%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET685+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 : n020.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 02:12:27 PM UTC 2026
% Result : Theorem 0.19s 15.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/15.43 % Computer : n020.cluster.edu
% 0.15/15.43 % Model : x86_64 x86_64
% 0.15/15.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.43 % Memory : 8046.5625MB
% 0.15/15.43 % OS : Linux 6.8.0-71-generic
% 0.15/15.43 % CPULimit : 300
% 0.15/15.43 % WCLimit : 300
% 0.15/15.43 % DateTime : Mon Sep 21 05:33:47 UTC 2026
% 0.15/15.44 % CPUTime :
% 0.15/15.45 % Drodi V4.1.1
% 0.19/15.55 % Refutation found
% 0.19/15.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/15.55 % SZS output start CNFRefutation for theBenchmark
% 0.19/15.55 fof(f1,axiom,(
% 0.19/15.55 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,binary_relation_type)=> ( member(C,image(D,B))<=> (? [E] :( ilf_type(E,set_type)& member(ordered_pair(E,C),D)& member(E,B) ) )) ) )) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f2,axiom,(
% 0.19/15.55 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,set_type)=> (! [E] :( ilf_type(E,set_type)=> (! [F] :( ilf_type(F,relation_type(B,C))=> ( member(ordered_pair(D,E),F)=> ( member(D,B)& member(E,C) ) ) ) )) )) )) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f3,axiom,(
% 0.19/15.55 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,set_type)=> (! [E] :( ilf_type(E,set_type)=> (! [F] :( ilf_type(F,set_type)=> ( F = ordered_pair(D,E)<=> F = unordered_pair(unordered_pair(D,E),singleton(D)) ) ) )) )) )) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f5,axiom,(
% 0.19/15.55 (! [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))) ) )) ) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f7,axiom,(
% 0.19/15.55 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ( ~ empty(C)& ilf_type(C,set_type) )=> ( ilf_type(B,member_type(C))<=> member(B,C) ) ) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f15,axiom,(
% 0.19/15.55 (! [B] :( ilf_type(B,set_type)=> ( ilf_type(B,binary_relation_type)<=> ( relation_like(B)& ilf_type(B,set_type) ) ) ) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f17,axiom,(
% 0.19/15.55 (! [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))) ) ) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f24,axiom,(
% 0.19/15.55 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,subset_type(cross_product(B,C)))=> relation_like(D) ) )) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f25,axiom,(
% 0.19/15.55 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(B,C))=> (! [E] :( ilf_type(E,set_type)=> image4(B,C,D,E) = image(D,E) ) )) )) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f26,axiom,(
% 0.19/15.55 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(B,C))=> (! [E] :( ilf_type(E,set_type)=> ilf_type(image4(B,C,D,E),subset_type(C)) ) )) )) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f27,axiom,(
% 0.19/15.55 (! [B] : ilf_type(B,set_type) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f28,conjecture,(
% 0.19/15.55 (! [B] :( ( ~ empty(B)& ilf_type(B,set_type) )=> (! [C] :( ( ~ empty(C)& ilf_type(C,set_type) )=> (! [D] :( ( ~ empty(D)& ilf_type(D,set_type) )=> (! [E] :( ilf_type(E,relation_type(D,B))=> (! [F] :( ilf_type(F,member_type(B))=> ( member(F,image4(D,B,E,C))<=> (? [G] :( ilf_type(G,member_type(D))& member(ordered_pair(G,F),E)& member(G,C) ) )) ) )) )) )) )) )),
% 0.19/15.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/15.55 fof(f29,negated_conjecture,(
% 0.19/15.55 ~((! [B] :( ( ~ empty(B)& ilf_type(B,set_type) )=> (! [C] :( ( ~ empty(C)& ilf_type(C,set_type) )=> (! [D] :( ( ~ empty(D)& ilf_type(D,set_type) )=> (! [E] :( ilf_type(E,relation_type(D,B))=> (! [F] :( ilf_type(F,member_type(B))=> ( member(F,image4(D,B,E,C))<=> (? [G] :( ilf_type(G,member_type(D))& member(ordered_pair(G,F),E)& member(G,C) ) )) ) )) )) )) )) ))),
% 0.19/15.55 inference(negated_conjecture,[status(cth)],[f28])).
% 0.19/15.55 fof(f30,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,binary_relation_type)|(member(C,image(D,B))<=>(?[E]: ((ilf_type(E,set_type)&member(ordered_pair(E,C),D))&member(E,B)))))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.19/15.55 fof(f31,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,binary_relation_type)|((~member(C,image(D,B))|(?[E]: ((ilf_type(E,set_type)&member(ordered_pair(E,C),D))&member(E,B))))&(member(C,image(D,B))|(![E]: ((~ilf_type(E,set_type)|~member(ordered_pair(E,C),D))|~member(E,B))))))))))),
% 0.19/15.55 inference(NNF_transformation,[status(thm)],[f30])).
% 0.19/15.55 fof(f32,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,binary_relation_type)|((~member(C,image(D,B))|((ilf_type(sK0_skl(D,C,B),set_type)&member(ordered_pair(sK0_skl(D,C,B),C),D))&member(sK0_skl(D,C,B),B)))&(member(C,image(D,B))|(![E]: ((~ilf_type(E,set_type)|~member(ordered_pair(E,C),D))|~member(E,B))))))))))),
% 0.19/15.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(E,sK0_skl(D,C,B))],[f31])).
% 0.19/15.55 fof(f34,plain,(
% 0.19/15.55 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,binary_relation_type)|~member(X1,image(X2,X0))|member(ordered_pair(sK0_skl(X2,X1,X0),X1),X2))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f32])).
% 0.19/15.55 fof(f35,plain,(
% 0.19/15.55 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,binary_relation_type)|~member(X1,image(X2,X0))|member(sK0_skl(X2,X1,X0),X0))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f32])).
