(sK17_skl,power_set(cross_product(sK15_skl,sK16_skl)))),
% 0.17/0.63 inference(forward_subsumption_resolution,[status(thm)],[f1087,f147])).
% 0.17/0.63 fof(f1139,plain,(
% 0.17/0.63 ![X0]: (~member(X0,sK17_skl)|member(X0,cross_product(sK15_skl,sK16_skl)))),
% 0.17/0.63 inference(resolution,[status(thm)],[f1138,f480])).
% 0.17/0.63 fof(f1151,plain,(
% 0.17/0.63 ![X0]: (member(sK7_skl(X0,sK17_skl),cross_product(sK15_skl,sK16_skl))|subset(sK17_skl,X0))),
% 0.17/0.63 inference(resolution,[status(thm)],[f1139,f395])).
% 0.17/0.63 fof(f1578,plain,(
% 0.17/0.63 subset(sK17_skl,cross_product(sK15_skl,sK16_skl))|subset(sK17_skl,cross_product(sK15_skl,sK16_skl))),
% 0.17/0.63 inference(resolution,[status(thm)],[f1151,f474])).
% 0.17/0.63 fof(f1589,plain,(
% 0.17/0.63 subset(sK17_skl,cross_product(sK15_skl,sK16_skl))),
% 0.17/0.63 inference(duplicate_literals_removal,[status(thm)],[f1578])).
% 0.17/0.63 fof(f1607,plain,(
% 0.17/0.63 intersection(sK17_skl,cross_product(sK15_skl,sK16_skl))=sK17_skl),
% 0.17/0.63 inference(resolution,[status(thm)],[f1589,f173])).
% 0.17/0.63 fof(f1608,plain,(
% 0.17/0.63 $false),
% 0.17/0.65 inference(forward_subsumption_resolution,[status(thm)],[f1607,f153])).
% 0.17/0.65 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.67 % Elapsed time: 0.243905 seconds
% 0.17/0.67 % CPU time: 1.415335 seconds
% 0.17/0.67 % Total memory used: 99.479 MB
% 0.17/0.67 % Net memory used: 98.155 MB
%------------------------------------------------------------------------------