%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET679+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 : n015.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 0.18s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET679+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
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:35:35 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.49 fof(f1,axiom,(
% 0.18/0.49 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ( member(C,B)<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) )) )),
% 0.18/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f2,axiom,(
% 0.18/0.49 (! [B] :( ilf_type(B,set_type)=> ~ member(B,empty_set) ) )),
% 0.18/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f8,axiom,(
% 0.18/0.49 (! [B] :( ilf_type(B,set_type)=> (! [C] :( ilf_type(C,set_type)=> ( not_equal(B,C)<=> B != C ) ) )) )),
% 0.18/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f9,axiom,(
% 0.18/0.49 (! [B] :( ilf_type(B,set_type)=> ( empty(B)<=> (! [C] :( ilf_type(C,set_type)=> ~ member(C,B) ) )) ) )),
% 0.18/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f23,axiom,(
% 0.18/0.49 (! [B] : ilf_type(B,set_type) )),
% 0.18/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f24,conjecture,(
% 0.18/0.49 (! [B] :( ( ~ empty(B)& ilf_type(B,set_type) )=> not_equal(identity_relation_of(B),empty_set) ) )),
% 0.18/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.49 fof(f25,negated_conjecture,(
% 0.18/0.49 ~((! [B] :( ( ~ empty(B)& ilf_type(B,set_type) )=> not_equal(identity_relation_of(B),empty_set) ) ))),
% 0.18/0.49 inference(negated_conjecture,[status(cth)],[f24])).
% 0.18/0.49 fof(f26,plain,(
% 0.18/0.49 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(member(C,B)<=>member(ordered_pair(C,C),identity_relation_of(B))))))),
% 0.18/0.49 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.18/0.49 fof(f27,plain,(
% 0.18/0.49 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|((~member(C,B)|member(ordered_pair(C,C),identity_relation_of(B)))&(member(C,B)|~member(ordered_pair(C,C),identity_relation_of(B)))))))),
% 0.18/0.49 inference(NNF_transformation,[status(thm)],[f26])).
% 0.18/0.49 fof(f28,plain,(
% 0.18/0.49 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|~member(X1,X0)|member(ordered_pair(X1,X1),identity_relation_of(X0)))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f27])).
% 0.18/0.49 fof(f30,plain,(
% 0.18/0.49 ![B]: (~ilf_type(B,set_type)|~member(B,empty_set))),
% 0.18/0.49 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.18/0.49 fof(f31,plain,(
% 0.18/0.49 ![X0]: (~ilf_type(X0,set_type)|~member(X0,empty_set))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f30])).
% 0.18/0.49 fof(f49,plain,(
% 0.18/0.49 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|(not_equal(B,C)<=>~B=C))))),
% 0.18/0.49 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.18/0.49 fof(f50,plain,(
% 0.18/0.49 ![B]: (~ilf_type(B,set_type)|(![C]: (~ilf_type(C,set_type)|((~not_equal(B,C)|~B=C)&(not_equal(B,C)|B=C)))))),
% 0.18/0.49 inference(NNF_transformation,[status(thm)],[f49])).
% 0.18/0.49 fof(f52,plain,(
% 0.18/0.49 ![X0,X1]: (~ilf_type(X0,set_type)|~ilf_type(X1,set_type)|not_equal(X0,X1)|X0=X1)),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f50])).
% 0.18/0.49 fof(f53,plain,(
% 0.18/0.49 ![B]: (~ilf_type(B,set_type)|(empty(B)<=>(![C]: (~ilf_type(C,set_type)|~member(C,B)))))),
% 0.18/0.49 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.18/0.49 fof(f54,plain,(
% 0.18/0.49 ![B]: (~ilf_type(B,set_type)|((~empty(B)|(![C]: (~ilf_type(C,set_type)|~member(C,B))))&(empty(B)|(?[C]: (ilf_type(C,set_type)&member(C,B))))))),
% 0.18/0.49 inference(NNF_transformation,[status(thm)],[f53])).
% 0.18/0.49 fof(f55,plain,(
% 0.18/0.49 ![B]: (~ilf_type(B,set_type)|((~empty(B)|(![C]: (~ilf_type(C,set_type)|~member(C,B))))&(empty(B)|(ilf_type(sK1_skl(B),set_type)&member(sK1_skl(B),B)))))),
% 0.18/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B))],[f54])).
% 0.18/0.49 fof(f58,plain,(
% 0.18/0.49 ![X0]: (~ilf_type(X0,set_type)|empty(X0)|member(sK1_skl(X0),X0))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f55])).
