%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU290+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:22:14 PM UTC 2026
% Result : Theorem 0.12s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU290+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n020.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Mon Sep 21 06:09:04 UTC 2026
% 0.12/0.56 % CPUTime :
% 0.12/0.57 % Drodi V4.1.1
% 0.12/0.58 % Refutation found
% 0.12/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.58 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.58 fof(f4,axiom,(
% 0.12/0.58 (! [A,B,C] :( element(C,powerset(cartesian_product2(A,B)))=> relation(C) ) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f6,axiom,(
% 0.12/0.58 (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> ( ( ( B = empty_set=> A = empty_set )=> ( quasi_total(C,A,B)<=> A = relation_dom_as_subset(A,B,C) ) )& ( B = empty_set=> ( A = empty_set| ( quasi_total(C,A,B)<=> C = empty_set ) ) ) ) ) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f7,axiom,(
% 0.12/0.58 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(D,relation_dom(A))& C = apply(A,D) ) )) )) )) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f17,axiom,(
% 0.12/0.58 (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> element(C,powerset(cartesian_product2(A,B))) ) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f32,axiom,(
% 0.12/0.58 (? [A] :( relation(A)& function(A)& one_to_one(A)& empty(A) ) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f44,axiom,(
% 0.12/0.58 (! [A,B,C] :( relation_of2(C,A,B)=> relation_dom_as_subset(A,B,C) = relation_dom(C) ) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f45,axiom,(
% 0.12/0.58 (! [A,B,C] :( relation_of2_as_subset(C,A,B)<=> relation_of2(C,A,B) ) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f52,axiom,(
% 0.12/0.58 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f53,conjecture,(
% 0.12/0.58 (! [A,B,C,D] :( ( function(D)& quasi_total(D,A,B)& relation_of2_as_subset(D,A,B) )=> ( in(C,A)=> ( B = empty_set| in(apply(D,C),relation_rng(D)) ) ) ) )),
% 0.12/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.58 fof(f54,negated_conjecture,(
% 0.12/0.58 ~((! [A,B,C,D] :( ( function(D)& quasi_total(D,A,B)& relation_of2_as_subset(D,A,B) )=> ( in(C,A)=> ( B = empty_set| in(apply(D,C),relation_rng(D)) ) ) ) ))),
% 0.12/0.58 inference(negated_conjecture,[status(cth)],[f53])).
% 0.12/0.58 fof(f63,plain,(
% 0.12/0.58 ![A,B,C]: (~element(C,powerset(cartesian_product2(A,B)))|relation(C))),
% 0.12/0.58 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.12/0.58 fof(f64,plain,(
% 0.12/0.58 ![C]: ((![A,B]: ~element(C,powerset(cartesian_product2(A,B))))|relation(C))),
% 0.12/0.58 inference(miniscoping,[status(thm)],[f63])).
% 0.12/0.58 fof(f65,plain,(
% 0.12/0.58 ![X0,X1,X2]: (~element(X0,powerset(cartesian_product2(X1,X2)))|relation(X0))),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f64])).
% 0.12/0.58 fof(f70,plain,(
% 0.12/0.58 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|(((B=empty_set&~A=empty_set)|(quasi_total(C,A,B)<=>A=relation_dom_as_subset(A,B,C)))&(~B=empty_set|(A=empty_set|(quasi_total(C,A,B)<=>C=empty_set)))))),
% 0.12/0.58 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.12/0.58 fof(f71,definition,(
% 0.12/0.58 ![A,B]: (sP0_prd(B,A)<=>(B=empty_set&~A=empty_set))),
% 0.12/0.58 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/0.58 fof(f72,plain,(
% 0.12/0.58 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|((sP0_prd(B,A)|(quasi_total(C,A,B)<=>A=relation_dom_as_subset(A,B,C)))&(~B=empty_set|(A=empty_set|(quasi_total(C,A,B)<=>C=empty_set)))))),
% 0.12/0.58 inference(formula_renaming,[status(thm)],[f70,f71])).
