TSTP Solution File: SET646+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:34:55 EDT 2023
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.06 % Problem : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% 0.01/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25 % Computer : n027.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 30 10:37:47 EDT 2023
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % Drodi V3.5.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.39 fof(f2,axiom,(
% 0.10/0.39 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,set_type)=> (! [E] :( ilf_type(E,set_type)=> ( member(ordered_pair(B,C),cross_product(D,E))<=> ( member(B,D)& member(C,E) ) ) ) )) )) )) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f3,axiom,(
% 0.10/0.39 (! [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))) ) )) ) )) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f5,axiom,(
% 0.10/0.39 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,set_type)=> ( D = singleton(C)<=> (! [E] :( ilf_type(E,set_type)=> ( member(E,D)<=> E = C ) ) )) ) )) )) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f12,axiom,(
% 0.10/0.39 (! [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))) ) ) )) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f17,axiom,(
% 0.10/0.39 (! [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) ) ) )) ) )) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f18,axiom,(
% 0.10/0.39 (! [B] :( ilf_type(B,set_type)=> ( ~ empty(power_set(B))& ilf_type(power_set(B),set_type) ) ) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f19,axiom,(
% 0.10/0.39 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ( ~ empty(C)& ilf_type(C,set_type) )=> ( ilf_type(B,member_type(C))<=> member(B,C) ) ) )) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f25,axiom,(
% 0.10/0.39 (! [B] : ilf_type(B,set_type) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f26,conjecture,(
% 0.10/0.39 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,set_type)=> (! [E] :( ilf_type(E,set_type)=> ( ( member(D,B)& member(E,C) )=> ilf_type(singleton(ordered_pair(D,E)),relation_type(B,C)) ) ) )) )) )) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f27,negated_conjecture,(
% 0.10/0.39 ~((! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,set_type)=> (! [E] :( ilf_type(E,set_type)=> ( ( member(D,B)& member(E,C) )=> ilf_type(singleton(ordered_pair(D,E)),relation_type(B,C)) ) ) )) )) )) ))),
% 0.10/0.39 inference(negated_conjecture,[status(cth)],[f26])).
% 0.10/0.39 fof(f32,plain,(
% 0.10/0.39 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|(![E]: (~ilf_type(E,set_type)|(member(ordered_pair(B,C),cross_product(D,E))<=>(member(B,D)&member(C,E))))))))))),
% 0.10/0.39 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.10/0.39 fof(f33,plain,(
% 0.10/0.39 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|(![E]: (~ilf_type(E,set_type)|((~member(ordered_pair(B,C),cross_product(D,E))|(member(B,D)&member(C,E)))&(member(ordered_pair(B,C),cross_product(D,E))|(~member(B,D)|~member(C,E)))))))))))),
% 0.10/0.39 inference(NNF_transformation,[status(esa)],[f32])).
% 0.10/0.39 fof(f36,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~ilf_type(X3,set_type)|member(ordered_pair(X0,X1),cross_product(X2,X3))|~member(X0,X2)|~member(X1,X3))),
% 0.10/0.39 inference(cnf_transformation,[status(esa)],[f33])).
% 0.10/0.39 fof(f37,plain,(
% 0.10/0.39 ![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)))))))))),
% 0.10/0.39 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.10/0.39 fof(f38,plain,(
% 0.10/0.39 ![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)))),
% 0.10/0.39 inference(cnf_transformation,[status(esa)],[f37])).
% 0.10/0.40 fof(f43,plain,(
% 0.10/0.40 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|(D=singleton(C)<=>(![E]: (~ilf_type(E,set_type)|(member(E,D)<=>E=C)))))))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.10/0.40 fof(f44,plain,(
% 0.10/0.40 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|((~D=singleton(C)|(![E]: (~ilf_type(E,set_type)|((~member(E,D)|E=C)&(member(E,D)|~E=C)))))&(D=singleton(C)|(?[E]: (ilf_type(E,set_type)&((~member(E,D)|~E=C)&(member(E,D)|E=C)))))))))))),
% 0.10/0.40 inference(NNF_transformation,[status(esa)],[f43])).
