%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET809+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 : n002.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 18.26s 2.92s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET809+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
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 05:41:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 18.26/2.92 % Refutation found
% 18.26/2.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.26/2.92 % SZS output start CNFRefutation for theBenchmark
% 18.26/2.92 fof(f12,axiom,(
% 18.26/2.92 (! [A] :( member(A,on)<=> ( set(A)& strict_well_order(member_predicate,A)& (! [X] :( member(X,A)=> subset(X,A) ) )) ) )),
% 18.26/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.26/2.92 fof(f13,axiom,(
% 18.26/2.92 (! [R,E] :( strict_well_order(R,E)<=> ( strict_order(R,E)& (! [A] :( ( subset(A,E)& (? [X] : member(X,A) ))=> (? [Y] : least(Y,R,A) )) )) ) )),
% 18.26/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.26/2.92 fof(f15,axiom,(
% 18.26/2.92 (! [X,Y] :( apply(member_predicate,X,Y)<=> member(X,Y) ) )),
% 18.26/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.26/2.92 fof(f16,axiom,(
% 18.26/2.92 (! [R,E] :( strict_order(R,E)<=> ( (! [X,Y] :( ( member(X,E)& member(Y,E) )=> ~ ( apply(R,X,Y)& apply(R,Y,X) ) ))& (! [X,Y,Z] :( ( member(X,E)& member(Y,E)& member(Z,E) )=> ( ( apply(R,X,Y)& apply(R,Y,Z) )=> apply(R,X,Z) ) ) )) ) )),
% 18.26/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.26/2.92 fof(f20,conjecture,(
% 18.26/2.92 (! [A] :( member(A,on)=> ~ member(A,A) ) )),
% 18.26/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.26/2.92 fof(f21,negated_conjecture,(
% 18.26/2.92 ~((! [A] :( member(A,on)=> ~ member(A,A) ) ))),
% 18.26/2.92 inference(negated_conjecture,[status(cth)],[f20])).
% 18.26/2.92 fof(f76,plain,(
% 18.26/2.92 ![A]: (member(A,on)<=>((set(A)&strict_well_order(member_predicate,A))&(![X]: (~member(X,A)|subset(X,A)))))),
% 18.26/2.92 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 18.26/2.92 fof(f77,plain,(
% 18.26/2.92 ![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))))))),
% 18.26/2.92 inference(NNF_transformation,[status(thm)],[f76])).
% 18.26/2.92 fof(f78,plain,(
% 18.26/2.92 (![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))))))),
% 18.26/2.92 inference(miniscoping,[status(thm)],[f77])).
% 18.26/2.92 fof(f79,plain,(
% 18.26/2.92 (![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)))))),
% 18.26/2.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(X,sK3_skl(A))],[f78])).
% 18.26/2.92 fof(f81,plain,(
% 18.26/2.92 ![X0]: (~member(X0,on)|strict_well_order(member_predicate,X0))),
% 18.26/2.92 inference(cnf_transformation,[status(thm)],[f79])).
% 18.26/2.92 fof(f85,plain,(
% 18.26/2.92 ![R,E]: (strict_well_order(R,E)<=>(strict_order(R,E)&(![A]: ((~subset(A,E)|(![X]: ~member(X,A)))|(?[Y]: least(Y,R,A))))))),
% 18.26/2.92 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 18.26/2.92 fof(f86,plain,(
% 18.26/2.92 ![R,E]: ((~strict_well_order(R,E)|(strict_order(R,E)&(![A]: ((~subset(A,E)|(![X]: ~member(X,A)))|(?[Y]: least(Y,R,A))))))&(strict_well_order(R,E)|(~strict_order(R,E)|(?[A]: ((subset(A,E)&(?[X]: member(X,A)))&(![Y]: ~least(Y,R,A)))))))),
% 18.26/2.92 inference(NNF_transformation,[status(thm)],[f85])).
% 18.26/2.92 fof(f87,plain,(
% 18.26/2.92 (![R,E]: (~strict_well_order(R,E)|(strict_order(R,E)&(![A]: ((~subset(A,E)|(![X]: ~member(X,A)))|(?[Y]: least(Y,R,A)))))))&(![R,E]: (strict_well_order(R,E)|(~strict_order(R,E)|(?[A]: ((subset(A,E)&(?[X]: member(X,A)))&(![Y]: ~least(Y,R,A)))))))),
% 18.26/2.92 inference(miniscoping,[status(thm)],[f86])).
% 18.26/2.92 fof(f88,plain,(
% 18.26/2.92 (![R,E]: (~strict_well_order(R,E)|(strict_order(R,E)&(![A]: ((~subset(A,E)|(![X]: ~member(X,A)))|least(sK4_skl(A,E,R),R,A))))))&(![R,E]: (strict_well_order(R,E)|(~strict_order(R,E)|((subset(sK5_skl(E,R),E)&member(sK6_skl(E,R),sK5_skl(E,R)))&(![Y]: ~least(Y,R,sK5_skl(E,R)))))))),
% 18.26/2.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(Y,sK4_skl(A,E,R)),skolemize(A,sK5_skl(E,R)),skolemize(X,sK6_skl(E,R))],[f87])).
