%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET641+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 : 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 02:12:23 PM UTC 2026
% Result : Theorem 0.08s 0.33s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET641+3 : TPTP v9.3.1. Released v2.2.0.
% 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 05:30:22 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.08/0.33 % Refutation found
% 0.08/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.33 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.33 fof(f1,axiom,(
% 0.08/0.33 (! [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))) ) )) ) )) )),
% 0.08/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.33 fof(f5,axiom,(
% 0.08/0.33 (! [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) ) ) )) ) )) )),
% 0.08/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.33 fof(f7,axiom,(
% 0.08/0.33 (! [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))) ) ) )) )),
% 0.08/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.33 fof(f10,axiom,(
% 0.08/0.33 (! [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) ) ) )) ) )) )),
% 0.08/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.33 fof(f12,axiom,(
% 0.08/0.33 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ( ~ empty(C)& ilf_type(C,set_type) )=> ( ilf_type(B,member_type(C))<=> member(B,C) ) ) )) )),
% 0.08/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.33 fof(f14,axiom,(
% 0.08/0.33 (! [B] :( ilf_type(B,set_type)=> ( empty(B)<=> (! [C] :( ilf_type(C,set_type)=> ~ member(C,B) ) )) ) )),
% 0.08/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.33 fof(f18,axiom,(
% 0.08/0.33 (! [B] : ilf_type(B,set_type) )),
% 0.08/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.33 fof(f19,conjecture,(
% 0.08/0.33 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,set_type)=> ( subset(B,cross_product(C,D))=> ilf_type(B,relation_type(C,D)) ) ) )) )) )),
% 0.08/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.33 fof(f20,negated_conjecture,(
% 0.08/0.33 ~((! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,set_type)=> ( subset(B,cross_product(C,D))=> ilf_type(B,relation_type(C,D)) ) ) )) )) ))),
% 0.08/0.33 inference(negated_conjecture,[status(cth)],[f19])).
% 0.08/0.33 fof(f21,plain,(
% 0.08/0.33 ![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)))))))))),
% 0.08/0.33 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.08/0.33 fof(f22,plain,(
% 0.08/0.33 ![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)))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f21])).
% 0.08/0.33 fof(f38,plain,(
% 0.08/0.33 ![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))))))))),
% 0.08/0.33 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.08/0.33 fof(f39,plain,(
% 0.08/0.33 ![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)))))))))),
% 0.08/0.33 inference(NNF_transformation,[status(thm)],[f38])).
% 0.08/0.33 fof(f40,plain,(
% 0.08/0.33 ![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(sK3_skl(C,B),set_type)&(member(sK3_skl(C,B),B)&~member(sK3_skl(C,B),C))))))))),
% 0.08/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B))],[f39])).
% 0.08/0.33 fof(f41,plain,(
% 0.08/0.33 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~subset(X0,X1)|~ilf_type(X2,set_type)|~member(X2,X0)|member(X2,X1))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f40])).
% 0.08/0.33 fof(f47,plain,(
% 0.08/0.33 ![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)))))))),
% 0.08/0.33 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.08/0.33 fof(f48,plain,(
% 0.08/0.33 ![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))))))))),
% 0.08/0.33 inference(NNF_transformation,[status(thm)],[f47])).
% 0.08/0.33 fof(f50,plain,(
% 0.08/0.33 ![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))))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f48])).
% 0.08/0.33 fof(f56,plain,(
% 0.08/0.33 ![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))))))))),
% 0.08/0.33 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.08/0.33 fof(f57,plain,(
% 0.08/0.33 ![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)))))))))),
% 0.08/0.33 inference(NNF_transformation,[status(thm)],[f56])).
% 0.08/0.33 fof(f58,plain,(
% 0.08/0.33 ![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(sK5_skl(C,B),set_type)&(member(sK5_skl(C,B),B)&~member(sK5_skl(C,B),C))))))))),
% 0.08/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(D,sK5_skl(C,B))],[f57])).
% 0.08/0.33 fof(f61,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|member(X0,power_set(X1))|member(sK5_skl(X1,X0),X0))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f58])).
% 0.08/0.33 fof(f62,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|member(X0,power_set(X1))|~member(sK5_skl(X1,X0),X1))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f58])).
% 0.08/0.33 fof(f66,plain,(
% 0.08/0.33 ![B]: (~ilf_type(B,set_type)|(![C]: ((empty(C)|~ilf_type(C,set_type))|(ilf_type(B,member_type(C))<=>member(B,C)))))),
% 0.08/0.33 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.08/0.33 fof(f67,plain,(
% 0.08/0.33 ![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))))))),
% 0.08/0.33 inference(NNF_transformation,[status(thm)],[f66])).