% 0.19/15.55 fof(f36,plain,(
% 0.19/15.55 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,binary_relation_type)|member(X1,image(X2,X0))|~ilf_type(X3,set_type)|~member(ordered_pair(X3,X1),X2)|~member(X3,X0))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f32])).
% 0.19/15.55 fof(f37,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|(![E]: (~ilf_type(E,set_type)|(![F]: (~ilf_type(F,relation_type(B,C))|(~member(ordered_pair(D,E),F)|(member(D,B)&member(E,C))))))))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.19/15.55 fof(f38,plain,(
% 0.19/15.55 ![X0,X1,X2,X3,X4]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~ilf_type(X3,set_type)|~ilf_type(X4,relation_type(X0,X1))|~member(ordered_pair(X2,X3),X4)|member(X2,X0))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f37])).
% 0.19/15.55 fof(f39,plain,(
% 0.19/15.55 ![X0,X1,X2,X3,X4]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~ilf_type(X3,set_type)|~ilf_type(X4,relation_type(X0,X1))|~member(ordered_pair(X2,X3),X4)|member(X3,X1))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f37])).
% 0.19/15.55 fof(f40,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|(![E]: (~ilf_type(E,set_type)|(![F]: (~ilf_type(F,set_type)|(F=ordered_pair(D,E)<=>F=unordered_pair(unordered_pair(D,E),singleton(D))))))))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.19/15.55 fof(f41,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|(![E]: (~ilf_type(E,set_type)|(![F]: (~ilf_type(F,set_type)|((~F=ordered_pair(D,E)|F=unordered_pair(unordered_pair(D,E),singleton(D)))&(F=ordered_pair(D,E)|~F=unordered_pair(unordered_pair(D,E),singleton(D)))))))))))))),
% 0.19/15.55 inference(NNF_transformation,[status(thm)],[f40])).
% 0.19/15.55 fof(f42,plain,(
% 0.19/15.55 (![B]: ~ilf_type(B,set_type))|((![C]: ~ilf_type(C,set_type))|(![D]: (~ilf_type(D,set_type)|(![E]: (~ilf_type(E,set_type)|(![F]: (~ilf_type(F,set_type)|((~F=ordered_pair(D,E)|F=unordered_pair(unordered_pair(D,E),singleton(D)))&(F=ordered_pair(D,E)|~F=unordered_pair(unordered_pair(D,E),singleton(D)))))))))))),
% 0.19/15.55 inference(miniscoping,[status(thm)],[f41])).
% 0.19/15.55 fof(f43,plain,(
% 0.19/15.55 ![X0,X1,X2,X3,X4]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~ilf_type(X3,set_type)|~ilf_type(X4,set_type)|~X4=ordered_pair(X2,X3)|X4=unordered_pair(unordered_pair(X2,X3),singleton(X2)))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f42])).
% 0.19/15.55 fof(f44,plain,(
% 0.19/15.55 ![X0,X1,X2,X3,X4]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~ilf_type(X3,set_type)|~ilf_type(X4,set_type)|X4=ordered_pair(X2,X3)|~X4=unordered_pair(unordered_pair(X2,X3),singleton(X2)))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f42])).
% 0.19/15.55 fof(f47,plain,(
% 0.19/15.55 ![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)))))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.19/15.55 fof(f48,plain,(
% 0.19/15.55 ![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)))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f47])).
% 0.19/15.55 fof(f49,plain,(
% 0.19/15.55 ![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))))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f47])).
% 0.19/15.55 fof(f53,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: ((empty(C)|~ilf_type(C,set_type))|(ilf_type(B,member_type(C))<=>member(B,C)))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.19/15.55 fof(f54,plain,(
% 0.19/15.55 ![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))))))),
% 0.19/15.55 inference(NNF_transformation,[status(thm)],[f53])).
% 0.19/15.55 fof(f55,plain,(
% 0.19/15.55 ![X0,X1]: (~ilf_type(X0,set_type)|empty(X1)|~ilf_type(X1,set_type)|~ilf_type(X0,member_type(X1))|member(X0,X1))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f54])).
% 0.19/15.55 fof(f56,plain,(
% 0.19/15.55 ![X0,X1]: (~ilf_type(X0,set_type)|empty(X1)|~ilf_type(X1,set_type)|ilf_type(X0,member_type(X1))|~member(X0,X1))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f54])).
% 0.19/15.55 fof(f76,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(ilf_type(B,binary_relation_type)<=>(relation_like(B)&ilf_type(B,set_type))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.19/15.55 fof(f77,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|((~ilf_type(B,binary_relation_type)|(relation_like(B)&ilf_type(B,set_type)))&(ilf_type(B,binary_relation_type)|(~relation_like(B)|~ilf_type(B,set_type)))))),
% 0.19/15.55 inference(NNF_transformation,[status(thm)],[f76])).
% 0.19/15.55 fof(f80,plain,(
% 0.19/15.55 ![X0]: (~ilf_type(X0,set_type)|ilf_type(X0,binary_relation_type)|~relation_like(X0)|~ilf_type(X0,set_type))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f77])).
% 0.19/15.55 fof(f83,plain,(
% 0.19/15.55 ![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)))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.19/15.55 fof(f84,plain,(
% 0.19/15.55 ![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))))))))),
% 0.19/15.55 inference(NNF_transformation,[status(thm)],[f83])).
% 0.19/15.55 fof(f85,plain,(
% 0.19/15.55 ![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))))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f84])).
% 0.19/15.55 fof(f119,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,subset_type(cross_product(B,C)))|relation_like(D))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.19/15.55 fof(f120,plain,(
% 0.19/15.55 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,subset_type(cross_product(X0,X1)))|relation_like(X2))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f119])).
% 0.19/15.55 fof(f121,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,relation_type(B,C))|(![E]: (~ilf_type(E,set_type)|image4(B,C,D,E)=image(D,E))))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.19/15.55 fof(f122,plain,(
% 0.19/15.55 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|~ilf_type(X3,set_type)|image4(X0,X1,X2,X3)=image(X2,X3))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f121])).
