%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET766+4 : 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 02:12:34 PM UTC 2026
% Result : Theorem 0.17s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n016.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:41:37 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.62 % Refutation found
% 0.17/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.62 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.62 fof(f14,axiom,(
% 0.17/0.62 (! [A,R] :( equivalence(R,A)<=> ( (! [X] :( member(X,A)=> apply(R,X,X) ))& (! [X,Y] :( ( member(X,A)& member(Y,A) )=> ( apply(R,X,Y)=> apply(R,Y,X) ) ))& (! [X,Y,Z] :( ( member(X,A)& member(Y,A)& member(Z,A) )=> ( ( apply(R,X,Y)& apply(R,Y,Z) )=> apply(R,X,Z) ) ) )) ) )),
% 0.17/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f15,axiom,(
% 0.17/0.62 (! [R,E,A,X] :( member(X,equivalence_class(A,E,R))<=> ( member(X,E)& apply(R,A,X) ) ) )),
% 0.17/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f17,conjecture,(
% 0.17/0.62 (! [E,R,A] :( ( equivalence(R,E)& member(A,E) )=> member(A,equivalence_class(A,E,R)) ) )),
% 0.17/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.17/0.62 fof(f18,negated_conjecture,(
% 0.17/0.62 ~((! [E,R,A] :( ( equivalence(R,E)& member(A,E) )=> member(A,equivalence_class(A,E,R)) ) ))),
% 0.17/0.62 inference(negated_conjecture,[status(cth)],[f17])).
% 0.17/0.62 fof(f93,plain,(
% 0.17/0.62 ![A,R]: (equivalence(R,A)<=>(((![X]: (~member(X,A)|apply(R,X,X)))&(![X,Y]: ((~member(X,A)|~member(Y,A))|(~apply(R,X,Y)|apply(R,Y,X)))))&(![X,Y,Z]: (((~member(X,A)|~member(Y,A))|~member(Z,A))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 0.17/0.62 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.17/0.62 fof(f94,definition,(
% 0.17/0.62 ![A,R]: (sP1_prd(R,A)<=>((![X]: (~member(X,A)|apply(R,X,X)))&(![X,Y]: ((~member(X,A)|~member(Y,A))|(~apply(R,X,Y)|apply(R,Y,X))))))),
% 0.17/0.62 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.17/0.62 fof(f95,plain,(
% 0.17/0.62 ![A,R]: (equivalence(R,A)<=>(sP1_prd(R,A)&(![X,Y,Z]: (((~member(X,A)|~member(Y,A))|~member(Z,A))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 0.17/0.62 inference(formula_renaming,[status(thm)],[f93,f94])).
% 0.17/0.62 fof(f96,plain,(
% 0.17/0.62 ![A,R]: ((~equivalence(R,A)|(sP1_prd(R,A)&(![X,Y,Z]: (((~member(X,A)|~member(Y,A))|~member(Z,A))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))&(equivalence(R,A)|(~sP1_prd(R,A)|(?[X,Y,Z]: (((member(X,A)&member(Y,A))&member(Z,A))&((apply(R,X,Y)&apply(R,Y,Z))&~apply(R,X,Z)))))))),
% 0.17/0.62 inference(NNF_transformation,[status(thm)],[f95])).
% 0.17/0.62 fof(f97,plain,(
% 0.17/0.62 (![A,R]: (~equivalence(R,A)|(sP1_prd(R,A)&(![X,Y,Z]: (((~member(X,A)|~member(Y,A))|~member(Z,A))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z)))))))&(![A,R]: (equivalence(R,A)|(~sP1_prd(R,A)|(?[X,Y,Z]: (((member(X,A)&member(Y,A))&member(Z,A))&((apply(R,X,Y)&apply(R,Y,Z))&~apply(R,X,Z)))))))),
% 0.17/0.62 inference(miniscoping,[status(thm)],[f96])).
% 0.17/0.62 fof(f98,plain,(
% 0.17/0.62 (![A,R]: (~equivalence(R,A)|(sP1_prd(R,A)&(![X,Y,Z]: (((~member(X,A)|~member(Y,A))|~member(Z,A))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z)))))))&(![A,R]: (equivalence(R,A)|(~sP1_prd(R,A)|(((member(sK7_skl(R,A),A)&member(sK8_skl(R,A),A))&member(sK9_skl(R,A),A))&((apply(R,sK7_skl(R,A),sK8_skl(R,A))&apply(R,sK8_skl(R,A),sK9_skl(R,A)))&~apply(R,sK7_skl(R,A),sK9_skl(R,A)))))))),
% 0.17/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(X,sK7_skl(R,A)),skolemize(Y,sK8_skl(R,A)),skolemize(Z,sK9_skl(R,A))],[f97])).