% 0.08/0.33 fof(f69,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|empty(X1)|~ilf_type(X1,set_type)|ilf_type(X0,member_type(X1))|~member(X0,X1))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f67])).
% 0.08/0.33 fof(f73,plain,(
% 0.08/0.33 ![B]: (~ilf_type(B,set_type)|(empty(B)<=>(![C]: (~ilf_type(C,set_type)|~member(C,B)))))),
% 0.08/0.33 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.08/0.33 fof(f74,plain,(
% 0.08/0.33 ![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))))))),
% 0.08/0.33 inference(NNF_transformation,[status(thm)],[f73])).
% 0.08/0.33 fof(f75,plain,(
% 0.08/0.33 ![B]: (~ilf_type(B,set_type)|((~empty(B)|(![C]: (~ilf_type(C,set_type)|~member(C,B))))&(empty(B)|(ilf_type(sK7_skl(B),set_type)&member(sK7_skl(B),B)))))),
% 0.08/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(C,sK7_skl(B))],[f74])).
% 0.08/0.33 fof(f76,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|~empty(X0)|~ilf_type(X1,set_type)|~member(X1,X0))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f75])).
% 0.08/0.33 fof(f92,plain,(
% 0.08/0.33 ![X0]: (ilf_type(X0,set_type))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f18])).
% 0.08/0.33 fof(f93,plain,(
% 0.08/0.33 (?[B]: (ilf_type(B,set_type)&(?[C]: (ilf_type(C,set_type)&(?[D]: (ilf_type(D,set_type)&(subset(B,cross_product(C,D))&~ilf_type(B,relation_type(C,D)))))))))),
% 0.08/0.33 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.08/0.33 fof(f94,plain,(
% 0.08/0.33 (ilf_type(sK11_skl,set_type)&(ilf_type(sK12_skl,set_type)&(ilf_type(sK13_skl,set_type)&(subset(sK11_skl,cross_product(sK12_skl,sK13_skl))&~ilf_type(sK11_skl,relation_type(sK12_skl,sK13_skl))))))),
% 0.08/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(B,sK11_skl),skolemize(C,sK12_skl),skolemize(D,sK13_skl)],[f93])).
% 0.08/0.33 fof(f98,plain,(
% 0.08/0.33 subset(sK11_skl,cross_product(sK12_skl,sK13_skl))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f94])).
% 0.08/0.33 fof(f99,plain,(
% 0.08/0.33 ~ilf_type(sK11_skl,relation_type(sK12_skl,sK13_skl))),
% 0.08/0.33 inference(cnf_transformation,[status(thm)],[f94])).
% 0.08/0.33 fof(f102,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|ilf_type(X0,member_type(X1))|~member(X0,X1))),
% 0.08/0.33 inference(backward_subsumption_resolution,[status(thm)],[f69,f76])).
% 0.08/0.33 fof(f113,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|member(X0,power_set(X1))|~member(sK5_skl(X1,X0),X1))),
% 0.08/0.33 inference(backward_subsumption_resolution,[status(thm)],[f62,f92])).
% 0.08/0.33 fof(f114,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|member(X0,power_set(X1))|member(sK5_skl(X1,X0),X0))),
% 0.08/0.33 inference(backward_subsumption_resolution,[status(thm)],[f61,f92])).
% 0.08/0.33 fof(f118,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|ilf_type(X1,subset_type(X0))|~ilf_type(X1,member_type(power_set(X0))))),
% 0.08/0.33 inference(backward_subsumption_resolution,[status(thm)],[f50,f92])).
% 0.08/0.33 fof(f122,plain,(
% 0.08/0.33 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.08/0.33 inference(backward_subsumption_resolution,[status(thm)],[f41,f92])).
% 0.08/0.33 fof(f128,plain,(
% 0.08/0.33 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,subset_type(cross_product(X0,X2)))|ilf_type(X1,relation_type(X0,X2)))),
% 0.08/0.33 inference(backward_subsumption_resolution,[status(thm)],[f22,f92])).
% 0.08/0.33 fof(f130,plain,(
% 0.08/0.33 ![X0,X1]: (~ilf_type(X0,set_type)|ilf_type(X1,member_type(X0))|~member(X1,X0))),
% 0.08/0.33 inference(forward_subsumption_resolution,[status(thm)],[f102,f92])).
