%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU262+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 : 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 02:22:10 PM UTC 2026
% Result : Theorem 1.20s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU262+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:59:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 1.20/0.62 % Refutation found
% 1.20/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.20/0.62 % SZS output start CNFRefutation for theBenchmark
% 1.20/0.62 fof(f2,axiom,(
% 1.20/0.62 (! [A,B,C] :( element(C,powerset(cartesian_product2(A,B)))=> relation(C) ) )),
% 1.20/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.62 fof(f4,axiom,(
% 1.20/0.62 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 1.20/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.62 fof(f5,axiom,(
% 1.20/0.62 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 1.20/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.62 fof(f6,axiom,(
% 1.20/0.62 (! [A] :( relation(A)=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(D,C),A) )) )) )) )),
% 1.20/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.62 fof(f18,axiom,(
% 1.20/0.62 (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> element(C,powerset(cartesian_product2(A,B))) ) )),
% 1.20/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.62 fof(f28,axiom,(
% 1.20/0.62 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 1.20/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.62 fof(f29,conjecture,(
% 1.20/0.62 (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> ( subset(relation_dom(C),A)& subset(relation_rng(C),B) ) ) )),
% 1.20/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.62 fof(f30,negated_conjecture,(
% 1.20/0.62 ~((! [A,B,C] :( relation_of2_as_subset(C,A,B)=> ( subset(relation_dom(C),A)& subset(relation_rng(C),B) ) ) ))),
% 1.20/0.62 inference(negated_conjecture,[status(cth)],[f29])).
% 1.20/0.62 fof(f33,axiom,(
% 1.20/0.62 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 1.20/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.20/0.62 fof(f41,plain,(
% 1.20/0.62 ![A,B,C]: (~element(C,powerset(cartesian_product2(A,B)))|relation(C))),
% 1.20/0.62 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 1.20/0.62 fof(f42,plain,(
% 1.20/0.62 ![C]: ((![A,B]: ~element(C,powerset(cartesian_product2(A,B))))|relation(C))),
% 1.20/0.62 inference(miniscoping,[status(thm)],[f41])).
% 1.20/0.62 fof(f43,plain,(
% 1.20/0.62 ![X0,X1,X2]: (~element(X0,powerset(cartesian_product2(X1,X2)))|relation(X0))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f42])).
% 1.20/0.62 fof(f45,plain,(
% 1.20/0.62 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 1.20/0.62 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 1.20/0.62 fof(f46,plain,(
% 1.20/0.62 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 1.20/0.62 inference(NNF_transformation,[status(thm)],[f45])).
% 1.20/0.62 fof(f47,plain,(
% 1.20/0.62 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 1.20/0.62 inference(miniscoping,[status(thm)],[f46])).
% 1.20/0.62 fof(f48,plain,(
% 1.20/0.62 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK0_skl(B,A),A)&~in(sK0_skl(B,A),B))))),
% 1.20/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f47])).
% 1.20/0.62 fof(f49,plain,(
% 1.20/0.62 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f48])).
% 1.20/0.62 fof(f50,plain,(
% 1.20/0.62 ![X0,X1]: (subset(X0,X1)|in(sK0_skl(X1,X0),X0))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f48])).
% 1.20/0.62 fof(f51,plain,(
% 1.20/0.62 ![X0,X1]: (subset(X0,X1)|~in(sK0_skl(X1,X0),X1))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f48])).
% 1.20/0.62 fof(f52,plain,(
% 1.20/0.62 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 1.20/0.62 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 1.20/0.62 fof(f53,plain,(
% 1.20/0.62 ![A]: (~relation(A)|(![B]: ((~B=relation_dom(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(C,D),A)))&(in(C,B)|(![D]: ~in(ordered_pair(C,D),A))))))&(B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 1.20/0.62 inference(NNF_transformation,[status(thm)],[f52])).
