%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET675+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 : n016.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 02:12:26 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET675+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:36:52 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.38 fof(f1,axiom,(
% 0.09/0.38 (! [B] :( ilf_type(B,binary_relation_type)=> image(B,domain_of(B)) = range_of(B) ) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f2,axiom,(
% 0.09/0.38 (! [B] :( ilf_type(B,binary_relation_type)=> inverse2(B,range_of(B)) = domain_of(B) ) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f3,axiom,(
% 0.09/0.38 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(B,C))=> ( image4(B,C,D,B) = range(B,C,D)& inverse4(B,C,D,C) = domain(B,C,D) ) ) )) )) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f4,axiom,(
% 0.09/0.38 (! [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))) ) )) ) )) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f12,axiom,(
% 0.09/0.38 (! [B] :( ilf_type(B,set_type)=> ( ilf_type(B,binary_relation_type)<=> ( relation_like(B)& ilf_type(B,set_type) ) ) ) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f23,axiom,(
% 0.09/0.38 (! [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) ) )) )) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f27,axiom,(
% 0.09/0.38 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(B,C))=> domain(B,C,D) = domain_of(D) ) )) )) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f29,axiom,(
% 0.09/0.38 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(B,C))=> range(B,C,D) = range_of(D) ) )) )) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f31,axiom,(
% 0.09/0.38 (! [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) ) )) )) )) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f33,axiom,(
% 0.09/0.38 (! [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)=> inverse4(B,C,D,E) = inverse2(D,E) ) )) )) )) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f35,axiom,(
% 0.09/0.38 (! [B] : ilf_type(B,set_type) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f36,conjecture,(
% 0.09/0.38 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(C,B))=> ( image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D)& inverse4(C,B,D,image4(C,B,D,C)) = domain(C,B,D) ) ) )) )) )),
% 0.09/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f37,negated_conjecture,(
% 0.09/0.38 ~((! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> (! [D] :( ilf_type(D,relation_type(C,B))=> ( image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D)& inverse4(C,B,D,image4(C,B,D,C)) = domain(C,B,D) ) ) )) )) ))),
% 0.09/0.38 inference(negated_conjecture,[status(cth)],[f36])).
% 0.09/0.38 fof(f38,plain,(
% 0.09/0.38 ![B]: (~ilf_type(B,binary_relation_type)|image(B,domain_of(B))=range_of(B))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.09/0.38 fof(f39,plain,(
% 0.09/0.38 ![X0]: (~ilf_type(X0,binary_relation_type)|image(X0,domain_of(X0))=range_of(X0))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f38])).
% 0.09/0.38 fof(f40,plain,(
% 0.09/0.38 ![B]: (~ilf_type(B,binary_relation_type)|inverse2(B,range_of(B))=domain_of(B))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.09/0.38 fof(f41,plain,(
% 0.09/0.38 ![X0]: (~ilf_type(X0,binary_relation_type)|inverse2(X0,range_of(X0))=domain_of(X0))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f40])).
% 0.09/0.38 fof(f42,plain,(
% 0.09/0.38 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,relation_type(B,C))|(image4(B,C,D,B)=range(B,C,D)&inverse4(B,C,D,C)=domain(B,C,D)))))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.09/0.38 fof(f43,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|image4(X0,X1,X2,X0)=range(X0,X1,X2))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f42])).
% 0.09/0.38 fof(f44,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|inverse4(X0,X1,X2,X1)=domain(X0,X1,X2))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f42])).
% 0.09/0.38 fof(f45,plain,(
% 0.09/0.38 ![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)))))))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.09/0.38 fof(f47,plain,(
% 0.09/0.38 ![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))))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f45])).
% 0.09/0.38 fof(f66,plain,(
% 0.09/0.38 ![B]: (~ilf_type(B,set_type)|(ilf_type(B,binary_relation_type)<=>(relation_like(B)&ilf_type(B,set_type))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.09/0.38 fof(f67,plain,(
% 0.09/0.38 ![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)))))),
% 0.09/0.38 inference(NNF_transformation,[status(thm)],[f66])).
% 0.09/0.38 fof(f70,plain,(
% 0.09/0.38 ![X0]: (~ilf_type(X0,set_type)|ilf_type(X0,binary_relation_type)|~relation_like(X0)|~ilf_type(X0,set_type))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f67])).