% 0.12/0.58 fof(f73,plain,(
% 0.12/0.58 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|((sP0_prd(B,A)|((~quasi_total(C,A,B)|A=relation_dom_as_subset(A,B,C))&(quasi_total(C,A,B)|~A=relation_dom_as_subset(A,B,C))))&(~B=empty_set|(A=empty_set|((~quasi_total(C,A,B)|C=empty_set)&(quasi_total(C,A,B)|~C=empty_set))))))),
% 0.12/0.58 inference(NNF_transformation,[status(thm)],[f72])).
% 0.12/0.58 fof(f74,plain,(
% 0.12/0.58 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|sP0_prd(X2,X1)|~quasi_total(X0,X1,X2)|X1=relation_dom_as_subset(X1,X2,X0))),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f73])).
% 0.12/0.58 fof(f78,plain,(
% 0.12/0.58 ![A]: ((~relation(A)|~function(A))|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))),
% 0.12/0.58 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.12/0.58 fof(f79,plain,(
% 0.12/0.58 ![A]: ((~relation(A)|~function(A))|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))&(in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D)))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 0.12/0.58 inference(NNF_transformation,[status(thm)],[f78])).
% 0.12/0.58 fof(f80,plain,(
% 0.12/0.58 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 0.12/0.58 inference(miniscoping,[status(thm)],[f79])).
% 0.12/0.58 fof(f81,plain,(
% 0.12/0.58 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(in(sK0_skl(C,B,A),relation_dom(A))&C=apply(A,sK0_skl(C,B,A)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|((~in(sK1_skl(B,A),B)|(![D]: (~in(D,relation_dom(A))|~sK1_skl(B,A)=apply(A,D))))&(in(sK1_skl(B,A),B)|(in(sK2_skl(B,A),relation_dom(A))&sK1_skl(B,A)=apply(A,sK2_skl(B,A)))))))))),
% 0.12/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(C,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f80])).
% 0.12/0.58 fof(f84,plain,(
% 0.12/0.58 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|in(X2,X1)|~in(X3,relation_dom(X0))|~X2=apply(X0,X3))),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f81])).
% 0.12/0.58 fof(f90,plain,(
% 0.12/0.58 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))))),
% 0.12/0.58 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.12/0.58 fof(f91,plain,(
% 0.12/0.58 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|element(X0,powerset(cartesian_product2(X1,X2))))),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f90])).
% 0.12/0.58 fof(f125,plain,(
% 0.12/0.58 (((relation(sK8_skl)&function(sK8_skl))&one_to_one(sK8_skl))&empty(sK8_skl))),
% 0.12/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f32])).
% 0.12/0.58 fof(f129,plain,(
% 0.12/0.58 empty(sK8_skl)),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f125])).
% 0.12/0.58 fof(f166,plain,(
% 0.12/0.58 ![A,B,C]: (~relation_of2(C,A,B)|relation_dom_as_subset(A,B,C)=relation_dom(C))),
% 0.12/0.58 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 0.12/0.58 fof(f167,plain,(
% 0.12/0.58 ![X0,X1,X2]: (~relation_of2(X0,X1,X2)|relation_dom_as_subset(X1,X2,X0)=relation_dom(X0))),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f166])).
% 0.12/0.58 fof(f168,plain,(
% 0.12/0.58 ![A,B,C]: ((~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B))&(relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 0.12/0.58 inference(NNF_transformation,[status(thm)],[f45])).
% 0.12/0.58 fof(f169,plain,(
% 0.12/0.58 (![A,B,C]: (~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B)))&(![A,B,C]: (relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 0.12/0.58 inference(miniscoping,[status(thm)],[f168])).
% 0.12/0.58 fof(f170,plain,(
% 0.12/0.58 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|relation_of2(X0,X1,X2))),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f169])).
% 0.12/0.58 fof(f188,plain,(
% 0.12/0.58 ![A]: (~empty(A)|A=empty_set)),
% 0.12/0.58 inference(pre_NNF_transformation,[status(thm)],[f52])).
% 0.12/0.58 fof(f189,plain,(
% 0.12/0.58 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f188])).
