%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:21:59 PM UTC 2026
% Result : Theorem 0.14s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:53:27 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.49 % Refutation found
% 0.14/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.49 fof(f4,axiom,(
% 0.14/0.49 (! [A] :( relation(A)=> (! [B,C] :( C = relation_inverse_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(D,E),A)& in(E,B) ) )) )) )) )),
% 0.14/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.49 fof(f5,axiom,(
% 0.14/0.49 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.14/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.49 fof(f6,axiom,(
% 0.14/0.49 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.14/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.49 fof(f32,conjecture,(
% 0.14/0.49 (! [A,B] :( relation(B)=> subset(relation_inverse_image(B,A),relation_dom(B)) ) )),
% 0.14/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.49 fof(f33,negated_conjecture,(
% 0.14/0.49 ~((! [A,B] :( relation(B)=> subset(relation_inverse_image(B,A),relation_dom(B)) ) ))),
% 0.14/0.49 inference(negated_conjecture,[status(cth)],[f32])).
% 0.14/0.49 fof(f47,plain,(
% 0.14/0.49 ![A]: (~relation(A)|(![B,C]: (C=relation_inverse_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))),
% 0.14/0.49 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/0.49 fof(f48,plain,(
% 0.14/0.49 ![A]: (~relation(A)|(![B,C]: ((~C=relation_inverse_image(A,B)|(![D]: ((~in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))&(in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B)))))))&(C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))))),
% 0.14/0.49 inference(NNF_transformation,[status(thm)],[f47])).
% 0.14/0.49 fof(f49,plain,(
% 0.14/0.49 ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B)))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))))))&(![B,C]: (C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))))),
% 0.14/0.49 inference(miniscoping,[status(thm)],[f48])).
% 0.14/0.49 fof(f50,plain,(
% 0.14/0.49 ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(D,sK0_skl(D,C,B,A)),A)&in(sK0_skl(D,C,B,A),B))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))))))&(![B,C]: (C=relation_inverse_image(A,B)|((~in(sK1_skl(C,B,A),C)|(![E]: (~in(ordered_pair(sK1_skl(C,B,A),E),A)|~in(E,B))))&(in(sK1_skl(C,B,A),C)|(in(ordered_pair(sK1_skl(C,B,A),sK2_skl(C,B,A)),A)&in(sK2_skl(C,B,A),B))))))))),
% 0.14/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(E,sK0_skl(D,C,B,A)),skolemize(D,sK1_skl(C,B,A)),skolemize(E,sK2_skl(C,B,A))],[f49])).
% 0.14/0.49 fof(f51,plain,(
% 0.14/0.49 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(ordered_pair(X3,sK0_skl(X3,X1,X2,X0)),X0))),
% 0.14/0.49 inference(cnf_transformation,[status(thm)],[f50])).
% 0.14/0.49 fof(f57,plain,(
% 0.14/0.49 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.14/0.49 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.14/0.49 fof(f58,plain,(
% 0.14/0.49 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.14/0.49 inference(NNF_transformation,[status(thm)],[f57])).
% 0.14/0.49 fof(f59,plain,(
% 0.14/0.49 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.14/0.49 inference(miniscoping,[status(thm)],[f58])).
% 0.14/0.49 fof(f60,plain,(
% 0.14/0.49 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK3_skl(B,A),A)&~in(sK3_skl(B,A),B))))),
% 0.14/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B,A))],[f59])).
% 0.14/0.49 fof(f62,plain,(
% 0.14/0.49 ![X0,X1]: (subset(X0,X1)|in(sK3_skl(X1,X0),X0))),
% 0.14/0.49 inference(cnf_transformation,[status(thm)],[f60])).
% 0.14/0.49 fof(f63,plain,(
% 0.14/0.49 ![X0,X1]: (subset(X0,X1)|~in(sK3_skl(X1,X0),X1))),
% 0.14/0.49 inference(cnf_transformation,[status(thm)],[f60])).
% 0.14/0.49 fof(f64,plain,(
% 0.14/0.49 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.14/0.49 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.14/0.49 fof(f65,plain,(
% 0.14/0.49 ![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)))))))))),
% 0.14/0.50 inference(NNF_transformation,[status(thm)],[f64])).