% 0.09/0.38 fof(f115,plain,(
% 0.09/0.38 ![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))))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.09/0.38 fof(f116,plain,(
% 0.09/0.38 ![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))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f115])).
% 0.09/0.38 fof(f127,plain,(
% 0.09/0.38 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,relation_type(B,C))|domain(B,C,D)=domain_of(D))))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.09/0.38 fof(f128,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|domain(X0,X1,X2)=domain_of(X2))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f127])).
% 0.09/0.38 fof(f131,plain,(
% 0.09/0.38 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(![D]: (~ilf_type(D,relation_type(B,C))|range(B,C,D)=range_of(D))))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.09/0.38 fof(f132,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|range(X0,X1,X2)=range_of(X2))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f131])).
% 0.09/0.38 fof(f135,plain,(
% 0.09/0.38 ![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))))))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 0.09/0.38 fof(f136,plain,(
% 0.09/0.38 ![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))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f135])).
% 0.09/0.38 fof(f139,plain,(
% 0.09/0.38 ![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)|inverse4(B,C,D,E)=inverse2(D,E))))))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 0.09/0.38 fof(f140,plain,(
% 0.09/0.38 ![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)|inverse4(X0,X1,X2,X3)=inverse2(X2,X3))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f139])).
% 0.09/0.38 fof(f143,plain,(
% 0.09/0.38 ![X0]: (ilf_type(X0,set_type))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f35])).
% 0.09/0.38 fof(f144,plain,(
% 0.09/0.38 (?[B]: (ilf_type(B,set_type)&(?[C]: (ilf_type(C,set_type)&(?[D]: (ilf_type(D,relation_type(C,B))&(~image4(C,B,D,inverse4(C,B,D,B))=range(C,B,D)|~inverse4(C,B,D,image4(C,B,D,C))=domain(C,B,D))))))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.09/0.38 fof(f145,plain,(
% 0.09/0.38 (ilf_type(sK10_skl,set_type)&(ilf_type(sK11_skl,set_type)&(ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl))&(~image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl))=range(sK11_skl,sK10_skl,sK12_skl)|~inverse4(sK11_skl,sK10_skl,sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl))=domain(sK11_skl,sK10_skl,sK12_skl)))))),
% 0.09/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(B,sK10_skl),skolemize(C,sK11_skl),skolemize(D,sK12_skl)],[f144])).
% 0.09/0.38 fof(f148,plain,(
% 0.09/0.38 ilf_type(sK12_skl,relation_type(sK11_skl,sK10_skl))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f145])).
% 0.09/0.38 fof(f149,plain,(
% 0.09/0.38 ~image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl))=range(sK11_skl,sK10_skl,sK12_skl)|~inverse4(sK11_skl,sK10_skl,sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl))=domain(sK11_skl,sK10_skl,sK12_skl)),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f145])).
% 0.09/0.38 fof(f150,definition,(
% 0.09/0.38 sQ0_spl <=> (image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl))=range(sK11_skl,sK10_skl,sK12_skl))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f152,plain,(
% 0.09/0.38 ~image4(sK11_skl,sK10_skl,sK12_skl,inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl))=range(sK11_skl,sK10_skl,sK12_skl)|sQ0_spl),
% 0.09/0.38 inference(component_clause,[status(thm)],[f150])).
% 0.09/0.38 fof(f153,definition,(
% 0.09/0.38 sQ1_spl <=> (inverse4(sK11_skl,sK10_skl,sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl))=domain(sK11_skl,sK10_skl,sK12_skl))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f155,plain,(
% 0.09/0.38 ~inverse4(sK11_skl,sK10_skl,sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl))=domain(sK11_skl,sK10_skl,sK12_skl)|sQ1_spl),
% 0.09/0.38 inference(component_clause,[status(thm)],[f153])).
% 0.09/0.38 fof(f156,plain,(
% 0.09/0.38 ~sQ0_spl|~sQ1_spl),
% 0.09/0.38 inference(split_clause,[status(thm)],[f149,f150,f153])).
% 0.09/0.38 fof(f161,plain,(
% 0.09/0.38 ![X0]: (~ilf_type(X0,set_type)|ilf_type(X0,binary_relation_type)|~relation_like(X0))),
% 0.09/0.38 inference(duplicate_literals_removal,[status(thm)],[f70])).
% 0.09/0.38 fof(f164,plain,(
% 0.09/0.38 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|inverse4(X0,X1,X2,X3)=inverse2(X2,X3))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f140,f143])).