% 0.19/15.55 fof(f123,plain,(
% 0.19/15.55 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,relation_type(B,C))|(![E]: (~ilf_type(E,set_type)|ilf_type(image4(B,C,D,E),subset_type(C)))))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 0.19/15.55 fof(f124,plain,(
% 0.19/15.55 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|~ilf_type(X3,set_type)|ilf_type(image4(X0,X1,X2,X3),subset_type(X1)))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f123])).
% 0.19/15.55 fof(f125,plain,(
% 0.19/15.55 ![X0]: (ilf_type(X0,set_type))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f27])).
% 0.19/15.55 fof(f126,plain,(
% 0.19/15.55 (?[B]: ((~empty(B)&ilf_type(B,set_type))&(?[C]: ((~empty(C)&ilf_type(C,set_type))&(?[D]: ((~empty(D)&ilf_type(D,set_type))&(?[E]: (ilf_type(E,relation_type(D,B))&(?[F]: (ilf_type(F,member_type(B))&(member(F,image4(D,B,E,C))<~>(?[G]: ((ilf_type(G,member_type(D))&member(ordered_pair(G,F),E))&member(G,C))))))))))))))),
% 0.19/15.55 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.19/15.55 fof(f127,plain,(
% 0.19/15.55 ?[B]: ((~empty(B)&ilf_type(B,set_type))&(?[C]: ((~empty(C)&ilf_type(C,set_type))&(?[D]: ((~empty(D)&ilf_type(D,set_type))&(?[E]: (ilf_type(E,relation_type(D,B))&(?[F]: (ilf_type(F,member_type(B))&((member(F,image4(D,B,E,C))|(?[G]: ((ilf_type(G,member_type(D))&member(ordered_pair(G,F),E))&member(G,C))))&(~member(F,image4(D,B,E,C))|(![G]: ((~ilf_type(G,member_type(D))|~member(ordered_pair(G,F),E))|~member(G,C))))))))))))))),
% 0.19/15.55 inference(NNF_transformation,[status(thm)],[f126])).
% 0.19/15.55 fof(f128,plain,(
% 0.19/15.55 ((~empty(sK11_skl)&ilf_type(sK11_skl,set_type))&((~empty(sK12_skl)&ilf_type(sK12_skl,set_type))&((~empty(sK13_skl)&ilf_type(sK13_skl,set_type))&(ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl))&(ilf_type(sK15_skl,member_type(sK11_skl))&((member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl))|((ilf_type(sK16_skl,member_type(sK13_skl))&member(ordered_pair(sK16_skl,sK15_skl),sK14_skl))&member(sK16_skl,sK12_skl)))&(~member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl))|(![G]: ((~ilf_type(G,member_type(sK13_skl))|~member(ordered_pair(G,sK15_skl),sK14_skl))|~member(G,sK12_skl))))))))))),
% 0.19/15.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(B,sK11_skl),skolemize(C,sK12_skl),skolemize(D,sK13_skl),skolemize(E,sK14_skl),skolemize(F,sK15_skl),skolemize(G,sK16_skl)],[f127])).
% 0.19/15.55 fof(f129,plain,(
% 0.19/15.55 ~empty(sK11_skl)),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f128])).
% 0.19/15.55 fof(f131,plain,(
% 0.19/15.55 ~empty(sK12_skl)),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f128])).
% 0.19/15.55 fof(f133,plain,(
% 0.19/15.55 ~empty(sK13_skl)),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f128])).
% 0.19/15.55 fof(f135,plain,(
% 0.19/15.55 ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f128])).
% 0.19/15.55 fof(f136,plain,(
% 0.19/15.55 ilf_type(sK15_skl,member_type(sK11_skl))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f128])).
% 0.19/15.55 fof(f138,plain,(
% 0.19/15.55 member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl))|member(ordered_pair(sK16_skl,sK15_skl),sK14_skl)),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f128])).
% 0.19/15.55 fof(f139,plain,(
% 0.19/15.55 member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl))|member(sK16_skl,sK12_skl)),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f128])).
% 0.19/15.55 fof(f140,plain,(
% 0.19/15.55 ![X0]: (~member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl))|~ilf_type(X0,member_type(sK13_skl))|~member(ordered_pair(X0,sK15_skl),sK14_skl)|~member(X0,sK12_skl))),
% 0.19/15.55 inference(cnf_transformation,[status(thm)],[f128])).
% 0.19/15.55 fof(f141,definition,(
% 0.19/15.55 ![X0]: (sQ0_spl <=> (~ilf_type(X0,set_type)))),
% 0.19/15.55 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.19/15.55 fof(f142,plain,(
% 0.19/15.55 ![X0]: (~ilf_type(X0,set_type)|~sQ0_spl)),
% 0.19/15.55 inference(component_clause,[status(thm)],[f141])).
% 0.19/15.55 fof(f144,definition,(
% 0.19/15.55 ![X2,X3,X4]: (sQ1_spl <=> (~ilf_type(X2,set_type)|~ilf_type(X3,set_type)|~ilf_type(X4,set_type)|~X4=ordered_pair(X2,X3)|X4=unordered_pair(unordered_pair(X2,X3),singleton(X2))))),
% 0.19/15.55 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.19/15.55 fof(f147,plain,(
% 0.19/15.55 sQ0_spl|sQ1_spl),
% 0.19/15.55 inference(split_clause,[status(thm)],[f43,f141,f144])).
% 0.19/15.55 fof(f148,definition,(
% 0.19/15.55 ![X2,X3,X4]: (sQ2_spl <=> (~ilf_type(X2,set_type)|~ilf_type(X3,set_type)|~ilf_type(X4,set_type)|X4=ordered_pair(X2,X3)|~X4=unordered_pair(unordered_pair(X2,X3),singleton(X2))))),
% 0.19/15.55 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.19/15.55 fof(f151,plain,(
% 0.19/15.55 sQ0_spl|sQ2_spl),
% 0.19/15.55 inference(split_clause,[status(thm)],[f44,f141,f148])).