% 0.12/0.58 fof(f190,plain,(
% 0.12/0.58 (?[A,B,C,D]: (((function(D)&quasi_total(D,A,B))&relation_of2_as_subset(D,A,B))&(in(C,A)&(~B=empty_set&~in(apply(D,C),relation_rng(D))))))),
% 0.12/0.58 inference(pre_NNF_transformation,[status(thm)],[f54])).
% 0.12/0.58 fof(f191,plain,(
% 0.12/0.58 ?[A,B,D]: (((function(D)&quasi_total(D,A,B))&relation_of2_as_subset(D,A,B))&(?[C]: (in(C,A)&(~B=empty_set&~in(apply(D,C),relation_rng(D))))))),
% 0.12/0.58 inference(miniscoping,[status(thm)],[f190])).
% 0.12/0.58 fof(f192,plain,(
% 0.12/0.58 (((function(sK22_skl)&quasi_total(sK22_skl,sK20_skl,sK21_skl))&relation_of2_as_subset(sK22_skl,sK20_skl,sK21_skl))&(in(sK23_skl,sK20_skl)&(~sK21_skl=empty_set&~in(apply(sK22_skl,sK23_skl),relation_rng(sK22_skl)))))),
% 0.12/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl]),skolemize(A,sK20_skl),skolemize(B,sK21_skl),skolemize(D,sK22_skl),skolemize(C,sK23_skl)],[f191])).
% 0.12/0.58 fof(f193,plain,(
% 0.12/0.58 function(sK22_skl)),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f192])).
% 0.12/0.58 fof(f194,plain,(
% 0.12/0.58 quasi_total(sK22_skl,sK20_skl,sK21_skl)),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f192])).
% 0.12/0.58 fof(f195,plain,(
% 0.12/0.58 relation_of2_as_subset(sK22_skl,sK20_skl,sK21_skl)),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f192])).
% 0.12/0.58 fof(f196,plain,(
% 0.12/0.58 in(sK23_skl,sK20_skl)),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f192])).
% 0.12/0.58 fof(f197,plain,(
% 0.12/0.58 ~sK21_skl=empty_set),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f192])).
% 0.12/0.58 fof(f198,plain,(
% 0.12/0.58 ~in(apply(sK22_skl,sK23_skl),relation_rng(sK22_skl))),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f192])).
% 0.12/0.58 fof(f205,plain,(
% 0.12/0.58 ![A,B]: ((~sP0_prd(B,A)|(B=empty_set&~A=empty_set))&(sP0_prd(B,A)|(~B=empty_set|A=empty_set)))),
% 0.12/0.58 inference(NNF_transformation,[status(thm)],[f71])).
% 0.12/0.58 fof(f206,plain,(
% 0.12/0.58 (![A,B]: (~sP0_prd(B,A)|(B=empty_set&~A=empty_set)))&(![A,B]: (sP0_prd(B,A)|(~B=empty_set|A=empty_set)))),
% 0.12/0.58 inference(miniscoping,[status(thm)],[f205])).
% 0.12/0.58 fof(f207,plain,(
% 0.12/0.58 ![X0,X1]: (~sP0_prd(X0,X1)|X0=empty_set)),
% 0.12/0.58 inference(cnf_transformation,[status(thm)],[f206])).
% 0.12/0.58 fof(f214,plain,(
% 0.12/0.58 ![X0,X1]: (~relation(X0)|~function(X0)|in(apply(X0,X1),relation_rng(X0))|~in(X1,relation_dom(X0)))),
% 0.12/0.58 inference(destructive_equality_resolution,[status(thm)],[f84])).
% 0.12/0.58 fof(f221,plain,(
% 0.12/0.58 ~relation_of2_as_subset(sK22_skl,sK20_skl,sK21_skl)|sP0_prd(sK21_skl,sK20_skl)|sK20_skl=relation_dom_as_subset(sK20_skl,sK21_skl,sK22_skl)),
% 0.12/0.58 inference(resolution,[status(thm)],[f74,f194])).
% 0.12/0.58 fof(f222,plain,(
% 0.12/0.58 sP0_prd(sK21_skl,sK20_skl)|sK20_skl=relation_dom_as_subset(sK20_skl,sK21_skl,sK22_skl)),
% 0.12/0.58 inference(forward_subsumption_resolution,[status(thm)],[f221,f195])).