% 0.09/0.38 fof(f166,plain,(
% 0.09/0.38 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~ilf_type(X2,relation_type(X0,X1))|image4(X0,X1,X2,X3)=image(X2,X3))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f136,f143])).
% 0.09/0.38 fof(f168,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X0,X2))|range(X0,X2,X1)=range_of(X1))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f132,f143])).
% 0.09/0.38 fof(f170,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X0,X2))|domain(X0,X2,X1)=domain_of(X1))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f128,f143])).
% 0.09/0.38 fof(f174,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,subset_type(cross_product(X0,X2)))|relation_like(X1))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f116,f143])).
% 0.09/0.38 fof(f190,plain,(
% 0.09/0.38 ![X0]: (ilf_type(X0,binary_relation_type)|~relation_like(X0))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f161,f143])).
% 0.09/0.38 fof(f195,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X0,X2))|ilf_type(X1,subset_type(cross_product(X0,X2))))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f47,f143])).
% 0.09/0.38 fof(f197,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X0,X2))|inverse4(X0,X2,X1,X2)=domain(X0,X2,X1))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f44,f143])).
% 0.09/0.38 fof(f198,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X0,X2))|image4(X0,X2,X1,X0)=range(X0,X2,X1))),
% 0.09/0.38 inference(backward_subsumption_resolution,[status(thm)],[f43,f143])).
% 0.09/0.38 fof(f201,plain,(
% 0.09/0.38 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X2,X0))|inverse4(X2,X0,X1,X3)=inverse2(X1,X3))),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f164,f143])).
% 0.09/0.38 fof(f203,plain,(
% 0.09/0.38 ![X0,X1,X2,X3]: (~ilf_type(X0,set_type)|~ilf_type(X1,relation_type(X2,X0))|image4(X2,X0,X1,X3)=image(X1,X3))),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f166,f143])).
% 0.09/0.38 fof(f205,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,relation_type(X1,X2))|range(X1,X2,X0)=range_of(X0))),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f168,f143])).
% 0.09/0.38 fof(f207,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,relation_type(X1,X2))|domain(X1,X2,X0)=domain_of(X0))),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f170,f143])).
% 0.09/0.38 fof(f209,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,subset_type(cross_product(X1,X2)))|relation_like(X0))),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f174,f143])).
% 0.09/0.38 fof(f223,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,relation_type(X1,X2))|ilf_type(X0,subset_type(cross_product(X1,X2))))),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f195,f143])).
% 0.09/0.38 fof(f225,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,relation_type(X1,X2))|inverse4(X1,X2,X0,X2)=domain(X1,X2,X0))),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f197,f143])).
% 0.09/0.38 fof(f226,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~ilf_type(X0,relation_type(X1,X2))|image4(X1,X2,X0,X1)=range(X1,X2,X0))),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f198,f143])).
% 0.09/0.38 fof(f228,definition,(
% 0.09/0.38 sQ2_spl <=> (ilf_type(sK10_skl,set_type))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f230,plain,(
% 0.09/0.38 ~ilf_type(sK10_skl,set_type)|sQ2_spl),
% 0.09/0.38 inference(component_clause,[status(thm)],[f228])).
% 0.09/0.38 fof(f235,plain,(
% 0.09/0.38 $false|sQ2_spl),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f230,f143])).
% 0.09/0.38 fof(f236,plain,(
% 0.09/0.38 sQ2_spl),
% 0.09/0.38 inference(contradiction_clause,[status(thm)],[f235])).
% 0.09/0.38 fof(f237,plain,(
% 0.09/0.38 ![X0]: (~ilf_type(sK10_skl,set_type)|inverse4(sK11_skl,sK10_skl,sK12_skl,X0)=inverse2(sK12_skl,X0))),
% 0.09/0.38 inference(resolution,[status(thm)],[f201,f148])).
% 0.09/0.38 fof(f238,definition,(
% 0.09/0.38 ![X0]: (sQ4_spl <=> (inverse4(sK11_skl,sK10_skl,sK12_skl,X0)=inverse2(sK12_skl,X0)))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f239,plain,(
% 0.09/0.38 ![X0]: (inverse4(sK11_skl,sK10_skl,sK12_skl,X0)=inverse2(sK12_skl,X0)|~sQ4_spl)),
% 0.09/0.38 inference(component_clause,[status(thm)],[f238])).