% 18.26/2.92 fof(f89,plain,(
% 18.26/2.92 ![X0,X1]: (~strict_well_order(X0,X1)|strict_order(X0,X1))),
% 18.26/2.92 inference(cnf_transformation,[status(thm)],[f88])).
% 18.26/2.92 fof(f103,plain,(
% 18.26/2.92 ![X,Y]: ((~apply(member_predicate,X,Y)|member(X,Y))&(apply(member_predicate,X,Y)|~member(X,Y)))),
% 18.26/2.92 inference(NNF_transformation,[status(thm)],[f15])).
% 18.26/2.92 fof(f104,plain,(
% 18.26/2.92 (![X,Y]: (~apply(member_predicate,X,Y)|member(X,Y)))&(![X,Y]: (apply(member_predicate,X,Y)|~member(X,Y)))),
% 18.26/2.92 inference(miniscoping,[status(thm)],[f103])).
% 18.26/2.92 fof(f106,plain,(
% 18.26/2.92 ![X0,X1]: (apply(member_predicate,X0,X1)|~member(X0,X1))),
% 18.26/2.92 inference(cnf_transformation,[status(thm)],[f104])).
% 18.26/2.92 fof(f107,plain,(
% 18.26/2.92 ![R,E]: (strict_order(R,E)<=>((![X,Y]: ((~member(X,E)|~member(Y,E))|(~apply(R,X,Y)|~apply(R,Y,X))))&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 18.26/2.92 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 18.26/2.92 fof(f108,definition,(
% 18.26/2.92 ![R,E,X,Y]: (sP0_prd(Y,X,E,R)<=>((~member(X,E)|~member(Y,E))|(~apply(R,X,Y)|~apply(R,Y,X))))),
% 18.26/2.92 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 18.26/2.92 fof(f109,plain,(
% 18.26/2.92 ![R,E]: (strict_order(R,E)<=>((![X,Y]: sP0_prd(Y,X,E,R))&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 18.26/2.92 inference(formula_renaming,[status(thm)],[f107,f108])).
% 18.26/2.92 fof(f110,plain,(
% 18.26/2.92 ![R,E]: ((~strict_order(R,E)|((![X,Y]: sP0_prd(Y,X,E,R))&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))&(strict_order(R,E)|((?[X,Y]: ~sP0_prd(Y,X,E,R))|(?[X,Y,Z]: (((member(X,E)&member(Y,E))&member(Z,E))&((apply(R,X,Y)&apply(R,Y,Z))&~apply(R,X,Z)))))))),
% 18.26/2.92 inference(NNF_transformation,[status(thm)],[f109])).
% 18.26/2.92 fof(f111,plain,(
% 18.26/2.92 (![R,E]: (~strict_order(R,E)|((![X,Y]: sP0_prd(Y,X,E,R))&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z)))))))&(![R,E]: (strict_order(R,E)|((?[X,Y]: ~sP0_prd(Y,X,E,R))|(?[X,Y,Z]: (((member(X,E)&member(Y,E))&member(Z,E))&((apply(R,X,Y)&apply(R,Y,Z))&~apply(R,X,Z)))))))),
% 18.26/2.92 inference(miniscoping,[status(thm)],[f110])).
% 18.26/2.92 fof(f112,plain,(
% 18.26/2.92 (![R,E]: (~strict_order(R,E)|((![X,Y]: sP0_prd(Y,X,E,R))&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z)))))))&(![R,E]: (strict_order(R,E)|(~sP0_prd(sK9_skl(E,R),sK8_skl(E,R),E,R)|(((member(sK10_skl(E,R),E)&member(sK11_skl(E,R),E))&member(sK12_skl(E,R),E))&((apply(R,sK10_skl(E,R),sK11_skl(E,R))&apply(R,sK11_skl(E,R),sK12_skl(E,R)))&~apply(R,sK10_skl(E,R),sK12_skl(E,R)))))))),
% 18.26/2.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl]),skolemize(X,sK8_skl(E,R)),skolemize(Y,sK9_skl(E,R)),skolemize(X,sK10_skl(E,R)),skolemize(Y,sK11_skl(E,R)),skolemize(Z,sK12_skl(E,R))],[f111])).
% 18.26/2.92 fof(f113,plain,(
% 18.26/2.92 ![X0,X1,X2,X3]: (~strict_order(X0,X1)|sP0_prd(X2,X3,X1,X0))),
% 18.26/2.92 inference(cnf_transformation,[status(thm)],[f112])).