% 0.12/0.58 fof(f238,plain,(
% 0.12/0.58 element(sK22_skl,powerset(cartesian_product2(sK20_skl,sK21_skl)))),
% 0.12/0.58 inference(resolution,[status(thm)],[f91,f195])).
% 0.12/0.58 fof(f260,plain,(
% 0.12/0.58 sK8_skl=empty_set),
% 0.12/0.58 inference(resolution,[status(thm)],[f129,f189])).
% 0.12/0.58 fof(f269,plain,(
% 0.12/0.58 relation(sK22_skl)),
% 0.12/0.58 inference(resolution,[status(thm)],[f238,f65])).
% 0.12/0.58 fof(f279,plain,(
% 0.12/0.58 ~sK21_skl=sK8_skl),
% 0.12/0.58 inference(backward_demodulation,[status(thm)],[f260,f197])).
% 0.12/0.58 fof(f496,plain,(
% 0.12/0.58 relation_of2(sK22_skl,sK20_skl,sK21_skl)),
% 0.12/0.58 inference(resolution,[status(thm)],[f170,f195])).
% 0.12/0.58 fof(f522,plain,(
% 0.12/0.58 relation_dom_as_subset(sK20_skl,sK21_skl,sK22_skl)=relation_dom(sK22_skl)),
% 0.12/0.58 inference(resolution,[status(thm)],[f496,f167])).
% 0.12/0.58 fof(f552,plain,(
% 0.12/0.58 ![X0,X1]: (~sP0_prd(X0,X1)|X0=sK8_skl)),
% 0.12/0.58 inference(forward_demodulation,[status(thm)],[f260,f207])).
% 0.12/0.58 fof(f557,plain,(
% 0.12/0.58 sP0_prd(sK21_skl,sK20_skl)|sK20_skl=relation_dom(sK22_skl)),
% 0.12/0.58 inference(backward_demodulation,[status(thm)],[f522,f222])).
% 0.12/0.58 fof(f559,plain,(
% 0.12/0.58 sK20_skl=relation_dom(sK22_skl)|sK21_skl=sK8_skl),
% 0.12/0.58 inference(resolution,[status(thm)],[f557,f552])).
% 0.12/0.58 fof(f560,plain,(
% 0.12/0.58 sK20_skl=relation_dom(sK22_skl)),
% 0.12/0.58 inference(forward_subsumption_resolution,[status(thm)],[f559,f279])).
% 0.12/0.58 fof(f652,plain,(
% 0.12/0.58 ![X0]: (~relation(sK22_skl)|~function(sK22_skl)|in(apply(sK22_skl,X0),relation_rng(sK22_skl))|~in(X0,sK20_skl))),
% 0.12/0.58 inference(paramodulation,[status(thm)],[f560,f214])).
% 0.12/0.58 fof(f653,plain,(
% 0.12/0.58 ![X0]: (~function(sK22_skl)|in(apply(sK22_skl,X0),relation_rng(sK22_skl))|~in(X0,sK20_skl))),
% 0.12/0.58 inference(forward_subsumption_resolution,[status(thm)],[f652,f269])).
% 0.12/0.58 fof(f960,plain,(
% 0.12/0.58 ![X0]: (in(apply(sK22_skl,X0),relation_rng(sK22_skl))|~in(X0,sK20_skl))),
% 0.12/0.58 inference(forward_subsumption_resolution,[status(thm)],[f653,f193])).
% 0.12/0.58 fof(f972,plain,(
% 0.12/0.58 in(apply(sK22_skl,sK23_skl),relation_rng(sK22_skl))),
% 0.12/0.58 inference(resolution,[status(thm)],[f960,f196])).
% 0.12/0.58 fof(f973,plain,(
% 0.12/0.58 $false),
% 0.12/0.58 inference(forward_subsumption_resolution,[status(thm)],[f972,f198])).
% 0.12/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.60 % Elapsed time: 0.040714 seconds
% 0.12/0.60 % CPU time: 0.141089 seconds
% 0.12/0.60 % Total memory used: 25.065 MB
% 0.12/0.60 % Net memory used: 24.947 MB
%------------------------------------------------------------------------------