%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET811+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:12:38 PM UTC 2026
% Result : Theorem 23.03s 3.80s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET811+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.74 % Computer : n017.cluster.edu
% 0.12/0.74 % Model : x86_64 x86_64
% 0.12/0.74 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.74 % Memory : 8046.5625MB
% 0.12/0.74 % OS : Linux 6.8.0-71-generic
% 0.12/0.74 % CPULimit : 300
% 0.12/0.74 % WCLimit : 300
% 0.12/0.74 % DateTime : Mon Sep 21 05:34:27 UTC 2026
% 0.12/0.75 % CPUTime :
% 0.12/0.76 % Drodi V4.1.1
% 23.03/3.80 % Refutation found
% 23.03/3.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.03/3.80 % SZS output start CNFRefutation for theBenchmark
% 23.03/3.80 fof(f1,axiom,(
% 23.03/3.80 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 23.03/3.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 23.03/3.80 fof(f2,axiom,(
% 23.03/3.80 (! [A,B] :( equal_set(A,B)<=> ( subset(A,B)& subset(B,A) ) ) )),
% 23.03/3.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 23.03/3.80 fof(f12,axiom,(
% 23.03/3.80 (! [A] :( member(A,on)<=> ( set(A)& strict_well_order(member_predicate,A)& (! [X] :( member(X,A)=> subset(X,A) ) )) ) )),
% 23.03/3.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 23.03/3.80 fof(f15,axiom,(
% 23.03/3.80 (! [X,Y] :( apply(member_predicate,X,Y)<=> member(X,Y) ) )),
% 23.03/3.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 23.03/3.80 fof(f18,axiom,(
% 23.03/3.80 (! [X,R,A,Y] :( member(Y,initial_segment(X,R,A))<=> ( member(Y,A)& apply(R,Y,X) ) ) )),
% 23.03/3.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 23.03/3.80 fof(f20,conjecture,(
% 23.03/3.80 (! [A] :( member(A,on)=> (! [X] :( member(X,A)=> equal_set(X,initial_segment(X,member_predicate,A)) ) )) )),
% 23.03/3.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 23.03/3.80 fof(f21,negated_conjecture,(
% 23.03/3.80 ~((! [A] :( member(A,on)=> (! [X] :( member(X,A)=> equal_set(X,initial_segment(X,member_predicate,A)) ) )) ))),
% 23.03/3.80 inference(negated_conjecture,[status(cth)],[f20])).
% 23.03/3.80 fof(f22,plain,(
% 23.03/3.80 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 23.03/3.80 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 23.03/3.80 fof(f23,plain,(
% 23.03/3.80 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 23.03/3.80 inference(NNF_transformation,[status(thm)],[f22])).
% 23.03/3.80 fof(f24,plain,(
% 23.03/3.80 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 23.03/3.80 inference(miniscoping,[status(thm)],[f23])).
% 23.03/3.80 fof(f25,plain,(
% 23.03/3.80 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(member(sK0_skl(B,A),A)&~member(sK0_skl(B,A),B))))),
% 23.03/3.80 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f24])).
% 23.03/3.80 fof(f26,plain,(
% 23.03/3.80 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f25])).
% 23.03/3.80 fof(f27,plain,(
% 23.03/3.80 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f25])).
% 23.03/3.80 fof(f28,plain,(
% 23.03/3.80 ![X0,X1]: (subset(X0,X1)|~member(sK0_skl(X1,X0),X1))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f25])).
% 23.03/3.80 fof(f29,plain,(
% 23.03/3.80 ![A,B]: ((~equal_set(A,B)|(subset(A,B)&subset(B,A)))&(equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 23.03/3.80 inference(NNF_transformation,[status(thm)],[f2])).
% 23.03/3.80 fof(f30,plain,(
% 23.03/3.80 (![A,B]: (~equal_set(A,B)|(subset(A,B)&subset(B,A))))&(![A,B]: (equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 23.03/3.80 inference(miniscoping,[status(thm)],[f29])).
% 23.03/3.80 fof(f33,plain,(
% 23.03/3.80 ![X0,X1]: (equal_set(X0,X1)|~subset(X0,X1)|~subset(X1,X0))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f30])).
% 23.03/3.80 fof(f76,plain,(
% 23.03/3.80 ![A]: (member(A,on)<=>((set(A)&strict_well_order(member_predicate,A))&(![X]: (~member(X,A)|subset(X,A)))))),
% 23.03/3.80 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 23.03/3.80 fof(f77,plain,(
% 23.03/3.80 ![A]: ((~member(A,on)|((set(A)&strict_well_order(member_predicate,A))&(![X]: (~member(X,A)|subset(X,A)))))&(member(A,on)|((~set(A)|~strict_well_order(member_predicate,A))|(?[X]: (member(X,A)&~subset(X,A))))))),
% 23.03/3.80 inference(NNF_transformation,[status(thm)],[f76])).