% 18.26/2.92 fof(f132,plain,(
% 18.26/2.92 (?[A]: (member(A,on)&member(A,A)))),
% 18.26/2.92 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 18.26/2.92 fof(f133,plain,(
% 18.26/2.92 (member(sK13_skl,on)&member(sK13_skl,sK13_skl))),
% 18.26/2.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f132])).
% 18.26/2.92 fof(f134,plain,(
% 18.26/2.92 member(sK13_skl,on)),
% 18.26/2.92 inference(cnf_transformation,[status(thm)],[f133])).
% 18.26/2.92 fof(f135,plain,(
% 18.26/2.92 member(sK13_skl,sK13_skl)),
% 18.26/2.92 inference(cnf_transformation,[status(thm)],[f133])).
% 18.26/2.92 fof(f136,plain,(
% 18.26/2.92 ![R,E,X,Y]: ((~sP0_prd(Y,X,E,R)|((~member(X,E)|~member(Y,E))|(~apply(R,X,Y)|~apply(R,Y,X))))&(sP0_prd(Y,X,E,R)|((member(X,E)&member(Y,E))&(apply(R,X,Y)&apply(R,Y,X)))))),
% 18.26/2.92 inference(NNF_transformation,[status(thm)],[f108])).
% 18.26/2.92 fof(f137,plain,(
% 18.26/2.92 (![R,E,X,Y]: (~sP0_prd(Y,X,E,R)|((~member(X,E)|~member(Y,E))|(~apply(R,X,Y)|~apply(R,Y,X)))))&(![R,E,X,Y]: (sP0_prd(Y,X,E,R)|((member(X,E)&member(Y,E))&(apply(R,X,Y)&apply(R,Y,X)))))),
% 18.26/2.92 inference(miniscoping,[status(thm)],[f136])).
% 18.26/2.92 fof(f138,plain,(
% 18.26/2.92 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|~member(X1,X2)|~member(X0,X2)|~apply(X3,X1,X0)|~apply(X3,X0,X1))),
% 18.26/2.92 inference(cnf_transformation,[status(thm)],[f137])).
% 18.26/2.92 fof(f422,plain,(
% 18.26/2.92 strict_well_order(member_predicate,sK13_skl)),
% 18.26/2.92 inference(resolution,[status(thm)],[f81,f134])).
% 18.26/2.92 fof(f423,plain,(
% 18.26/2.92 strict_order(member_predicate,sK13_skl)),
% 18.26/2.92 inference(resolution,[status(thm)],[f422,f89])).
% 18.26/2.92 fof(f808,plain,(
% 18.26/2.92 apply(member_predicate,sK13_skl,sK13_skl)),
% 18.26/2.92 inference(resolution,[status(thm)],[f106,f135])).
% 18.26/2.93 fof(f859,plain,(
% 18.26/2.93 ![X0,X1]: (sP0_prd(X0,X1,sK13_skl,member_predicate))),
% 18.26/2.93 inference(resolution,[status(thm)],[f113,f423])).
% 18.26/2.93 fof(f1316,plain,(
% 18.26/2.93 ![X0,X1]: (~sP0_prd(X0,sK13_skl,sK13_skl,X1)|~member(X0,sK13_skl)|~apply(X1,sK13_skl,X0)|~apply(X1,X0,sK13_skl))),
% 18.26/2.93 inference(resolution,[status(thm)],[f138,f135])).
% 18.26/2.93 fof(f1369,plain,(
% 18.26/2.93 ![X0]: (~sP0_prd(sK13_skl,sK13_skl,sK13_skl,X0)|~apply(X0,sK13_skl,sK13_skl)|~apply(X0,sK13_skl,sK13_skl))),
% 18.26/2.93 inference(resolution,[status(thm)],[f1316,f135])).
% 18.26/2.93 fof(f1370,plain,(
% 18.26/2.93 ![X0]: (~sP0_prd(sK13_skl,sK13_skl,sK13_skl,X0)|~apply(X0,sK13_skl,sK13_skl))),
% 18.26/2.93 inference(duplicate_literals_removal,[status(thm)],[f1369])).
% 18.26/2.93 fof(f7871,plain,(
% 18.26/2.93 ~apply(member_predicate,sK13_skl,sK13_skl)),
% 18.26/2.93 inference(resolution,[status(thm)],[f1370,f859])).
% 18.26/2.93 fof(f7876,plain,(
% 18.26/2.93 $false),
% 18.26/2.93 inference(forward_subsumption_resolution,[status(thm)],[f7871,f808])).
% 18.26/2.93 % SZS output end CNFRefutation for theBenchmark.p
% 18.26/2.95 % Elapsed time: 2.568632 seconds
% 18.26/2.95 % CPU time: 20.087403 seconds
% 18.26/2.95 % Total memory used: 223.642 MB
% 18.26/2.95 % Net memory used: 206.499 MB
%------------------------------------------------------------------------------