%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:21:46 PM UTC 2026
% Result : Theorem 0.10s 0.54s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:55:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.54 % Refutation found
% 0.10/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.54 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.54 fof(f4,axiom,(
% 0.10/0.54 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 0.10/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.54 fof(f11,axiom,(
% 0.10/0.54 (! [A,B] :( disjoint(A,B)<=> set_intersection2(A,B) = empty_set ) )),
% 0.10/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.54 fof(f23,lemma,(
% 0.10/0.54 (! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) )),
% 0.10/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.54 fof(f27,axiom,(
% 0.10/0.54 (! [A,B] :( disjoint(A,B)=> disjoint(B,A) ) )),
% 0.10/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.54 fof(f39,lemma,(
% 0.10/0.54 (! [A,B] : subset(set_difference(A,B),A) )),
% 0.10/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.54 fof(f42,axiom,(
% 0.10/0.54 (! [A] : set_difference(A,empty_set) = A )),
% 0.10/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.54 fof(f47,lemma,(
% 0.10/0.54 (! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) )),
% 0.10/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.54 fof(f55,conjecture,(
% 0.10/0.54 (! [A,B] :( disjoint(A,B)<=> set_difference(A,B) = A ) )),
% 0.10/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.54 fof(f56,negated_conjecture,(
% 0.10/0.54 ~((! [A,B] :( disjoint(A,B)<=> set_difference(A,B) = A ) ))),
% 0.10/0.54 inference(negated_conjecture,[status(cth)],[f55])).
% 0.10/0.54 fof(f64,plain,(
% 0.10/0.54 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.54 fof(f109,plain,(
% 0.10/0.54 ![A,B]: ((~disjoint(A,B)|set_intersection2(A,B)=empty_set)&(disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 0.10/0.54 inference(NNF_transformation,[status(thm)],[f11])).
% 0.10/0.54 fof(f110,plain,(
% 0.10/0.54 (![A,B]: (~disjoint(A,B)|set_intersection2(A,B)=empty_set))&(![A,B]: (disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 0.10/0.54 inference(miniscoping,[status(thm)],[f109])).
% 0.10/0.54 fof(f111,plain,(
% 0.10/0.54 ![X0,X1]: (~disjoint(X0,X1)|set_intersection2(X0,X1)=empty_set)),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f110])).
% 0.10/0.54 fof(f112,plain,(
% 0.10/0.54 ![X0,X1]: (disjoint(X0,X1)|~set_intersection2(X0,X1)=empty_set)),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f110])).
% 0.10/0.54 fof(f131,plain,(
% 0.10/0.54 ![A,B]: ((~set_difference(A,B)=empty_set|subset(A,B))&(set_difference(A,B)=empty_set|~subset(A,B)))),
% 0.10/0.54 inference(NNF_transformation,[status(thm)],[f23])).
% 0.10/0.54 fof(f132,plain,(
% 0.10/0.54 (![A,B]: (~set_difference(A,B)=empty_set|subset(A,B)))&(![A,B]: (set_difference(A,B)=empty_set|~subset(A,B)))),
% 0.10/0.54 inference(miniscoping,[status(thm)],[f131])).
% 0.10/0.54 fof(f134,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,X1)=empty_set|~subset(X0,X1))),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f132])).
% 0.10/0.54 fof(f141,plain,(
% 0.10/0.54 ![A,B]: (~disjoint(A,B)|disjoint(B,A))),
% 0.10/0.54 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.10/0.54 fof(f142,plain,(
% 0.10/0.54 ![X0,X1]: (~disjoint(X0,X1)|disjoint(X1,X0))),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f141])).
% 0.10/0.54 fof(f167,plain,(
% 0.10/0.54 ![X0,X1]: (subset(set_difference(X0,X1),X0))),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f39])).
% 0.10/0.54 fof(f173,plain,(
% 0.10/0.54 ![X0]: (set_difference(X0,empty_set)=X0)),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f42])).
% 0.10/0.54 fof(f185,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,set_difference(X0,X1))=set_intersection2(X0,X1))),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f47])).
% 0.10/0.54 fof(f203,plain,(
% 0.10/0.54 (?[A,B]: (disjoint(A,B)<~>set_difference(A,B)=A))),
% 0.10/0.54 inference(pre_NNF_transformation,[status(thm)],[f56])).