% 0.19/15.55 fof(f152,definition,(
% 0.19/15.55 sQ3_spl <=> (member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)))),
% 0.19/15.55 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.19/15.55 fof(f153,plain,(
% 0.19/15.55 member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl))|~sQ3_spl),
% 0.19/15.55 inference(component_clause,[status(thm)],[f152])).
% 0.19/15.55 fof(f154,plain,(
% 0.19/15.55 ~member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl))|sQ3_spl),
% 0.19/15.55 inference(component_clause,[status(thm)],[f152])).
% 0.19/15.55 fof(f159,definition,(
% 0.19/15.55 sQ5_spl <=> (member(ordered_pair(sK16_skl,sK15_skl),sK14_skl))),
% 0.19/15.55 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.19/15.55 fof(f160,plain,(
% 0.19/15.55 member(ordered_pair(sK16_skl,sK15_skl),sK14_skl)|~sQ5_spl),
% 0.19/15.55 inference(component_clause,[status(thm)],[f159])).
% 0.19/15.55 fof(f162,plain,(
% 0.19/15.55 sQ3_spl|sQ5_spl),
% 0.19/15.55 inference(split_clause,[status(thm)],[f138,f152,f159])).
% 0.19/15.55 fof(f163,definition,(
% 0.19/15.56 sQ6_spl <=> (member(sK16_skl,sK12_skl))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f164,plain,(
% 0.19/15.56 member(sK16_skl,sK12_skl)|~sQ6_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f163])).
% 0.19/15.56 fof(f166,plain,(
% 0.19/15.56 sQ3_spl|sQ6_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f139,f152,f163])).
% 0.19/15.56 fof(f167,definition,(
% 0.19/15.56 ![X0]: (sQ7_spl <=> (~ilf_type(X0,member_type(sK13_skl))|~member(ordered_pair(X0,sK15_skl),sK14_skl)|~member(X0,sK12_skl)))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f168,plain,(
% 0.19/15.56 ![X0]: (~ilf_type(X0,member_type(sK13_skl))|~member(ordered_pair(X0,sK15_skl),sK14_skl)|~member(X0,sK12_skl)|~sQ7_spl)),
% 0.19/15.56 inference(component_clause,[status(thm)],[f167])).
% 0.19/15.56 fof(f170,plain,(
% 0.19/15.56 ~sQ3_spl|sQ7_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f140,f152,f167])).
% 0.19/15.56 fof(f171,plain,(
% 0.19/15.56 ![X0]: (~ilf_type(X0,set_type)|ilf_type(X0,binary_relation_type)|~relation_like(X0))),
% 0.19/15.56 inference(duplicate_literals_removal,[status(thm)],[f80])).
% 0.19/15.56 fof(f172,plain,(
% 0.19/15.56 ![X0,X1,X2,X3,X4]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~ilf_type(X3,relation_type(X4,X0))|~member(ordered_pair(X1,X2),X3)|member(X1,X4))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f38,f125])).
% 0.19/15.56 fof(f173,plain,(
% 0.19/15.56 ![X0,X1,X2,X3,X4]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~ilf_type(X3,relation_type(X4,X0))|~member(ordered_pair(X1,X2),X3)|member(X2,X0))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f39,f125])).
% 0.19/15.56 fof(f174,plain,(
% 0.19/15.56 ![X0,X1]: (empty(X0)|~ilf_type(X0,set_type)|~ilf_type(X1,member_type(X0))|member(X1,X0))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f55,f125])).
% 0.19/15.56 fof(f175,plain,(
% 0.19/15.56 $false|~sQ0_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f142,f125])).
% 0.19/15.56 fof(f176,plain,(
% 0.19/15.56 ~sQ0_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f175])).
% 0.19/15.56 fof(f179,plain,(
% 0.19/15.56 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,binary_relation_type)|~member(X0,image(X1,X2))|member(ordered_pair(sK0_skl(X1,X0,X2),X0),X1))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f34,f125])).
% 0.19/15.56 fof(f180,plain,(
% 0.19/15.56 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,binary_relation_type)|~member(X0,image(X1,X2))|member(sK0_skl(X1,X0,X2),X2))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f35,f125])).
% 0.19/15.56 fof(f181,plain,(
% 0.19/15.56 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,binary_relation_type)|member(X0,image(X1,X2))|~ilf_type(X3,set_type)|~member(ordered_pair(X3,X0),X1)|~member(X3,X2))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f36,f125])).
% 0.19/15.56 fof(f182,plain,(
% 0.19/15.56 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,subset_type(cross_product(X2,X0)))|ilf_type(X1,relation_type(X2,X0)))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f48,f125])).
% 0.19/15.56 fof(f183,plain,(
% 0.19/15.56 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X2,X0))|ilf_type(X1,subset_type(cross_product(X2,X0))))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f49,f125])).
% 0.19/15.56 fof(f184,plain,(
% 0.19/15.56 ~ilf_type(sK11_skl,set_type)|ilf_type(sK14_skl,subset_type(cross_product(sK13_skl,sK11_skl)))),
% 0.19/15.56 inference(resolution,[status(thm)],[f135,f183])).
% 0.19/15.56 fof(f185,plain,(
% 0.19/15.56 ![X0,X1]: (~ilf_type(sK11_skl,set_type)|~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~member(ordered_pair(X0,X1),sK14_skl)|member(X1,sK11_skl))),
% 0.19/15.56 inference(resolution,[status(thm)],[f135,f173])).