% 1.20/0.62 fof(f54,plain,(
% 1.20/0.62 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(C,D),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 1.20/0.62 inference(miniscoping,[status(thm)],[f53])).
% 1.20/0.62 fof(f55,plain,(
% 1.20/0.62 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sK1_skl(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sK2_skl(B,A),B)|(![D]: ~in(ordered_pair(sK2_skl(B,A),D),A)))&(in(sK2_skl(B,A),B)|in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),A)))))))),
% 1.20/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f54])).
% 1.20/0.62 fof(f56,plain,(
% 1.20/0.62 ![X0,X1,X2]: (~relation(X0)|~X1=relation_dom(X0)|~in(X2,X1)|in(ordered_pair(X2,sK1_skl(X2,X1,X0)),X0))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f55])).
% 1.20/0.62 fof(f60,plain,(
% 1.20/0.62 ![A]: (~relation(A)|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(D,C),A)))))))),
% 1.20/0.62 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 1.20/0.62 fof(f61,plain,(
% 1.20/0.62 ![A]: (~relation(A)|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(D,C),A)))&(in(C,B)|(![D]: ~in(ordered_pair(D,C),A))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 1.20/0.62 inference(NNF_transformation,[status(thm)],[f60])).
% 1.20/0.62 fof(f62,plain,(
% 1.20/0.62 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(D,C),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 1.20/0.62 inference(miniscoping,[status(thm)],[f61])).
% 1.20/0.62 fof(f63,plain,(
% 1.20/0.62 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|in(ordered_pair(sK4_skl(C,B,A),C),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|((~in(sK5_skl(B,A),B)|(![D]: ~in(ordered_pair(D,sK5_skl(B,A)),A)))&(in(sK5_skl(B,A),B)|in(ordered_pair(sK6_skl(B,A),sK5_skl(B,A)),A)))))))),
% 1.20/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(D,sK4_skl(C,B,A)),skolemize(C,sK5_skl(B,A)),skolemize(D,sK6_skl(B,A))],[f62])).
% 1.20/0.62 fof(f64,plain,(
% 1.20/0.62 ![X0,X1,X2]: (~relation(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(ordered_pair(sK4_skl(X2,X1,X0),X2),X0))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f63])).
% 1.20/0.62 fof(f69,plain,(
% 1.20/0.62 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))))),
% 1.20/0.62 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 1.20/0.62 fof(f70,plain,(
% 1.20/0.62 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|element(X0,powerset(cartesian_product2(X1,X2))))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f69])).
% 1.20/0.62 fof(f89,plain,(
% 1.20/0.62 ![A,B,C,D]: ((~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 1.20/0.62 inference(NNF_transformation,[status(thm)],[f28])).
% 1.20/0.62 fof(f90,plain,(
% 1.20/0.62 (![A,B,C,D]: (~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D))))&(![A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 1.20/0.62 inference(miniscoping,[status(thm)],[f89])).
% 1.20/0.62 fof(f91,plain,(
% 1.20/0.62 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f90])).
% 1.20/0.62 fof(f92,plain,(
% 1.20/0.62 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f90])).
% 1.20/0.62 fof(f94,plain,(
% 1.20/0.62 (?[A,B,C]: (relation_of2_as_subset(C,A,B)&(~subset(relation_dom(C),A)|~subset(relation_rng(C),B))))),
% 1.20/0.62 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 1.20/0.62 fof(f95,plain,(
% 1.20/0.62 (relation_of2_as_subset(sK14_skl,sK12_skl,sK13_skl)&(~subset(relation_dom(sK14_skl),sK12_skl)|~subset(relation_rng(sK14_skl),sK13_skl)))),
% 1.20/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(A,sK12_skl),skolemize(B,sK13_skl),skolemize(C,sK14_skl)],[f94])).
% 1.20/0.62 fof(f96,plain,(
% 1.20/0.62 relation_of2_as_subset(sK14_skl,sK12_skl,sK13_skl)),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f95])).