% 0.08/0.33 fof(f136,plain,(
% 0.08/0.33 ![X0,X1]: (member(X0,power_set(X1))|~member(sK5_skl(X1,X0),X1))),
% 0.08/0.33 inference(forward_subsumption_resolution,[status(thm)],[f113,f92])).
% 0.08/0.33 fof(f137,plain,(
% 0.08/0.33 ![X0,X1]: (member(X0,power_set(X1))|member(sK5_skl(X1,X0),X0))),
% 0.08/0.33 inference(forward_subsumption_resolution,[status(thm)],[f114,f92])).
% 0.08/0.33 fof(f139,plain,(
% 0.08/0.33 ![X0,X1]: (ilf_type(X0,subset_type(X1))|~ilf_type(X0,member_type(power_set(X1))))),
% 0.08/0.33 inference(forward_subsumption_resolution,[status(thm)],[f118,f92])).
% 0.08/0.33 fof(f143,plain,(
% 0.08/0.33 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~subset(X1,X0)|~member(X2,X1)|member(X2,X0))),
% 0.08/0.33 inference(forward_subsumption_resolution,[status(thm)],[f122,f92])).
% 0.08/0.33 fof(f149,plain,(
% 0.08/0.33 ![X0,X1,X2]: (~ilf_type(X0,subset_type(cross_product(X1,X2)))|ilf_type(X0,relation_type(X1,X2)))),
% 0.08/0.33 inference(forward_subsumption_resolution,[status(thm)],[f128,f92])).
% 0.08/0.33 fof(f159,plain,(
% 0.08/0.33 ![X0,X1]: (ilf_type(X0,subset_type(X1))|~ilf_type(power_set(X1),set_type)|~member(X0,power_set(X1)))),
% 0.08/0.33 inference(resolution,[status(thm)],[f139,f130])).
% 0.08/0.33 fof(f161,plain,(
% 0.08/0.33 ![X0,X1]: (ilf_type(X0,subset_type(X1))|~member(X0,power_set(X1)))),
% 0.08/0.33 inference(forward_subsumption_resolution,[status(thm)],[f159,f92])).
% 0.08/0.33 fof(f181,plain,(
% 0.08/0.33 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.08/0.33 inference(resolution,[status(thm)],[f143,f92])).
% 0.08/0.33 fof(f187,plain,(
% 0.08/0.33 ![X0]: (~member(X0,sK11_skl)|member(X0,cross_product(sK12_skl,sK13_skl)))),
% 0.08/0.33 inference(resolution,[status(thm)],[f181,f98])).
% 0.08/0.33 fof(f192,plain,(
% 0.08/0.33 ![X0]: (~member(sK5_skl(cross_product(sK12_skl,sK13_skl),X0),sK11_skl)|member(X0,power_set(cross_product(sK12_skl,sK13_skl))))),
% 0.08/0.33 inference(resolution,[status(thm)],[f187,f136])).
% 0.08/0.33 fof(f205,plain,(
% 0.08/0.33 ![X0,X1,X2]: (ilf_type(X0,relation_type(X1,X2))|~member(X0,power_set(cross_product(X1,X2))))),
% 0.08/0.33 inference(resolution,[status(thm)],[f149,f161])).
% 0.08/0.33 fof(f251,plain,(
% 0.08/0.33 member(sK11_skl,power_set(cross_product(sK12_skl,sK13_skl)))|member(sK11_skl,power_set(cross_product(sK12_skl,sK13_skl)))),
% 0.08/0.33 inference(resolution,[status(thm)],[f192,f137])).
% 0.08/0.33 fof(f253,plain,(
% 0.08/0.33 member(sK11_skl,power_set(cross_product(sK12_skl,sK13_skl)))),
% 0.08/0.33 inference(duplicate_literals_removal,[status(thm)],[f251])).
% 0.08/0.33 fof(f254,plain,(
% 0.08/0.33 ilf_type(sK11_skl,relation_type(sK12_skl,sK13_skl))),
% 0.08/0.33 inference(resolution,[status(thm)],[f253,f205])).
% 0.08/0.33 fof(f256,plain,(
% 0.08/0.33 $false),
% 0.08/0.33 inference(forward_subsumption_resolution,[status(thm)],[f254,f99])).
% 0.08/0.33 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.35 % Elapsed time: 0.041254 seconds
% 0.08/0.35 % CPU time: 0.113334 seconds
% 0.08/0.35 % Total memory used: 82.929 MB
% 0.08/0.35 % Net memory used: 82.721 MB
%------------------------------------------------------------------------------