% 0.19/15.56 fof(f186,plain,(
% 0.19/15.56 ![X0,X1]: (~ilf_type(sK11_skl,set_type)|~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~member(ordered_pair(X0,X1),sK14_skl)|member(X0,sK13_skl))),
% 0.19/15.56 inference(resolution,[status(thm)],[f135,f172])).
% 0.19/15.56 fof(f187,definition,(
% 0.19/15.56 sQ8_spl <=> (ilf_type(sK11_skl,set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f189,plain,(
% 0.19/15.56 ~ilf_type(sK11_skl,set_type)|sQ8_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f187])).
% 0.19/15.56 fof(f190,definition,(
% 0.19/15.56 sQ9_spl <=> (ilf_type(sK14_skl,subset_type(cross_product(sK13_skl,sK11_skl))))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f191,plain,(
% 0.19/15.56 ilf_type(sK14_skl,subset_type(cross_product(sK13_skl,sK11_skl)))|~sQ9_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f190])).
% 0.19/15.56 fof(f193,plain,(
% 0.19/15.56 ~sQ8_spl|sQ9_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f184,f187,f190])).
% 0.19/15.56 fof(f194,definition,(
% 0.19/15.56 ![X0,X1]: (sQ10_spl <=> (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~member(ordered_pair(X0,X1),sK14_skl)|member(X1,sK11_skl)))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f197,plain,(
% 0.19/15.56 ~sQ8_spl|sQ10_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f185,f187,f194])).
% 0.19/15.56 fof(f198,definition,(
% 0.19/15.56 ![X0,X1]: (sQ11_spl <=> (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~member(ordered_pair(X0,X1),sK14_skl)|member(X0,sK13_skl)))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f199,plain,(
% 0.19/15.56 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~member(ordered_pair(X0,X1),sK14_skl)|member(X0,sK13_skl)|~sQ11_spl)),
% 0.19/15.56 inference(component_clause,[status(thm)],[f198])).
% 0.19/15.56 fof(f201,plain,(
% 0.19/15.56 ~sQ8_spl|sQ11_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f186,f187,f198])).
% 0.19/15.56 fof(f202,plain,(
% 0.19/15.56 $false|sQ8_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f189,f125])).
% 0.19/15.56 fof(f203,plain,(
% 0.19/15.56 sQ8_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f202])).
% 0.19/15.56 fof(f205,plain,(
% 0.19/15.56 ![X0,X1]: (~ilf_type(X0,set_type)|~member(ordered_pair(X1,X0),sK14_skl)|member(X1,sK13_skl)|~sQ11_spl)),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f199,f125])).
% 0.19/15.56 fof(f206,plain,(
% 0.19/15.56 empty(sK11_skl)|~ilf_type(sK11_skl,set_type)|member(sK15_skl,sK11_skl)),
% 0.19/15.56 inference(resolution,[status(thm)],[f136,f174])).
% 0.19/15.56 fof(f207,definition,(
% 0.19/15.56 sQ12_spl <=> (empty(sK11_skl))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f208,plain,(
% 0.19/15.56 empty(sK11_skl)|~sQ12_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f207])).
% 0.19/15.56 fof(f210,definition,(
% 0.19/15.56 sQ13_spl <=> (member(sK15_skl,sK11_skl))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f211,plain,(
% 0.19/15.56 member(sK15_skl,sK11_skl)|~sQ13_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f210])).
% 0.19/15.56 fof(f213,plain,(
% 0.19/15.56 sQ12_spl|~sQ8_spl|sQ13_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f206,f207,f187,f210])).
% 0.19/15.56 fof(f214,plain,(
% 0.19/15.56 $false|~sQ12_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f208,f129])).
% 0.19/15.56 fof(f215,plain,(
% 0.19/15.56 ~sQ12_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f214])).
% 0.19/15.56 fof(f216,plain,(
% 0.19/15.56 ~ilf_type(sK11_skl,set_type)|ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl))|~sQ9_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f191,f182])).
% 0.19/15.56 fof(f217,definition,(
% 0.19/15.56 sQ14_spl <=> (ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl)))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f220,plain,(
% 0.19/15.56 ~sQ8_spl|sQ14_spl|~sQ9_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f216,f187,f217,f190])).
% 0.19/15.56 fof(f221,plain,(
% 0.19/15.56 ![X0,X1]: (empty(X0)|~ilf_type(X0,set_type)|ilf_type(X1,member_type(X0))|~member(X1,X0))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f56,f125])).
% 0.19/15.56 fof(f222,plain,(
% 0.19/15.56 empty(sK11_skl)|~ilf_type(sK11_skl,set_type)|ilf_type(sK15_skl,member_type(sK11_skl))|~sQ13_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f221,f211])).
% 0.19/15.56 fof(f223,definition,(
% 0.19/15.56 sQ15_spl <=> (ilf_type(sK15_skl,member_type(sK11_skl)))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f226,plain,(
% 0.19/15.56 sQ12_spl|~sQ8_spl|sQ15_spl|~sQ13_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f222,f207,f187,f223,f210])).
% 0.19/15.56 fof(f229,definition,(
% 0.19/15.56 sQ16_spl <=> (ilf_type(sK15_skl,set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f231,plain,(
% 0.19/15.56 ~ilf_type(sK15_skl,set_type)|sQ16_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f229])).
% 0.19/15.56 fof(f233,plain,(
% 0.19/15.56 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X2,X0))|~ilf_type(X3,set_type)|image4(X2,X0,X1,X3)=image(X1,X3))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f122,f125])).
% 0.19/15.56 fof(f234,plain,(
% 0.19/15.56 ![X0]: (~ilf_type(sK11_skl,set_type)|~ilf_type(X0,set_type)|image4(sK13_skl,sK11_skl,sK14_skl,X0)=image(sK14_skl,X0))),
% 0.19/15.56 inference(resolution,[status(thm)],[f233,f135])).