% 23.03/3.80 fof(f78,plain,(
% 23.03/3.80 (![A]: (~member(A,on)|((set(A)&strict_well_order(member_predicate,A))&(![X]: (~member(X,A)|subset(X,A))))))&(![A]: (member(A,on)|((~set(A)|~strict_well_order(member_predicate,A))|(?[X]: (member(X,A)&~subset(X,A))))))),
% 23.03/3.80 inference(miniscoping,[status(thm)],[f77])).
% 23.03/3.80 fof(f79,plain,(
% 23.03/3.80 (![A]: (~member(A,on)|((set(A)&strict_well_order(member_predicate,A))&(![X]: (~member(X,A)|subset(X,A))))))&(![A]: (member(A,on)|((~set(A)|~strict_well_order(member_predicate,A))|(member(sK3_skl(A),A)&~subset(sK3_skl(A),A)))))),
% 23.03/3.80 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(X,sK3_skl(A))],[f78])).
% 23.03/3.80 fof(f82,plain,(
% 23.03/3.80 ![X0,X1]: (~member(X0,on)|~member(X1,X0)|subset(X1,X0))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f79])).
% 23.03/3.80 fof(f103,plain,(
% 23.03/3.80 ![X,Y]: ((~apply(member_predicate,X,Y)|member(X,Y))&(apply(member_predicate,X,Y)|~member(X,Y)))),
% 23.03/3.80 inference(NNF_transformation,[status(thm)],[f15])).
% 23.03/3.80 fof(f104,plain,(
% 23.03/3.80 (![X,Y]: (~apply(member_predicate,X,Y)|member(X,Y)))&(![X,Y]: (apply(member_predicate,X,Y)|~member(X,Y)))),
% 23.03/3.80 inference(miniscoping,[status(thm)],[f103])).
% 23.03/3.80 fof(f105,plain,(
% 23.03/3.80 ![X0,X1]: (~apply(member_predicate,X0,X1)|member(X0,X1))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f104])).
% 23.03/3.80 fof(f106,plain,(
% 23.03/3.80 ![X0,X1]: (apply(member_predicate,X0,X1)|~member(X0,X1))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f104])).
% 23.03/3.80 fof(f123,plain,(
% 23.03/3.80 ![X,R,A,Y]: ((~member(Y,initial_segment(X,R,A))|(member(Y,A)&apply(R,Y,X)))&(member(Y,initial_segment(X,R,A))|(~member(Y,A)|~apply(R,Y,X))))),
% 23.03/3.80 inference(NNF_transformation,[status(thm)],[f18])).
% 23.03/3.80 fof(f124,plain,(
% 23.03/3.80 (![X,R,A,Y]: (~member(Y,initial_segment(X,R,A))|(member(Y,A)&apply(R,Y,X))))&(![X,R,A,Y]: (member(Y,initial_segment(X,R,A))|(~member(Y,A)|~apply(R,Y,X))))),
% 23.03/3.80 inference(miniscoping,[status(thm)],[f123])).
% 23.03/3.80 fof(f126,plain,(
% 23.03/3.80 ![X0,X1,X2,X3]: (~member(X0,initial_segment(X1,X2,X3))|apply(X2,X0,X1))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f124])).
% 23.03/3.80 fof(f127,plain,(
% 23.03/3.80 ![X0,X1,X2,X3]: (member(X0,initial_segment(X1,X2,X3))|~member(X0,X3)|~apply(X2,X0,X1))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f124])).
% 23.03/3.80 fof(f132,plain,(
% 23.03/3.80 (?[A]: (member(A,on)&(?[X]: (member(X,A)&~equal_set(X,initial_segment(X,member_predicate,A))))))),
% 23.03/3.80 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 23.03/3.80 fof(f133,plain,(
% 23.03/3.80 (member(sK13_skl,on)&(member(sK14_skl,sK13_skl)&~equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))))),
% 23.03/3.80 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(X,sK14_skl)],[f132])).
% 23.03/3.80 fof(f134,plain,(
% 23.03/3.80 member(sK13_skl,on)),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f133])).
% 23.03/3.80 fof(f135,plain,(
% 23.03/3.80 member(sK14_skl,sK13_skl)),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f133])).
% 23.03/3.80 fof(f136,plain,(
% 23.03/3.80 ~equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))),
% 23.03/3.80 inference(cnf_transformation,[status(thm)],[f133])).
% 23.03/3.80 fof(f151,plain,(
% 23.03/3.80 ![X0]: (~member(X0,sK13_skl)|subset(X0,sK13_skl))),
% 23.03/3.80 inference(resolution,[status(thm)],[f82,f134])).
% 23.03/3.80 fof(f163,plain,(
% 23.03/3.80 ![X0,X1,X2]: (subset(X0,X1)|~subset(X0,X2)|member(sK0_skl(X1,X0),X2))),
% 23.03/3.80 inference(resolution,[status(thm)],[f27,f26])).