% 0.10/0.54 fof(f204,plain,(
% 0.10/0.54 ?[A,B]: ((disjoint(A,B)|set_difference(A,B)=A)&(~disjoint(A,B)|~set_difference(A,B)=A))),
% 0.10/0.54 inference(NNF_transformation,[status(thm)],[f203])).
% 0.10/0.54 fof(f205,plain,(
% 0.10/0.54 ((disjoint(sK10_skl,sK11_skl)|set_difference(sK10_skl,sK11_skl)=sK10_skl)&(~disjoint(sK10_skl,sK11_skl)|~set_difference(sK10_skl,sK11_skl)=sK10_skl))),
% 0.10/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(A,sK10_skl),skolemize(B,sK11_skl)],[f204])).
% 0.10/0.54 fof(f206,plain,(
% 0.10/0.54 disjoint(sK10_skl,sK11_skl)|set_difference(sK10_skl,sK11_skl)=sK10_skl),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f205])).
% 0.10/0.54 fof(f207,plain,(
% 0.10/0.54 ~disjoint(sK10_skl,sK11_skl)|~set_difference(sK10_skl,sK11_skl)=sK10_skl),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f205])).
% 0.10/0.54 fof(f213,definition,(
% 0.10/0.54 sQ0_spl <=> (disjoint(sK10_skl,sK11_skl))),
% 0.10/0.54 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.54 fof(f214,plain,(
% 0.10/0.54 disjoint(sK10_skl,sK11_skl)|~sQ0_spl),
% 0.10/0.54 inference(component_clause,[status(thm)],[f213])).
% 0.10/0.54 fof(f216,definition,(
% 0.10/0.54 sQ1_spl <=> (set_difference(sK10_skl,sK11_skl)=sK10_skl)),
% 0.10/0.54 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.54 fof(f217,plain,(
% 0.10/0.54 set_difference(sK10_skl,sK11_skl)=sK10_skl|~sQ1_spl),
% 0.10/0.54 inference(component_clause,[status(thm)],[f216])).
% 0.10/0.54 fof(f218,plain,(
% 0.10/0.54 ~set_difference(sK10_skl,sK11_skl)=sK10_skl|sQ1_spl),
% 0.10/0.54 inference(component_clause,[status(thm)],[f216])).
% 0.10/0.54 fof(f219,plain,(
% 0.10/0.54 sQ0_spl|sQ1_spl),
% 0.10/0.54 inference(split_clause,[status(thm)],[f206,f213,f216])).
% 0.10/0.54 fof(f220,plain,(
% 0.10/0.54 ~sQ0_spl|~sQ1_spl),
% 0.10/0.54 inference(split_clause,[status(thm)],[f207,f213,f216])).
% 0.10/0.54 fof(f234,plain,(
% 0.10/0.54 disjoint(sK11_skl,sK10_skl)|~sQ0_spl),
% 0.10/0.54 inference(resolution,[status(thm)],[f214,f142])).
% 0.10/0.54 fof(f236,plain,(
% 0.10/0.54 set_intersection2(sK11_skl,sK10_skl)=empty_set|~sQ0_spl),
% 0.10/0.54 inference(resolution,[status(thm)],[f234,f111])).
% 0.10/0.54 fof(f258,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(set_difference(X0,X1),X0)=empty_set)),
% 0.10/0.54 inference(resolution,[status(thm)],[f134,f167])).
% 0.10/0.54 fof(f262,plain,(
% 0.10/0.54 ![X0]: (set_difference(X0,X0)=empty_set)),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f173,f258])).
% 0.10/0.54 fof(f285,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(set_difference(X0,X1),empty_set)=set_intersection2(set_difference(X0,X1),X0))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f258,f185])).
% 0.10/0.54 fof(f287,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,set_intersection2(X0,X1))=set_intersection2(X0,set_difference(X0,X1)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f185,f185])).
% 0.10/0.54 fof(f296,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,X1)=set_intersection2(set_difference(X0,X1),X0))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f173,f285])).
% 0.10/0.54 fof(f297,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,X1)=set_intersection2(X0,set_difference(X0,X1)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f64,f296])).