% 0.17/0.62 fof(f99,plain,(
% 0.17/0.62 ![X0,X1]: (~equivalence(X0,X1)|sP1_prd(X0,X1))),
% 0.17/0.62 inference(cnf_transformation,[status(thm)],[f98])).
% 0.17/0.62 fof(f107,plain,(
% 0.17/0.62 ![R,E,A,X]: ((~member(X,equivalence_class(A,E,R))|(member(X,E)&apply(R,A,X)))&(member(X,equivalence_class(A,E,R))|(~member(X,E)|~apply(R,A,X))))),
% 0.17/0.62 inference(NNF_transformation,[status(thm)],[f15])).
% 0.17/0.62 fof(f108,plain,(
% 0.17/0.62 (![R,E,A,X]: (~member(X,equivalence_class(A,E,R))|(member(X,E)&apply(R,A,X))))&(![R,E,A,X]: (member(X,equivalence_class(A,E,R))|(~member(X,E)|~apply(R,A,X))))),
% 0.17/0.62 inference(miniscoping,[status(thm)],[f107])).
% 0.17/0.62 fof(f111,plain,(
% 0.17/0.62 ![X0,X1,X2,X3]: (member(X0,equivalence_class(X1,X2,X3))|~member(X0,X2)|~apply(X3,X1,X0))),
% 0.17/0.62 inference(cnf_transformation,[status(thm)],[f108])).
% 0.17/0.62 fof(f126,plain,(
% 0.17/0.62 (?[E,R,A]: ((equivalence(R,E)&member(A,E))&~member(A,equivalence_class(A,E,R))))),
% 0.17/0.62 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.17/0.62 fof(f127,plain,(
% 0.17/0.62 ((equivalence(sK15_skl,sK14_skl)&member(sK16_skl,sK14_skl))&~member(sK16_skl,equivalence_class(sK16_skl,sK14_skl,sK15_skl)))),
% 0.17/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(E,sK14_skl),skolemize(R,sK15_skl),skolemize(A,sK16_skl)],[f126])).
% 0.17/0.64 fof(f128,plain,(
% 0.17/0.64 equivalence(sK15_skl,sK14_skl)),
% 0.17/0.64 inference(cnf_transformation,[status(thm)],[f127])).
% 0.17/0.64 fof(f129,plain,(
% 0.17/0.64 member(sK16_skl,sK14_skl)),
% 0.17/0.64 inference(cnf_transformation,[status(thm)],[f127])).
% 0.17/0.64 fof(f130,plain,(
% 0.17/0.64 ~member(sK16_skl,equivalence_class(sK16_skl,sK14_skl,sK15_skl))),
% 0.17/0.64 inference(cnf_transformation,[status(thm)],[f127])).
% 0.17/0.64 fof(f141,definition,(
% 0.17/0.64 ![A,R,X]: (sP3_prd(X,R,A)<=>(~member(X,A)|apply(R,X,X)))),
% 0.17/0.64 introduced(definition,[new_symbols(definition,[sP3_prd])],[])).
% 0.17/0.64 fof(f142,plain,(
% 0.17/0.64 ![A,R]: (sP1_prd(R,A)<=>((![X]: sP3_prd(X,R,A))&(![X,Y]: ((~member(X,A)|~member(Y,A))|(~apply(R,X,Y)|apply(R,Y,X))))))),
% 0.17/0.64 inference(formula_renaming,[status(thm)],[f94,f141])).
% 0.17/0.64 fof(f143,plain,(
% 0.17/0.64 ![A,R]: ((~sP1_prd(R,A)|((![X]: sP3_prd(X,R,A))&(![X,Y]: ((~member(X,A)|~member(Y,A))|(~apply(R,X,Y)|apply(R,Y,X))))))&(sP1_prd(R,A)|((?[X]: ~sP3_prd(X,R,A))|(?[X,Y]: ((member(X,A)&member(Y,A))&(apply(R,X,Y)&~apply(R,Y,X)))))))),
% 0.17/0.64 inference(NNF_transformation,[status(thm)],[f142])).
% 0.17/0.64 fof(f144,plain,(
% 0.17/0.64 (![A,R]: (~sP1_prd(R,A)|((![X]: sP3_prd(X,R,A))&(![X,Y]: ((~member(X,A)|~member(Y,A))|(~apply(R,X,Y)|apply(R,Y,X)))))))&(![A,R]: (sP1_prd(R,A)|((?[X]: ~sP3_prd(X,R,A))|(?[X,Y]: ((member(X,A)&member(Y,A))&(apply(R,X,Y)&~apply(R,Y,X)))))))),
% 0.17/0.64 inference(miniscoping,[status(thm)],[f143])).