% 1.20/0.62 fof(f97,plain,(
% 1.20/0.62 ~subset(relation_dom(sK14_skl),sK12_skl)|~subset(relation_rng(sK14_skl),sK13_skl)),
% 1.20/0.62 inference(cnf_transformation,[status(thm)],[f95])).
% 1.20/0.64 fof(f102,plain,(
% 1.20/0.64 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 1.20/0.64 inference(NNF_transformation,[status(thm)],[f33])).
% 1.20/0.64 fof(f103,plain,(
% 1.20/0.64 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 1.20/0.64 inference(miniscoping,[status(thm)],[f102])).
% 1.20/0.64 fof(f104,plain,(
% 1.20/0.64 ![X0,X1]: (~element(X0,powerset(X1))|subset(X0,X1))),
% 1.20/0.64 inference(cnf_transformation,[status(thm)],[f103])).
% 1.20/0.64 fof(f120,plain,(
% 1.20/0.64 ![X0,X1]: (~relation(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,sK1_skl(X1,relation_dom(X0),X0)),X0))),
% 1.20/0.64 inference(destructive_equality_resolution,[status(thm)],[f56])).
% 1.20/0.64 fof(f122,plain,(
% 1.20/0.64 ![X0,X1]: (~relation(X0)|~in(X1,relation_rng(X0))|in(ordered_pair(sK4_skl(X1,relation_rng(X0),X0),X1),X0))),
% 1.20/0.64 inference(destructive_equality_resolution,[status(thm)],[f64])).
% 1.20/0.64 fof(f125,plain,(
% 1.20/0.64 ![X0,X1,X2]: (relation(X0)|~relation_of2_as_subset(X0,X1,X2))),
% 1.20/0.64 inference(resolution,[status(thm)],[f43,f70])).
% 1.20/0.64 fof(f134,plain,(
% 1.20/0.64 relation(sK14_skl)),
% 1.20/0.64 inference(resolution,[status(thm)],[f125,f96])).
% 1.20/0.64 fof(f141,plain,(
% 1.20/0.64 ![X0]: (~in(X0,relation_dom(sK14_skl))|in(ordered_pair(X0,sK1_skl(X0,relation_dom(sK14_skl),sK14_skl)),sK14_skl))),
% 1.20/0.64 inference(resolution,[status(thm)],[f120,f134])).
% 1.20/0.64 fof(f142,plain,(
% 1.20/0.64 ![X0]: (in(ordered_pair(sK0_skl(X0,relation_dom(sK14_skl)),sK1_skl(sK0_skl(X0,relation_dom(sK14_skl)),relation_dom(sK14_skl),sK14_skl)),sK14_skl)|subset(relation_dom(sK14_skl),X0))),
% 1.20/0.64 inference(resolution,[status(thm)],[f141,f50])).
% 1.20/0.64 fof(f152,plain,(
% 1.20/0.64 ![X0,X1]: (~relation(X0)|in(ordered_pair(sK4_skl(sK0_skl(X1,relation_rng(X0)),relation_rng(X0),X0),sK0_skl(X1,relation_rng(X0))),X0)|subset(relation_rng(X0),X1))),
% 1.20/0.64 inference(resolution,[status(thm)],[f122,f50])).
% 1.20/0.64 fof(f191,plain,(
% 1.20/0.64 ![X0,X1,X2]: (subset(X0,cartesian_product2(X1,X2))|~relation_of2_as_subset(X0,X1,X2))),
% 1.20/0.64 inference(resolution,[status(thm)],[f104,f70])).
% 1.20/0.64 fof(f192,plain,(
% 1.20/0.64 ![X0,X1,X2,X3]: (~relation_of2_as_subset(X0,X1,X2)|~in(X3,X0)|in(X3,cartesian_product2(X1,X2)))),
% 1.20/0.64 inference(resolution,[status(thm)],[f191,f49])).