% 0.10/0.40 fof(f45,plain,(
% 0.10/0.40 (![B]: ~ilf_type(B,set_type))|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|((~D=singleton(C)|(![E]: (~ilf_type(E,set_type)|((~member(E,D)|E=C)&(member(E,D)|~E=C)))))&(D=singleton(C)|(?[E]: (ilf_type(E,set_type)&((~member(E,D)|~E=C)&(member(E,D)|E=C))))))))))),
% 0.10/0.40 inference(miniscoping,[status(esa)],[f44])).
% 0.10/0.40 fof(f46,plain,(
% 0.10/0.40 (![B]: ~ilf_type(B,set_type))|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,set_type)|((~D=singleton(C)|(![E]: (~ilf_type(E,set_type)|((~member(E,D)|E=C)&(member(E,D)|~E=C)))))&(D=singleton(C)|(ilf_type(sk0_1(D,C),set_type)&((~member(sk0_1(D,C),D)|~sk0_1(D,C)=C)&(member(sk0_1(D,C),D)|sk0_1(D,C)=C)))))))))),
% 0.10/0.40 inference(skolemization,[status(esa)],[f45])).
% 0.10/0.40 fof(f47,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~X2=singleton(X1)|~ilf_type(X3,set_type)|~member(X3,X2)|X3=X1)),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f46])).
% 0.10/0.40 fof(f67,plain,(
% 0.10/0.40 ![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)))))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.10/0.40 fof(f68,plain,(
% 0.10/0.40 ![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))))))))),
% 0.10/0.40 inference(NNF_transformation,[status(esa)],[f67])).
% 0.10/0.40 fof(f70,plain,(
% 0.10/0.40 ![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))))),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f68])).
% 0.10/0.40 fof(f91,plain,(
% 0.10/0.40 ![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))))))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 0.10/0.40 fof(f92,plain,(
% 0.10/0.40 ![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)))))))))),
% 0.10/0.40 inference(NNF_transformation,[status(esa)],[f91])).
% 0.10/0.40 fof(f93,plain,(
% 0.10/0.40 ![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(sk0_5(C,B),set_type)&(member(sk0_5(C,B),B)&~member(sk0_5(C,B),C))))))))),
% 0.10/0.40 inference(skolemization,[status(esa)],[f92])).
% 0.10/0.40 fof(f96,plain,(
% 0.10/0.40 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|member(X0,power_set(X1))|member(sk0_5(X1,X0),X0))),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f93])).
% 0.10/0.40 fof(f97,plain,(
% 0.10/0.40 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|member(X0,power_set(X1))|~member(sk0_5(X1,X0),X1))),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f93])).
% 0.10/0.40 fof(f98,plain,(
% 0.10/0.40 ![B]: (~ilf_type(B,set_type)|(~empty(power_set(B))&ilf_type(power_set(B),set_type)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 0.10/0.40 fof(f99,plain,(
% 0.10/0.40 ![X0]: (~ilf_type(X0,set_type)|~empty(power_set(X0)))),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f98])).
% 0.10/0.40 fof(f101,plain,(
% 0.10/0.40 ![B]: (~ilf_type(B,set_type)|(![C]: ((empty(C)|~ilf_type(C,set_type))|(ilf_type(B,member_type(C))<=>member(B,C)))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 0.10/0.40 fof(f102,plain,(
% 0.10/0.40 ![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))))))),
% 0.10/0.40 inference(NNF_transformation,[status(esa)],[f101])).
% 0.10/0.40 fof(f104,plain,(
% 0.10/0.40 ![X0,X1]: (~ilf_type(X0,set_type)|empty(X1)|~ilf_type(X1,set_type)|ilf_type(X0,member_type(X1))|~member(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f102])).