% 0.18/0.49 fof(f107,plain,(
% 0.18/0.49 ![X0]: (ilf_type(X0,set_type))),
% 0.18/0.49 inference(cnf_transformation,[status(thm)],[f23])).
% 0.18/0.49 fof(f108,plain,(
% 0.18/0.49 (?[B]: ((~empty(B)&ilf_type(B,set_type))&~not_equal(identity_relation_of(B),empty_set)))),
% 0.18/0.49 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.18/0.49 fof(f109,plain,(
% 0.18/0.49 ((~empty(sK9_skl)&ilf_type(sK9_skl,set_type))&~not_equal(identity_relation_of(sK9_skl),empty_set))),
% 0.18/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(B,sK9_skl)],[f108])).
% 0.18/0.49 fof(f110,plain,(
% 0.18/0.49 ~empty(sK9_skl)),
% 0.18/0.50 inference(cnf_transformation,[status(thm)],[f109])).
% 0.18/0.50 fof(f112,plain,(
% 0.18/0.50 ~not_equal(identity_relation_of(sK9_skl),empty_set)),
% 0.18/0.50 inference(cnf_transformation,[status(thm)],[f109])).
% 0.18/0.50 fof(f118,plain,(
% 0.18/0.50 ![X0,X1]: (~ilf_type(X0,set_type)|~member(X0,X1)|member(ordered_pair(X0,X0),identity_relation_of(X1)))),
% 0.18/0.50 inference(forward_subsumption_resolution,[status(thm)],[f28,f107])).
% 0.18/0.50 fof(f120,plain,(
% 0.18/0.50 ![X0]: (~member(X0,empty_set))),
% 0.18/0.50 inference(forward_subsumption_resolution,[status(thm)],[f31,f107])).
% 0.18/0.50 fof(f130,plain,(
% 0.18/0.50 ![X0,X1]: (~ilf_type(X0,set_type)|not_equal(X1,X0)|X1=X0)),
% 0.18/0.50 inference(forward_subsumption_resolution,[status(thm)],[f52,f107])).
% 0.18/0.50 fof(f131,plain,(
% 0.18/0.50 ![X0,X1]: (not_equal(X0,X1)|X0=X1)),
% 0.18/0.50 inference(resolution,[status(thm)],[f130,f107])).
% 0.18/0.50 fof(f133,plain,(
% 0.18/0.50 identity_relation_of(sK9_skl)=empty_set),
% 0.18/0.50 inference(resolution,[status(thm)],[f131,f112])).
% 0.18/0.50 fof(f165,plain,(
% 0.18/0.50 ![X0]: (empty(X0)|member(sK1_skl(X0),X0))),
% 0.18/0.50 inference(forward_subsumption_resolution,[status(thm)],[f58,f107])).
% 0.18/0.50 fof(f168,plain,(
% 0.18/0.50 ![X0]: (empty(X0)|~ilf_type(sK1_skl(X0),set_type)|member(ordered_pair(sK1_skl(X0),sK1_skl(X0)),identity_relation_of(X0)))),
% 0.18/0.50 inference(resolution,[status(thm)],[f165,f118])).
% 0.18/0.50 fof(f169,plain,(
% 0.18/0.50 ![X0]: (empty(X0)|member(ordered_pair(sK1_skl(X0),sK1_skl(X0)),identity_relation_of(X0)))),
% 0.18/0.50 inference(forward_subsumption_resolution,[status(thm)],[f168,f107])).
% 0.18/0.50 fof(f182,plain,(
% 0.18/0.50 empty(sK9_skl)|member(ordered_pair(sK1_skl(sK9_skl),sK1_skl(sK9_skl)),empty_set)),
% 0.18/0.50 inference(paramodulation,[status(thm)],[f133,f169])).
% 0.18/0.50 fof(f186,plain,(
% 0.18/0.50 member(ordered_pair(sK1_skl(sK9_skl),sK1_skl(sK9_skl)),empty_set)),
% 0.18/0.50 inference(forward_subsumption_resolution,[status(thm)],[f182,f110])).
% 0.18/0.50 fof(f187,plain,(
% 0.18/0.50 $false),
% 0.18/0.50 inference(forward_subsumption_resolution,[status(thm)],[f186,f120])).
% 0.18/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.51 % Elapsed time: 0.060455 seconds
% 0.18/0.51 % CPU time: 0.162346 seconds
% 0.18/0.51 % Total memory used: 48.583 MB
% 0.18/0.51 % Net memory used: 48.509 MB
%------------------------------------------------------------------------------