% 0.09/0.38 fof(f241,plain,(
% 0.09/0.38 ~sQ2_spl|sQ4_spl),
% 0.09/0.38 inference(split_clause,[status(thm)],[f237,f228,f238])).
% 0.09/0.38 fof(f242,plain,(
% 0.09/0.38 ~image4(sK11_skl,sK10_skl,sK12_skl,inverse2(sK12_skl,sK10_skl))=range(sK11_skl,sK10_skl,sK12_skl)|~sQ4_spl|sQ0_spl),
% 0.09/0.38 inference(backward_demodulation,[status(thm)],[f239,f152])).
% 0.09/0.38 fof(f251,plain,(
% 0.09/0.38 ![X0]: (~ilf_type(sK10_skl,set_type)|image4(sK11_skl,sK10_skl,sK12_skl,X0)=image(sK12_skl,X0))),
% 0.09/0.38 inference(resolution,[status(thm)],[f203,f148])).
% 0.09/0.38 fof(f252,definition,(
% 0.09/0.38 ![X0]: (sQ6_spl <=> (image4(sK11_skl,sK10_skl,sK12_skl,X0)=image(sK12_skl,X0)))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f253,plain,(
% 0.09/0.38 ![X0]: (image4(sK11_skl,sK10_skl,sK12_skl,X0)=image(sK12_skl,X0)|~sQ6_spl)),
% 0.09/0.38 inference(component_clause,[status(thm)],[f252])).
% 0.09/0.38 fof(f255,plain,(
% 0.09/0.38 ~sQ2_spl|sQ6_spl),
% 0.09/0.38 inference(split_clause,[status(thm)],[f251,f228,f252])).
% 0.09/0.38 fof(f256,plain,(
% 0.09/0.38 ~image(sK12_skl,inverse2(sK12_skl,sK10_skl))=range(sK11_skl,sK10_skl,sK12_skl)|~sQ6_spl|~sQ4_spl|sQ0_spl),
% 0.09/0.38 inference(backward_demodulation,[status(thm)],[f253,f242])).
% 0.09/0.38 fof(f259,plain,(
% 0.09/0.38 range(sK11_skl,sK10_skl,sK12_skl)=range_of(sK12_skl)),
% 0.09/0.38 inference(resolution,[status(thm)],[f205,f148])).
% 0.09/0.38 fof(f261,plain,(
% 0.09/0.38 ~image(sK12_skl,inverse2(sK12_skl,sK10_skl))=range_of(sK12_skl)|~sQ6_spl|~sQ4_spl|sQ0_spl),
% 0.09/0.38 inference(backward_demodulation,[status(thm)],[f259,f256])).
% 0.09/0.38 fof(f263,plain,(
% 0.09/0.38 domain(sK11_skl,sK10_skl,sK12_skl)=domain_of(sK12_skl)),
% 0.09/0.38 inference(resolution,[status(thm)],[f207,f148])).
% 0.09/0.38 fof(f364,plain,(
% 0.09/0.38 ilf_type(sK12_skl,subset_type(cross_product(sK11_skl,sK10_skl)))),
% 0.09/0.38 inference(resolution,[status(thm)],[f223,f148])).
% 0.09/0.38 fof(f372,plain,(
% 0.09/0.38 inverse4(sK11_skl,sK10_skl,sK12_skl,sK10_skl)=domain(sK11_skl,sK10_skl,sK12_skl)),
% 0.09/0.38 inference(resolution,[status(thm)],[f225,f148])).
% 0.09/0.38 fof(f375,plain,(
% 0.09/0.38 inverse2(sK12_skl,sK10_skl)=domain(sK11_skl,sK10_skl,sK12_skl)|~sQ4_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f239,f372])).
% 0.09/0.38 fof(f376,plain,(
% 0.09/0.38 ~image(sK12_skl,domain_of(sK12_skl))=range_of(sK12_skl)|~sQ6_spl|~sQ4_spl|sQ0_spl),
% 0.09/0.38 inference(backward_demodulation,[status(thm)],[f377,f261])).
% 0.09/0.38 fof(f377,plain,(
% 0.09/0.38 inverse2(sK12_skl,sK10_skl)=domain_of(sK12_skl)|~sQ4_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f263,f375])).