% 0.10/0.40 fof(f127,plain,(
% 0.10/0.40 ![X0]: (ilf_type(X0,set_type))),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f25])).
% 0.10/0.40 fof(f128,plain,(
% 0.10/0.40 (?[B]: (ilf_type(B,set_type)&(?[C]: (ilf_type(C,set_type)&(?[D]: (ilf_type(D,set_type)&(?[E]: (ilf_type(E,set_type)&((member(D,B)&member(E,C))&~ilf_type(singleton(ordered_pair(D,E)),relation_type(B,C)))))))))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 0.10/0.40 fof(f129,plain,(
% 0.10/0.40 (ilf_type(sk0_11,set_type)&(ilf_type(sk0_12,set_type)&(ilf_type(sk0_13,set_type)&(ilf_type(sk0_14,set_type)&((member(sk0_13,sk0_11)&member(sk0_14,sk0_12))&~ilf_type(singleton(ordered_pair(sk0_13,sk0_14)),relation_type(sk0_11,sk0_12)))))))),
% 0.10/0.40 inference(skolemization,[status(esa)],[f128])).
% 0.10/0.40 fof(f134,plain,(
% 0.10/0.40 member(sk0_13,sk0_11)),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f129])).
% 0.10/0.40 fof(f135,plain,(
% 0.10/0.40 member(sk0_14,sk0_12)),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f129])).
% 0.10/0.40 fof(f136,plain,(
% 0.10/0.40 ~ilf_type(singleton(ordered_pair(sk0_13,sk0_14)),relation_type(sk0_11,sk0_12))),
% 0.10/0.40 inference(cnf_transformation,[status(esa)],[f129])).
% 0.10/0.40 fof(f137,plain,(
% 0.10/0.40 spl0_0 <=> ~ilf_type(X0,set_type)),
% 0.10/0.40 introduced(split_symbol_definition)).
% 0.10/0.40 fof(f138,plain,(
% 0.10/0.40 ![X0]: (~ilf_type(X0,set_type)|~spl0_0)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f137])).
% 0.10/0.40 fof(f140,plain,(
% 0.10/0.40 spl0_1 <=> ~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|~X2=singleton(X1)|~ilf_type(X3,set_type)|~member(X3,X2)|X3=X1),
% 0.10/0.40 introduced(split_symbol_definition)).
% 0.10/0.40 fof(f141,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~X1=singleton(X0)|~ilf_type(X2,set_type)|~member(X2,X1)|X2=X0|~spl0_1)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f140])).
% 0.10/0.40 fof(f143,plain,(
% 0.10/0.40 spl0_0|spl0_1),
% 0.10/0.40 inference(split_clause,[status(thm)],[f47,f137,f140])).
% 0.10/0.40 fof(f168,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,subset_type(cross_product(X2,X0)))|ilf_type(X1,relation_type(X2,X0)))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f38,f127])).
% 0.10/0.40 fof(f171,plain,(
% 0.10/0.40 ![X0]: (~empty(power_set(X0)))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f99,f127])).
% 0.10/0.40 fof(f190,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,set_type)|member(ordered_pair(X3,X0),cross_product(X1,X2))|~member(X3,X1)|~member(X0,X2))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f36,f127])).
% 0.10/0.40 fof(f193,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|member(ordered_pair(X2,X0),cross_product(X3,X1))|~member(X2,X3)|~member(X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f190,f127])).
% 0.10/0.40 fof(f194,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|member(ordered_pair(X1,X2),cross_product(X3,X0))|~member(X1,X3)|~member(X2,X0))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f193,f127])).
% 0.10/0.40 fof(f199,plain,(
% 0.10/0.40 $false|~spl0_0),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f138,f127])).
% 0.10/0.40 fof(f200,plain,(
% 0.10/0.40 ~spl0_0),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f199])).