% 0.19/15.56 fof(f235,definition,(
% 0.19/15.56 ![X0]: (sQ17_spl <=> (~ilf_type(X0,set_type)|image4(sK13_skl,sK11_skl,sK14_skl,X0)=image(sK14_skl,X0)))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f236,plain,(
% 0.19/15.56 ![X0]: (~ilf_type(X0,set_type)|image4(sK13_skl,sK11_skl,sK14_skl,X0)=image(sK14_skl,X0)|~sQ17_spl)),
% 0.19/15.56 inference(component_clause,[status(thm)],[f235])).
% 0.19/15.56 fof(f238,plain,(
% 0.19/15.56 ~sQ8_spl|sQ17_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f234,f187,f235])).
% 0.19/15.56 fof(f239,plain,(
% 0.19/15.56 ![X0]: (image4(sK13_skl,sK11_skl,sK14_skl,X0)=image(sK14_skl,X0)|~sQ17_spl)),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f236,f125])).
% 0.19/15.56 fof(f240,plain,(
% 0.19/15.56 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X2,X0))|~ilf_type(X3,set_type)|ilf_type(image4(X2,X0,X1,X3),subset_type(X0)))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f124,f125])).
% 0.19/15.56 fof(f241,plain,(
% 0.19/15.56 ![X0]: (~ilf_type(sK11_skl,set_type)|~ilf_type(X0,set_type)|ilf_type(image4(sK13_skl,sK11_skl,sK14_skl,X0),subset_type(sK11_skl)))),
% 0.19/15.56 inference(resolution,[status(thm)],[f240,f135])).
% 0.19/15.56 fof(f242,definition,(
% 0.19/15.56 ![X0]: (sQ18_spl <=> (~ilf_type(X0,set_type)|ilf_type(image4(sK13_skl,sK11_skl,sK14_skl,X0),subset_type(sK11_skl))))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f245,plain,(
% 0.19/15.56 ~sQ8_spl|sQ18_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f241,f187,f242])).
% 0.19/15.56 fof(f270,definition,(
% 0.19/15.56 sQ20_spl <=> (ilf_type(image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl),set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f272,plain,(
% 0.19/15.56 ~ilf_type(image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl),set_type)|sQ20_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f270])).
% 0.19/15.56 fof(f277,plain,(
% 0.19/15.56 $false|sQ20_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f272,f125])).
% 0.19/15.56 fof(f278,plain,(
% 0.19/15.56 sQ20_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f277])).
% 0.19/15.56 fof(f279,plain,(
% 0.19/15.56 $false|sQ16_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f231,f125])).
% 0.19/15.56 fof(f280,plain,(
% 0.19/15.56 sQ16_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f279])).
% 0.19/15.56 fof(f282,definition,(
% 0.19/15.56 sQ22_spl <=> (empty(sK13_skl))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f283,plain,(
% 0.19/15.56 empty(sK13_skl)|~sQ22_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f282])).
% 0.19/15.56 fof(f285,definition,(
% 0.19/15.56 sQ23_spl <=> (ilf_type(sK13_skl,set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f287,plain,(
% 0.19/15.56 ~ilf_type(sK13_skl,set_type)|sQ23_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f285])).
% 0.19/15.56 fof(f294,definition,(
% 0.19/15.56 sQ25_spl <=> (ilf_type(sK16_skl,set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f296,plain,(
% 0.19/15.56 ~ilf_type(sK16_skl,set_type)|sQ25_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f294])).
% 0.19/15.56 fof(f299,plain,(
% 0.19/15.56 $false|sQ23_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f287,f125])).
% 0.19/15.56 fof(f300,plain,(
% 0.19/15.56 sQ23_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f299])).
% 0.19/15.56 fof(f301,plain,(
% 0.19/15.56 $false|sQ25_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f296,f125])).
% 0.19/15.56 fof(f302,plain,(
% 0.19/15.56 sQ25_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f301])).
% 0.19/15.56 fof(f305,definition,(
% 0.19/15.56 sQ26_spl <=> (empty(sK12_skl))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f306,plain,(
% 0.19/15.56 empty(sK12_skl)|~sQ26_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f305])).
% 0.19/15.56 fof(f309,definition,(
% 0.19/15.56 sQ27_spl <=> (ilf_type(sK12_skl,set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f311,plain,(
% 0.19/15.56 ~ilf_type(sK12_skl,set_type)|sQ27_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f309])).
% 0.19/15.56 fof(f347,plain,(
% 0.19/15.56 ![X0]: (ilf_type(X0,binary_relation_type)|~relation_like(X0))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f171,f125])).
% 0.19/15.56 fof(f348,plain,(
% 0.19/15.56 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X0,subset_type(X1))|ilf_type(X0,member_type(power_set(X1))))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f85,f125])).
% 0.19/15.56 fof(f349,plain,(
% 0.19/15.56 ~ilf_type(sK14_skl,set_type)|ilf_type(sK14_skl,member_type(power_set(cross_product(sK13_skl,sK11_skl))))|~sQ9_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f348,f191])).
% 0.19/15.56 fof(f350,definition,(
% 0.19/15.56 sQ29_spl <=> (ilf_type(sK14_skl,set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f352,plain,(
% 0.19/15.56 ~ilf_type(sK14_skl,set_type)|sQ29_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f350])).
% 0.19/15.56 fof(f353,definition,(
% 0.19/15.56 sQ30_spl <=> (ilf_type(sK14_skl,member_type(power_set(cross_product(sK13_skl,sK11_skl)))))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f356,plain,(
% 0.19/15.56 ~sQ29_spl|sQ30_spl|~sQ9_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f349,f350,f353,f190])).
% 0.19/15.56 fof(f357,plain,(
% 0.19/15.56 $false|sQ29_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f352,f125])).
% 0.19/15.56 fof(f358,plain,(
% 0.19/15.56 sQ29_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f357])).