% 23.03/3.80 fof(f424,plain,(
% 23.03/3.80 subset(sK14_skl,sK13_skl)),
% 23.03/3.80 inference(resolution,[status(thm)],[f151,f135])).
% 23.03/3.80 fof(f425,plain,(
% 23.03/3.80 ![X0]: (subset(sK14_skl,X0)|member(sK0_skl(X0,sK14_skl),sK13_skl))),
% 23.03/3.80 inference(resolution,[status(thm)],[f424,f163])).
% 23.03/3.80 fof(f463,plain,(
% 23.03/3.80 ![X0,X1,X2,X3]: (apply(X0,sK0_skl(X1,initial_segment(X2,X0,X3)),X2)|subset(initial_segment(X2,X0,X3),X1))),
% 23.03/3.80 inference(resolution,[status(thm)],[f126,f27])).
% 23.03/3.80 fof(f581,plain,(
% 23.03/3.80 ![X0,X1,X2]: (subset(initial_segment(X0,member_predicate,X1),X2)|member(sK0_skl(X2,initial_segment(X0,member_predicate,X1)),X0))),
% 23.03/3.80 inference(resolution,[status(thm)],[f463,f105])).
% 23.03/3.80 fof(f608,plain,(
% 23.03/3.80 ![X0,X1]: (subset(initial_segment(X0,member_predicate,X1),X0)|subset(initial_segment(X0,member_predicate,X1),X0))),
% 23.03/3.80 inference(resolution,[status(thm)],[f581,f28])).
% 23.03/3.80 fof(f625,plain,(
% 23.03/3.80 ![X0,X1]: (subset(initial_segment(X0,member_predicate,X1),X0))),
% 23.03/3.80 inference(duplicate_literals_removal,[status(thm)],[f608])).
% 23.03/3.80 fof(f923,plain,(
% 23.03/3.80 ![X0,X1]: (equal_set(X0,initial_segment(X0,member_predicate,X1))|~subset(X0,initial_segment(X0,member_predicate,X1)))),
% 23.03/3.80 inference(resolution,[status(thm)],[f625,f33])).
% 23.03/3.80 fof(f924,plain,(
% 23.03/3.80 ![X0,X1,X2,X3]: (~member(sK0_skl(initial_segment(X0,X1,X2),X3),X2)|~apply(X1,sK0_skl(initial_segment(X0,X1,X2),X3),X0)|subset(X3,initial_segment(X0,X1,X2)))),
% 23.03/3.80 inference(resolution,[status(thm)],[f127,f28])).
% 23.03/3.80 fof(f941,plain,(
% 23.03/3.80 ![X0,X1,X2]: (~member(sK0_skl(initial_segment(X0,member_predicate,X1),X2),X1)|subset(X2,initial_segment(X0,member_predicate,X1))|~member(sK0_skl(initial_segment(X0,member_predicate,X1),X2),X0))),
% 23.03/3.80 inference(resolution,[status(thm)],[f924,f106])).
% 23.81/3.85 fof(f1515,plain,(
% 23.81/3.85 ![X0]: (subset(sK14_skl,initial_segment(X0,member_predicate,sK13_skl))|~member(sK0_skl(initial_segment(X0,member_predicate,sK13_skl),sK14_skl),X0)|subset(sK14_skl,initial_segment(X0,member_predicate,sK13_skl)))),
% 23.81/3.85 inference(resolution,[status(thm)],[f941,f425])).
% 23.81/3.85 fof(f1555,plain,(
% 23.81/3.85 ![X0]: (subset(sK14_skl,initial_segment(X0,member_predicate,sK13_skl))|~member(sK0_skl(initial_segment(X0,member_predicate,sK13_skl),sK14_skl),X0))),
% 23.81/3.85 inference(duplicate_literals_removal,[status(thm)],[f1515])).
% 23.81/3.85 fof(f2731,plain,(
% 23.81/3.85 subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))|subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))),
% 23.81/3.85 inference(resolution,[status(thm)],[f1555,f27])).
% 23.81/3.85 fof(f2752,plain,(
% 23.81/3.85 subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))),
% 23.81/3.85 inference(duplicate_literals_removal,[status(thm)],[f2731])).
% 23.81/3.85 fof(f2758,plain,(
% 23.81/3.85 equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))),
% 23.81/3.85 inference(resolution,[status(thm)],[f2752,f923])).
% 23.81/3.85 fof(f2762,plain,(
% 23.81/3.85 $false),
% 23.81/3.85 inference(forward_subsumption_resolution,[status(thm)],[f2758,f136])).
% 23.81/3.85 % SZS output end CNFRefutation for theBenchmark.p
% 23.81/3.89 % Elapsed time: 3.128013 seconds
% 23.81/3.89 % CPU time: 24.244912 seconds
% 23.81/3.89 % Total memory used: 247.380 MB
% 23.81/3.89 % Net memory used: 229.912 MB
%------------------------------------------------------------------------------