% 0.10/0.40 fof(f201,plain,(
% 0.10/0.40 ![X0,X2]: (~ilf_type(X0,set_type)|~ilf_type(singleton(X0),set_type)|~ilf_type(X2,set_type)|~member(X2,singleton(X0))|X2=X0|~spl0_1)),
% 0.10/0.40 inference(destructive_equality_resolution,[status(esa)],[f141])).
% 0.10/0.40 fof(f202,plain,(
% 0.10/0.40 ![X0,X1]: (~ilf_type(singleton(X0),set_type)|~ilf_type(X1,set_type)|~member(X1,singleton(X0))|X1=X0|~spl0_1)),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f201,f127])).
% 0.10/0.40 fof(f213,plain,(
% 0.10/0.40 ![X0,X1]: (~ilf_type(X0,set_type)|~member(X0,singleton(X1))|X0=X1|~spl0_1)),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f202,f127])).
% 0.10/0.40 fof(f214,plain,(
% 0.10/0.40 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1|~spl0_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f213,f127])).
% 0.10/0.40 fof(f461,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (member(ordered_pair(X0,X1),cross_product(X2,X3))|~member(X0,X2)|~member(X1,X3))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f194,f127])).
% 0.10/0.40 fof(f503,plain,(
% 0.10/0.40 ![X0,X1]: (~ilf_type(X0,set_type)|member(X1,power_set(X0))|member(sk0_5(X0,X1),X1))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f96,f127])).
% 0.10/0.40 fof(f504,plain,(
% 0.10/0.40 ![X0,X1]: (member(X0,power_set(X1))|member(sk0_5(X1,X0),X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f503,f127])).
% 0.10/0.40 fof(f506,plain,(
% 0.10/0.40 ![X0,X1]: (member(singleton(X0),power_set(X1))|sk0_5(X1,singleton(X0))=X0|~spl0_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f504,f214])).
% 0.10/0.40 fof(f507,plain,(
% 0.10/0.40 ![X0,X1]: (~ilf_type(X0,set_type)|member(X1,power_set(X0))|~member(sk0_5(X0,X1),X0))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f97,f127])).
% 0.10/0.40 fof(f508,plain,(
% 0.10/0.40 ![X0,X1]: (member(X0,power_set(X1))|~member(sk0_5(X1,X0),X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f507,f127])).
% 0.10/0.40 fof(f522,plain,(
% 0.10/0.40 ![X0,X1]: (empty(X0)|~ilf_type(X0,set_type)|ilf_type(X1,member_type(X0))|~member(X1,X0))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f104,f127])).
% 0.10/0.40 fof(f523,plain,(
% 0.10/0.40 ![X0,X1]: (empty(X0)|ilf_type(X1,member_type(X0))|~member(X1,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f522,f127])).
% 0.10/0.40 fof(f524,plain,(
% 0.10/0.40 ![X0,X1]: (~ilf_type(X0,set_type)|ilf_type(X0,subset_type(X1))|~ilf_type(X0,member_type(power_set(X1))))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f70,f127])).
% 0.10/0.40 fof(f525,plain,(
% 0.10/0.40 ![X0,X1]: (ilf_type(X0,subset_type(X1))|~ilf_type(X0,member_type(power_set(X1))))),
% 0.10/0.40 inference(resolution,[status(thm)],[f524,f127])).
% 0.10/0.40 fof(f528,plain,(
% 0.10/0.40 ![X0,X1]: (ilf_type(X0,subset_type(X1))|empty(power_set(X1))|~member(X0,power_set(X1)))),
% 0.10/0.40 inference(resolution,[status(thm)],[f525,f523])).
% 0.10/0.40 fof(f529,plain,(
% 0.10/0.40 ![X0,X1]: (ilf_type(X0,subset_type(X1))|~member(X0,power_set(X1)))),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f528,f171])).