% 0.19/15.56 fof(f384,plain,(
% 0.19/15.56 ![X0,X1]: (~member(ordered_pair(X0,X1),sK14_skl)|member(X0,sK13_skl)|~sQ11_spl)),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f205,f125])).
% 0.19/15.56 fof(f385,plain,(
% 0.19/15.56 member(sK15_skl,image(sK14_skl,sK12_skl))|~sQ17_spl|~sQ3_spl),
% 0.19/15.56 inference(backward_demodulation,[status(thm)],[f239,f153])).
% 0.19/15.56 fof(f387,plain,(
% 0.19/15.56 ~ilf_type(sK15_skl,set_type)|~ilf_type(sK14_skl,binary_relation_type)|member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK12_skl)|~sQ17_spl|~sQ3_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f385,f180])).
% 0.19/15.56 fof(f388,plain,(
% 0.19/15.56 ~ilf_type(sK15_skl,set_type)|~ilf_type(sK14_skl,binary_relation_type)|member(ordered_pair(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK15_skl),sK14_skl)|~sQ17_spl|~sQ3_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f385,f179])).
% 0.19/15.56 fof(f391,definition,(
% 0.19/15.56 sQ31_spl <=> (ilf_type(sK14_skl,binary_relation_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f393,plain,(
% 0.19/15.56 ~ilf_type(sK14_skl,binary_relation_type)|sQ31_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f391])).
% 0.19/15.56 fof(f394,definition,(
% 0.19/15.56 sQ32_spl <=> (member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK12_skl))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f397,plain,(
% 0.19/15.56 ~sQ16_spl|~sQ31_spl|sQ32_spl|~sQ17_spl|~sQ3_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f387,f229,f391,f394,f235,f152])).
% 0.19/15.56 fof(f398,definition,(
% 0.19/15.56 sQ33_spl <=> (member(ordered_pair(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK15_skl),sK14_skl))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f399,plain,(
% 0.19/15.56 member(ordered_pair(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK15_skl),sK14_skl)|~sQ33_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f398])).
% 0.19/15.56 fof(f401,plain,(
% 0.19/15.56 ~sQ16_spl|~sQ31_spl|sQ33_spl|~sQ17_spl|~sQ3_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f388,f229,f391,f398,f235,f152])).
% 0.19/15.56 fof(f406,definition,(
% 0.19/15.56 sQ35_spl <=> (ilf_type(image(sK14_skl,sK12_skl),set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f408,plain,(
% 0.19/15.56 ~ilf_type(image(sK14_skl,sK12_skl),set_type)|sQ35_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f406])).
% 0.19/15.56 fof(f413,plain,(
% 0.19/15.56 $false|sQ27_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f311,f125])).
% 0.19/15.56 fof(f414,plain,(
% 0.19/15.56 sQ27_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f413])).
% 0.19/15.56 fof(f415,plain,(
% 0.19/15.56 ~member(sK15_skl,image(sK14_skl,sK12_skl))|~sQ17_spl|sQ3_spl),
% 0.19/15.56 inference(forward_demodulation,[status(thm)],[f239,f154])).
% 0.19/15.56 fof(f416,plain,(
% 0.19/15.56 $false|~sQ22_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f283,f133])).
% 0.19/15.56 fof(f417,plain,(
% 0.19/15.56 ~sQ22_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f416])).
% 0.19/15.56 fof(f441,plain,(
% 0.19/15.56 ![X0]: (~ilf_type(sK15_skl,set_type)|~ilf_type(sK14_skl,binary_relation_type)|member(sK15_skl,image(sK14_skl,X0))|~ilf_type(sK16_skl,set_type)|~member(sK16_skl,X0)|~sQ5_spl)),
% 0.19/15.56 inference(resolution,[status(thm)],[f160,f181])).
% 0.19/15.56 fof(f444,definition,(
% 0.19/15.56 ![X0]: (sQ37_spl <=> (member(sK15_skl,image(sK14_skl,X0))|~member(sK16_skl,X0)))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f445,plain,(
% 0.19/15.56 ![X0]: (member(sK15_skl,image(sK14_skl,X0))|~member(sK16_skl,X0)|~sQ37_spl)),
% 0.19/15.56 inference(component_clause,[status(thm)],[f444])).
% 0.19/15.56 fof(f447,plain,(
% 0.19/15.56 ~sQ16_spl|~sQ31_spl|sQ37_spl|~sQ25_spl|~sQ5_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f441,f229,f391,f444,f294,f159])).
% 0.19/15.56 fof(f451,definition,(
% 0.19/15.56 sQ39_spl <=> (ilf_type(ordered_pair(sK16_skl,sK15_skl),set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f453,plain,(
% 0.19/15.56 ~ilf_type(ordered_pair(sK16_skl,sK15_skl),set_type)|sQ39_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f451])).
% 0.19/15.56 fof(f459,plain,(
% 0.19/15.56 $false|sQ39_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f453,f125])).
% 0.19/15.56 fof(f460,plain,(
% 0.19/15.56 sQ39_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f459])).
% 0.19/15.56 fof(f485,definition,(
% 0.19/15.56 sQ41_spl <=> (relation_like(sK14_skl))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f486,plain,(
% 0.19/15.56 relation_like(sK14_skl)|~sQ41_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f485])).
% 0.19/15.56 fof(f557,plain,(
% 0.19/15.56 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,subset_type(cross_product(X2,X0)))|relation_like(X1))),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f120,f125])).
% 0.19/15.56 fof(f561,plain,(
% 0.19/15.56 ~ilf_type(sK11_skl,set_type)|relation_like(sK14_skl)|~sQ9_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f557,f191])).
% 0.19/15.56 fof(f565,plain,(
% 0.19/15.56 ~sQ8_spl|sQ41_spl|~sQ9_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f561,f187,f485,f190])).
% 0.19/15.56 fof(f613,plain,(
% 0.19/15.56 ilf_type(sK14_skl,binary_relation_type)|~sQ41_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f486,f347])).