% 1.20/0.64 fof(f226,plain,(
% 1.20/0.64 ![X0]: (~in(X0,sK14_skl)|in(X0,cartesian_product2(sK12_skl,sK13_skl)))),
% 1.20/0.64 inference(resolution,[status(thm)],[f192,f96])).
% 1.20/0.64 fof(f269,plain,(
% 1.20/0.64 ![X0,X1]: (in(X0,sK12_skl)|~in(ordered_pair(X0,X1),sK14_skl))),
% 1.20/0.64 inference(resolution,[status(thm)],[f91,f226])).
% 1.20/0.64 fof(f270,plain,(
% 1.20/0.64 ![X0,X1]: (in(X0,sK13_skl)|~in(ordered_pair(X1,X0),sK14_skl))),
% 1.20/0.64 inference(resolution,[status(thm)],[f92,f226])).
% 1.20/0.64 fof(f276,plain,(
% 1.20/0.64 ![X0]: (in(sK0_skl(X0,relation_dom(sK14_skl)),sK12_skl)|subset(relation_dom(sK14_skl),X0))),
% 1.20/0.64 inference(resolution,[status(thm)],[f269,f142])).
% 1.20/0.64 fof(f331,plain,(
% 1.20/0.64 subset(relation_dom(sK14_skl),sK12_skl)|subset(relation_dom(sK14_skl),sK12_skl)),
% 1.20/0.64 inference(resolution,[status(thm)],[f276,f51])).
% 1.20/0.64 fof(f334,plain,(
% 1.20/0.64 ~subset(relation_rng(sK14_skl),sK13_skl)),
% 1.20/0.64 inference(backward_subsumption_resolution,[status(thm)],[f97,f335])).
% 1.20/0.64 fof(f335,plain,(
% 1.20/0.64 subset(relation_dom(sK14_skl),sK12_skl)),
% 1.20/0.64 inference(duplicate_literals_removal,[status(thm)],[f331])).
% 1.20/0.64 fof(f388,plain,(
% 1.20/0.64 ![X0]: (in(ordered_pair(sK4_skl(sK0_skl(X0,relation_rng(sK14_skl)),relation_rng(sK14_skl),sK14_skl),sK0_skl(X0,relation_rng(sK14_skl))),sK14_skl)|subset(relation_rng(sK14_skl),X0))),
% 1.20/0.64 inference(resolution,[status(thm)],[f152,f134])).
% 1.20/0.64 fof(f503,plain,(
% 1.20/0.64 ![X0]: (subset(relation_rng(sK14_skl),X0)|in(sK0_skl(X0,relation_rng(sK14_skl)),sK13_skl))),
% 1.20/0.64 inference(resolution,[status(thm)],[f388,f270])).
% 1.20/0.64 fof(f819,plain,(
% 1.20/0.64 subset(relation_rng(sK14_skl),sK13_skl)|subset(relation_rng(sK14_skl),sK13_skl)),
% 1.20/0.64 inference(resolution,[status(thm)],[f503,f51])).
% 1.20/0.64 fof(f822,plain,(
% 1.20/0.64 subset(relation_rng(sK14_skl),sK13_skl)),
% 1.20/0.64 inference(duplicate_literals_removal,[status(thm)],[f819])).
% 1.20/0.64 fof(f823,plain,(
% 1.20/0.64 $false),
% 1.20/0.64 inference(forward_subsumption_resolution,[status(thm)],[f822,f334])).
% 1.20/0.64 % SZS output end CNFRefutation for theBenchmark.p
% 1.20/0.64 % Elapsed time: 0.266348 seconds
% 1.20/0.64 % CPU time: 1.827226 seconds
% 1.20/0.64 % Total memory used: 128.417 MB
% 1.20/0.64 % Net memory used: 125.401 MB
%------------------------------------------------------------------------------