% 0.10/0.40 fof(f958,plain,(
% 0.10/0.40 ![X0,X1]: (ilf_type(singleton(X0),subset_type(X1))|sk0_5(X1,singleton(X0))=X0|~spl0_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f529,f506])).
% 0.10/0.40 fof(f1034,plain,(
% 0.10/0.40 ![X0,X1,X2]: (sk0_5(cross_product(X0,X1),singleton(X2))=X2|~ilf_type(X1,set_type)|ilf_type(singleton(X2),relation_type(X0,X1))|~spl0_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f958,f168])).
% 0.10/0.40 fof(f1035,plain,(
% 0.10/0.40 ![X0,X1,X2]: (sk0_5(cross_product(X0,X1),singleton(X2))=X2|ilf_type(singleton(X2),relation_type(X0,X1))|~spl0_1)),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f1034,f127])).
% 0.10/0.40 fof(f1163,plain,(
% 0.10/0.40 sk0_5(cross_product(sk0_11,sk0_12),singleton(ordered_pair(sk0_13,sk0_14)))=ordered_pair(sk0_13,sk0_14)|~spl0_1),
% 0.10/0.40 inference(resolution,[status(thm)],[f1035,f136])).
% 0.10/0.40 fof(f1533,plain,(
% 0.10/0.40 spl0_15 <=> member(singleton(ordered_pair(sk0_13,sk0_14)),power_set(cross_product(sk0_11,sk0_12)))),
% 0.10/0.40 introduced(split_symbol_definition)).
% 0.10/0.40 fof(f1534,plain,(
% 0.10/0.40 member(singleton(ordered_pair(sk0_13,sk0_14)),power_set(cross_product(sk0_11,sk0_12)))|~spl0_15),
% 0.10/0.40 inference(component_clause,[status(thm)],[f1533])).
% 0.10/0.40 fof(f1543,plain,(
% 0.10/0.40 spl0_17 <=> member(ordered_pair(sk0_13,sk0_14),cross_product(sk0_11,sk0_12))),
% 0.10/0.40 introduced(split_symbol_definition)).
% 0.10/0.40 fof(f1545,plain,(
% 0.10/0.40 ~member(ordered_pair(sk0_13,sk0_14),cross_product(sk0_11,sk0_12))|spl0_17),
% 0.10/0.40 inference(component_clause,[status(thm)],[f1543])).
% 0.10/0.40 fof(f1546,plain,(
% 0.10/0.40 member(singleton(ordered_pair(sk0_13,sk0_14)),power_set(cross_product(sk0_11,sk0_12)))|~member(ordered_pair(sk0_13,sk0_14),cross_product(sk0_11,sk0_12))|~spl0_1),
% 0.10/0.40 inference(paramodulation,[status(thm)],[f1163,f508])).
% 0.10/0.40 fof(f1547,plain,(
% 0.10/0.40 spl0_15|~spl0_17|~spl0_1),
% 0.10/0.40 inference(split_clause,[status(thm)],[f1546,f1533,f1543,f140])).
% 0.10/0.40 fof(f1549,plain,(
% 0.10/0.40 ilf_type(singleton(ordered_pair(sk0_13,sk0_14)),subset_type(cross_product(sk0_11,sk0_12)))|~spl0_15),
% 0.10/0.40 inference(resolution,[status(thm)],[f1534,f529])).
% 0.10/0.40 fof(f1557,plain,(
% 0.10/0.40 spl0_18 <=> ilf_type(sk0_12,set_type)),
% 0.10/0.40 introduced(split_symbol_definition)).
% 0.10/0.40 fof(f1559,plain,(
% 0.10/0.40 ~ilf_type(sk0_12,set_type)|spl0_18),
% 0.10/0.40 inference(component_clause,[status(thm)],[f1557])).