% 0.19/15.56 fof(f614,plain,(
% 0.19/15.56 $false|sQ31_spl|~sQ41_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f613,f393])).
% 0.19/15.56 fof(f615,plain,(
% 0.19/15.56 sQ31_spl|~sQ41_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f614])).
% 0.19/15.56 fof(f627,definition,(
% 0.19/15.56 sQ51_spl <=> (ilf_type(sK9_skl(ordered_pair(sK16_skl,sK15_skl),sK14_skl),set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f629,plain,(
% 0.19/15.56 ~ilf_type(sK9_skl(ordered_pair(sK16_skl,sK15_skl),sK14_skl),set_type)|sQ51_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f627])).
% 0.19/15.56 fof(f633,definition,(
% 0.19/15.56 sQ53_spl <=> (ilf_type(sK8_skl(ordered_pair(sK16_skl,sK15_skl),sK14_skl),set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f635,plain,(
% 0.19/15.56 ~ilf_type(sK8_skl(ordered_pair(sK16_skl,sK15_skl),sK14_skl),set_type)|sQ53_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f633])).
% 0.19/15.56 fof(f637,plain,(
% 0.19/15.56 $false|sQ53_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f635,f125])).
% 0.19/15.56 fof(f638,plain,(
% 0.19/15.56 sQ53_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f637])).
% 0.19/15.56 fof(f639,plain,(
% 0.19/15.56 $false|sQ51_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f629,f125])).
% 0.19/15.56 fof(f640,plain,(
% 0.19/15.56 sQ51_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f639])).
% 0.19/15.56 fof(f642,plain,(
% 0.19/15.56 member(sK15_skl,image(sK14_skl,sK12_skl))|~sQ37_spl|~sQ6_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f445,f164])).
% 0.19/15.56 fof(f643,plain,(
% 0.19/15.56 $false|~sQ17_spl|sQ3_spl|~sQ37_spl|~sQ6_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f642,f415])).
% 0.19/15.56 fof(f644,plain,(
% 0.19/15.56 ~sQ17_spl|sQ3_spl|~sQ37_spl|~sQ6_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f643])).
% 0.19/15.56 fof(f646,plain,(
% 0.19/15.56 $false|sQ35_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f408,f125])).
% 0.19/15.56 fof(f647,plain,(
% 0.19/15.56 sQ35_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f646])).
% 0.19/15.56 fof(f648,plain,(
% 0.19/15.56 $false|~sQ26_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f306,f131])).
% 0.19/15.56 fof(f649,plain,(
% 0.19/15.56 ~sQ26_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f648])).
% 0.19/15.56 fof(f729,definition,(
% 0.19/15.56 sQ60_spl <=> (ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f731,plain,(
% 0.19/15.56 ~ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),set_type)|sQ60_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f729])).
% 0.19/15.56 fof(f749,plain,(
% 0.19/15.56 ~ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),member_type(sK13_skl))|~member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK12_skl)|~sQ33_spl|~sQ7_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f399,f168])).
% 0.19/15.56 fof(f750,plain,(
% 0.19/15.56 member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK13_skl)|~sQ33_spl|~sQ11_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f399,f384])).
% 0.19/15.56 fof(f756,definition,(
% 0.19/15.56 sQ63_spl <=> (ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),member_type(sK13_skl)))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f759,plain,(
% 0.19/15.56 ~sQ63_spl|~sQ32_spl|~sQ33_spl|~sQ7_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f749,f756,f394,f398,f167])).
% 0.19/15.56 fof(f764,definition,(
% 0.19/15.56 sQ65_spl <=> (ilf_type(ordered_pair(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK15_skl),set_type))),
% 0.19/15.56 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 0.19/15.56 fof(f766,plain,(
% 0.19/15.56 ~ilf_type(ordered_pair(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK15_skl),set_type)|sQ65_spl),
% 0.19/15.56 inference(component_clause,[status(thm)],[f764])).
% 0.19/15.56 fof(f776,plain,(
% 0.19/15.56 $false|sQ60_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f731,f125])).
% 0.19/15.56 fof(f777,plain,(
% 0.19/15.56 sQ60_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f776])).
% 0.19/15.56 fof(f778,plain,(
% 0.19/15.56 $false|sQ65_spl),
% 0.19/15.56 inference(forward_subsumption_resolution,[status(thm)],[f766,f125])).
% 0.19/15.56 fof(f779,plain,(
% 0.19/15.56 sQ65_spl),
% 0.19/15.56 inference(contradiction_clause,[status(thm)],[f778])).
% 0.19/15.56 fof(f793,plain,(
% 0.19/15.56 empty(sK13_skl)|~ilf_type(sK13_skl,set_type)|ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),member_type(sK13_skl))|~sQ33_spl|~sQ11_spl),
% 0.19/15.56 inference(resolution,[status(thm)],[f750,f221])).
% 0.19/15.56 fof(f799,plain,(
% 0.19/15.56 sQ22_spl|~sQ23_spl|sQ63_spl|~sQ33_spl|~sQ11_spl),
% 0.19/15.56 inference(split_clause,[status(thm)],[f793,f282,f285,f756,f398,f198])).
% 0.19/15.56 fof(f800,plain,(
% 0.19/15.56 $false),
% 0.19/15.56 inference(sat_refutation,[status(thm)],[f147,f151,f162,f166,f170,f176,f193,f197,f201,f203,f213,f215,f220,f226,f238,f245,f278,f280,f300,f302,f356,f358,f397,f401,f414,f417,f447,f460,f565,f615,f638,f640,f644,f647,f649,f759,f777,f779,f799])).
% 0.19/15.56 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/15.57 % Elapsed time: 0.119574 seconds
% 0.19/15.57 % CPU time: 0.755070 seconds
% 0.19/15.57 % Total memory used: 97.232 MB
% 0.19/15.57 % Net memory used: 96.385 MB
%------------------------------------------------------------------------------