% 0.10/0.54 fof(f319,definition,(
% 0.10/0.54 sQ5_spl <=> (empty_set=empty_set)),
% 0.10/0.54 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.10/0.54 fof(f321,plain,(
% 0.10/0.54 ~empty_set=empty_set|sQ5_spl),
% 0.10/0.54 inference(component_clause,[status(thm)],[f319])).
% 0.10/0.54 fof(f323,plain,(
% 0.10/0.54 $false|sQ5_spl),
% 0.10/0.54 inference(trivial_equality_resolution,[status(thm)],[f321])).
% 0.10/0.54 fof(f324,plain,(
% 0.10/0.54 sQ5_spl),
% 0.10/0.54 inference(contradiction_clause,[status(thm)],[f323])).
% 0.10/0.54 fof(f325,plain,(
% 0.10/0.54 set_difference(sK10_skl,sK10_skl)=set_intersection2(sK10_skl,sK11_skl)|~sQ1_spl),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f217,f185])).
% 0.10/0.54 fof(f330,plain,(
% 0.10/0.54 empty_set=set_intersection2(sK10_skl,sK11_skl)|~sQ1_spl),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f262,f325])).
% 0.10/0.54 fof(f331,plain,(
% 0.10/0.54 empty_set=set_intersection2(sK11_skl,sK10_skl)|~sQ1_spl),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f64,f330])).
% 0.10/0.54 fof(f332,plain,(
% 0.10/0.54 disjoint(sK11_skl,sK10_skl)|~sQ1_spl),
% 0.10/0.54 inference(resolution,[status(thm)],[f331,f112])).
% 0.10/0.54 fof(f342,plain,(
% 0.10/0.54 disjoint(sK10_skl,sK11_skl)|~sQ1_spl),
% 0.10/0.54 inference(resolution,[status(thm)],[f332,f142])).
% 0.10/0.54 fof(f343,plain,(
% 0.10/0.54 sQ0_spl|~sQ1_spl),
% 0.10/0.54 inference(split_clause,[status(thm)],[f342,f213,f216])).
% 0.10/0.54 fof(f354,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,set_difference(X0,X1))=set_intersection2(X0,set_intersection2(X0,X1)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f185,f297])).
% 0.10/0.54 fof(f363,plain,(
% 0.10/0.54 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X0,set_intersection2(X0,X1)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f185,f354])).
% 0.10/0.54 fof(f368,plain,(
% 0.10/0.54 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X0,set_intersection2(X1,X0)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f64,f363])).
% 0.10/0.54 fof(f486,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,set_intersection2(X0,X1))=set_difference(X0,X1))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f297,f287])).
% 0.10/0.54 fof(f488,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,set_intersection2(X0,X1))=set_difference(X0,set_intersection2(X1,X0)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f368,f486])).
% 0.10/0.54 fof(f503,plain,(
% 0.10/0.54 ![X0,X1]: (set_difference(X0,X1)=set_difference(X0,set_intersection2(X1,X0)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f486,f488])).
% 0.10/0.54 fof(f588,plain,(
% 0.10/0.54 set_difference(sK10_skl,sK11_skl)=set_difference(sK10_skl,empty_set)|~sQ0_spl),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f236,f503])).
% 0.10/0.54 fof(f596,plain,(
% 0.10/0.54 set_difference(sK10_skl,sK11_skl)=sK10_skl|~sQ0_spl),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f173,f588])).
% 0.10/0.54 fof(f597,plain,(
% 0.10/0.54 $false|sQ1_spl|~sQ0_spl),
% 0.10/0.54 inference(forward_subsumption_resolution,[status(thm)],[f596,f218])).
% 0.10/0.54 fof(f598,plain,(
% 0.10/0.54 sQ1_spl|~sQ0_spl),
% 0.10/0.54 inference(contradiction_clause,[status(thm)],[f597])).
% 0.10/0.54 fof(f599,plain,(
% 0.10/0.54 $false),
% 0.10/0.54 inference(sat_refutation,[status(thm)],[f219,f220,f324,f343,f598])).
% 0.10/0.54 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.54 % Elapsed time: 0.161470 seconds
% 0.10/0.54 % CPU time: 0.971309 seconds
% 0.10/0.54 % Total memory used: 116.701 MB
% 0.10/0.54 % Net memory used: 114.972 MB
%------------------------------------------------------------------------------