% 0.10/0.40 fof(f1560,plain,(
% 0.10/0.40 spl0_19 <=> ilf_type(singleton(ordered_pair(sk0_13,sk0_14)),relation_type(sk0_11,sk0_12))),
% 0.10/0.40 introduced(split_symbol_definition)).
% 0.10/0.40 fof(f1561,plain,(
% 0.10/0.41 ilf_type(singleton(ordered_pair(sk0_13,sk0_14)),relation_type(sk0_11,sk0_12))|~spl0_19),
% 0.10/0.41 inference(component_clause,[status(thm)],[f1560])).
% 0.10/0.41 fof(f1563,plain,(
% 0.10/0.41 ~ilf_type(sk0_12,set_type)|ilf_type(singleton(ordered_pair(sk0_13,sk0_14)),relation_type(sk0_11,sk0_12))|~spl0_15),
% 0.10/0.41 inference(resolution,[status(thm)],[f1549,f168])).
% 0.10/0.41 fof(f1564,plain,(
% 0.10/0.41 ~spl0_18|spl0_19|~spl0_15),
% 0.10/0.41 inference(split_clause,[status(thm)],[f1563,f1557,f1560,f1533])).
% 0.10/0.41 fof(f1566,plain,(
% 0.10/0.41 $false|spl0_18),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1559,f127])).
% 0.10/0.41 fof(f1567,plain,(
% 0.10/0.41 spl0_18),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f1566])).
% 0.10/0.41 fof(f1568,plain,(
% 0.10/0.41 $false|~spl0_19),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1561,f136])).
% 0.10/0.41 fof(f1569,plain,(
% 0.10/0.41 ~spl0_19),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f1568])).
% 0.10/0.41 fof(f1786,plain,(
% 0.10/0.41 spl0_20 <=> member(sk0_13,sk0_11)),
% 0.10/0.41 introduced(split_symbol_definition)).
% 0.10/0.41 fof(f1788,plain,(
% 0.10/0.41 ~member(sk0_13,sk0_11)|spl0_20),
% 0.10/0.41 inference(component_clause,[status(thm)],[f1786])).
% 0.10/0.41 fof(f1789,plain,(
% 0.10/0.41 spl0_21 <=> member(sk0_14,sk0_12)),
% 0.10/0.41 introduced(split_symbol_definition)).
% 0.10/0.41 fof(f1791,plain,(
% 0.10/0.41 ~member(sk0_14,sk0_12)|spl0_21),
% 0.10/0.41 inference(component_clause,[status(thm)],[f1789])).
% 0.10/0.41 fof(f1792,plain,(
% 0.10/0.41 ~member(sk0_13,sk0_11)|~member(sk0_14,sk0_12)|spl0_17),
% 0.10/0.41 inference(resolution,[status(thm)],[f1545,f461])).
% 0.10/0.41 fof(f1793,plain,(
% 0.10/0.41 ~spl0_20|~spl0_21|spl0_17),
% 0.10/0.41 inference(split_clause,[status(thm)],[f1792,f1786,f1789,f1543])).
% 0.10/0.41 fof(f1820,plain,(
% 0.10/0.41 $false|spl0_20),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1788,f134])).
% 0.10/0.41 fof(f1821,plain,(
% 0.10/0.41 spl0_20),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f1820])).
% 0.10/0.41 fof(f1822,plain,(
% 0.10/0.41 $false|spl0_21),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f1791,f135])).
% 0.10/0.41 fof(f1823,plain,(
% 0.10/0.41 spl0_21),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f1822])).
% 0.10/0.41 fof(f1824,plain,(
% 0.10/0.41 $false),
% 0.10/0.41 inference(sat_refutation,[status(thm)],[f143,f200,f1547,f1564,f1567,f1569,f1793,f1821,f1823])).
% 0.10/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.41 % Elapsed time: 0.149708 seconds
% 0.10/0.41 % CPU time: 1.075625 seconds
% 0.10/0.41 % Memory used: 58.792 MB
%------------------------------------------------------------------------------