% 0.17/0.64 fof(f145,plain,(
% 0.17/0.64 (![A,R]: (~sP1_prd(R,A)|((![X]: sP3_prd(X,R,A))&(![X,Y]: ((~member(X,A)|~member(Y,A))|(~apply(R,X,Y)|apply(R,Y,X)))))))&(![A,R]: (sP1_prd(R,A)|(~sP3_prd(sK20_skl(R,A),R,A)|((member(sK21_skl(R,A),A)&member(sK22_skl(R,A),A))&(apply(R,sK21_skl(R,A),sK22_skl(R,A))&~apply(R,sK22_skl(R,A),sK21_skl(R,A)))))))),
% 0.17/0.64 inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl]),skolemize(X,sK20_skl(R,A)),skolemize(X,sK21_skl(R,A)),skolemize(Y,sK22_skl(R,A))],[f144])).
% 0.17/0.64 fof(f146,plain,(
% 0.17/0.64 ![X0,X1,X2]: (~sP1_prd(X0,X1)|sP3_prd(X2,X0,X1))),
% 0.17/0.64 inference(cnf_transformation,[status(thm)],[f145])).
% 0.17/0.64 fof(f157,plain,(
% 0.17/0.64 ![A,R,X]: ((~sP3_prd(X,R,A)|(~member(X,A)|apply(R,X,X)))&(sP3_prd(X,R,A)|(member(X,A)&~apply(R,X,X))))),
% 0.17/0.64 inference(NNF_transformation,[status(thm)],[f141])).
% 0.17/0.64 fof(f158,plain,(
% 0.17/0.64 (![A,R,X]: (~sP3_prd(X,R,A)|(~member(X,A)|apply(R,X,X))))&(![A,R,X]: (sP3_prd(X,R,A)|(member(X,A)&~apply(R,X,X))))),
% 0.17/0.64 inference(miniscoping,[status(thm)],[f157])).
% 0.17/0.64 fof(f159,plain,(
% 0.17/0.64 ![X0,X1,X2]: (~sP3_prd(X0,X1,X2)|~member(X0,X2)|apply(X1,X0,X0))),
% 0.17/0.64 inference(cnf_transformation,[status(thm)],[f158])).
% 0.17/0.64 fof(f165,plain,(
% 0.17/0.64 sP1_prd(sK15_skl,sK14_skl)),
% 0.17/0.64 inference(resolution,[status(thm)],[f99,f128])).
% 0.17/0.64 fof(f169,plain,(
% 0.17/0.64 ![X0]: (sP3_prd(X0,sK15_skl,sK14_skl))),
% 0.17/0.64 inference(resolution,[status(thm)],[f146,f165])).
% 0.17/0.64 fof(f171,plain,(
% 0.17/0.64 ![X0]: (~member(X0,sK14_skl)|apply(sK15_skl,X0,X0))),
% 0.17/0.64 inference(resolution,[status(thm)],[f169,f159])).
% 0.17/0.64 fof(f177,plain,(
% 0.17/0.64 apply(sK15_skl,sK16_skl,sK16_skl)),
% 0.17/0.64 inference(resolution,[status(thm)],[f171,f129])).
% 0.17/0.64 fof(f179,plain,(
% 0.17/0.64 ![X0]: (member(sK16_skl,equivalence_class(sK16_skl,X0,sK15_skl))|~member(sK16_skl,X0))),
% 0.17/0.64 inference(resolution,[status(thm)],[f177,f111])).
% 0.17/0.64 fof(f182,plain,(
% 0.17/0.64 member(sK16_skl,equivalence_class(sK16_skl,sK14_skl,sK15_skl))),
% 0.17/0.64 inference(resolution,[status(thm)],[f179,f129])).
% 0.17/0.64 fof(f186,plain,(
% 0.17/0.64 $false),
% 0.17/0.64 inference(forward_subsumption_resolution,[status(thm)],[f182,f130])).
% 0.17/0.64 % SZS output end CNFRefutation for theBenchmark.p
% 0.27/0.66 % Elapsed time: 0.201819 seconds
% 0.27/0.66 % CPU time: 0.949634 seconds
% 0.27/0.66 % Total memory used: 92.889 MB
% 0.27/0.66 % Net memory used: 91.976 MB
%------------------------------------------------------------------------------