% 0.09/0.38 fof(f379,plain,(
% 0.09/0.38 image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl)=range(sK11_skl,sK10_skl,sK12_skl)),
% 0.09/0.38 inference(resolution,[status(thm)],[f226,f148])).
% 0.09/0.38 fof(f382,plain,(
% 0.09/0.38 image(sK12_skl,sK11_skl)=range(sK11_skl,sK10_skl,sK12_skl)|~sQ6_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f253,f379])).
% 0.09/0.38 fof(f383,plain,(
% 0.09/0.38 image(sK12_skl,sK11_skl)=range_of(sK12_skl)|~sQ6_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f259,f382])).
% 0.09/0.38 fof(f414,plain,(
% 0.09/0.38 relation_like(sK12_skl)),
% 0.09/0.38 inference(resolution,[status(thm)],[f364,f209])).
% 0.09/0.38 fof(f419,plain,(
% 0.09/0.38 ilf_type(sK12_skl,binary_relation_type)),
% 0.09/0.38 inference(resolution,[status(thm)],[f414,f190])).
% 0.09/0.38 fof(f428,plain,(
% 0.09/0.38 inverse2(sK12_skl,range_of(sK12_skl))=domain_of(sK12_skl)),
% 0.09/0.38 inference(resolution,[status(thm)],[f419,f41])).
% 0.09/0.38 fof(f429,plain,(
% 0.09/0.38 image(sK12_skl,domain_of(sK12_skl))=range_of(sK12_skl)),
% 0.09/0.38 inference(resolution,[status(thm)],[f419,f39])).
% 0.09/0.38 fof(f430,plain,(
% 0.09/0.38 $false|~sQ6_spl|~sQ4_spl|sQ0_spl),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f429,f376])).
% 0.09/0.38 fof(f431,plain,(
% 0.09/0.38 ~sQ6_spl|~sQ4_spl|sQ0_spl),
% 0.09/0.38 inference(contradiction_clause,[status(thm)],[f430])).
% 0.09/0.38 fof(f432,plain,(
% 0.09/0.38 ~inverse2(sK12_skl,image4(sK11_skl,sK10_skl,sK12_skl,sK11_skl))=domain(sK11_skl,sK10_skl,sK12_skl)|~sQ4_spl|sQ1_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f239,f155])).
% 0.09/0.38 fof(f433,plain,(
% 0.09/0.38 ~inverse2(sK12_skl,image(sK12_skl,sK11_skl))=domain(sK11_skl,sK10_skl,sK12_skl)|~sQ6_spl|~sQ4_spl|sQ1_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f253,f432])).
% 0.09/0.38 fof(f434,plain,(
% 0.09/0.38 ~inverse2(sK12_skl,range_of(sK12_skl))=domain(sK11_skl,sK10_skl,sK12_skl)|~sQ6_spl|~sQ4_spl|sQ1_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f383,f433])).
% 0.09/0.38 fof(f435,plain,(
% 0.09/0.38 ~domain_of(sK12_skl)=domain(sK11_skl,sK10_skl,sK12_skl)|~sQ6_spl|~sQ4_spl|sQ1_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f428,f434])).
% 0.09/0.38 fof(f436,plain,(
% 0.09/0.38 ~domain_of(sK12_skl)=domain_of(sK12_skl)|~sQ6_spl|~sQ4_spl|sQ1_spl),
% 0.09/0.38 inference(forward_demodulation,[status(thm)],[f263,f435])).
% 0.09/0.38 fof(f437,plain,(
% 0.09/0.38 $false|~sQ6_spl|~sQ4_spl|sQ1_spl),
% 0.09/0.38 inference(trivial_equality_resolution,[status(thm)],[f436])).
% 0.09/0.38 fof(f438,plain,(
% 0.09/0.38 ~sQ6_spl|~sQ4_spl|sQ1_spl),
% 0.09/0.38 inference(contradiction_clause,[status(thm)],[f437])).
% 0.09/0.38 fof(f439,plain,(
% 0.09/0.38 $false),
% 0.09/0.38 inference(sat_refutation,[status(thm)],[f156,f236,f241,f255,f431,f438])).
% 0.09/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.41 % Elapsed time: 0.046742 seconds
% 0.14/0.41 % CPU time: 0.105065 seconds
% 0.14/0.41 % Total memory used: 18.800 MB
% 0.14/0.41 % Net memory used: 18.719 MB
%------------------------------------------------------------------------------