% 0.14/0.50 fof(f66,plain,(
% 0.14/0.50 ![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)))))))))),
% 0.14/0.50 inference(miniscoping,[status(thm)],[f65])).
% 0.14/0.50 fof(f67,plain,(
% 0.14/0.50 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sK4_skl(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sK5_skl(B,A),B)|(![D]: ~in(ordered_pair(sK5_skl(B,A),D),A)))&(in(sK5_skl(B,A),B)|in(ordered_pair(sK5_skl(B,A),sK6_skl(B,A)),A)))))))),
% 0.14/0.50 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))],[f66])).
% 0.14/0.50 fof(f69,plain,(
% 0.14/0.50 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.14/0.50 inference(cnf_transformation,[status(thm)],[f67])).
% 0.14/0.50 fof(f106,plain,(
% 0.14/0.50 (?[A,B]: (relation(B)&~subset(relation_inverse_image(B,A),relation_dom(B))))),
% 0.14/0.50 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 0.14/0.50 fof(f107,plain,(
% 0.14/0.50 ?[B]: (relation(B)&(?[A]: ~subset(relation_inverse_image(B,A),relation_dom(B))))),
% 0.14/0.50 inference(miniscoping,[status(thm)],[f106])).
% 0.14/0.50 fof(f108,plain,(
% 0.14/0.50 (relation(sK14_skl)&~subset(relation_inverse_image(sK14_skl,sK15_skl),relation_dom(sK14_skl)))),
% 0.14/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(B,sK14_skl),skolemize(A,sK15_skl)],[f107])).
% 0.14/0.50 fof(f109,plain,(
% 0.14/0.50 relation(sK14_skl)),
% 0.14/0.50 inference(cnf_transformation,[status(thm)],[f108])).
% 0.14/0.50 fof(f110,plain,(
% 0.14/0.50 ~subset(relation_inverse_image(sK14_skl,sK15_skl),relation_dom(sK14_skl))),
% 0.14/0.50 inference(cnf_transformation,[status(thm)],[f108])).
% 0.14/0.50 fof(f133,plain,(
% 0.14/0.50 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|in(ordered_pair(X1,sK0_skl(X1,relation_inverse_image(X0,X2),X2,X0)),X0))),
% 0.14/0.50 inference(destructive_equality_resolution,[status(thm)],[f51])).
% 0.14/0.50 fof(f137,plain,(
% 0.14/0.50 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.14/0.50 inference(destructive_equality_resolution,[status(thm)],[f69])).
% 0.14/0.50 fof(f150,plain,(
% 0.14/0.50 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|~relation(X0)|in(X1,relation_dom(X0)))),
% 0.14/0.50 inference(resolution,[status(thm)],[f133,f137])).
% 0.14/0.50 fof(f152,plain,(
% 0.14/0.50 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|in(X1,relation_dom(X0)))),
% 0.14/0.50 inference(duplicate_literals_removal,[status(thm)],[f150])).
% 0.14/0.50 fof(f157,plain,(
% 0.14/0.50 ![X0,X1]: (~in(X0,relation_inverse_image(sK14_skl,X1))|in(X0,relation_dom(sK14_skl)))),
% 0.14/0.50 inference(resolution,[status(thm)],[f152,f109])).
% 0.14/0.50 fof(f212,plain,(
% 0.14/0.50 ![X0,X1]: (subset(relation_inverse_image(sK14_skl,X0),X1)|in(sK3_skl(X1,relation_inverse_image(sK14_skl,X0)),relation_dom(sK14_skl)))),
% 0.14/0.50 inference(resolution,[status(thm)],[f62,f157])).
% 0.14/0.50 fof(f222,plain,(
% 0.14/0.50 ![X0]: (subset(relation_inverse_image(sK14_skl,X0),relation_dom(sK14_skl))|subset(relation_inverse_image(sK14_skl,X0),relation_dom(sK14_skl)))),
% 0.14/0.50 inference(resolution,[status(thm)],[f212,f63])).
% 0.14/0.50 fof(f225,plain,(
% 0.14/0.50 ![X0]: (subset(relation_inverse_image(sK14_skl,X0),relation_dom(sK14_skl)))),
% 0.14/0.50 inference(duplicate_literals_removal,[status(thm)],[f222])).
% 0.14/0.50 fof(f226,plain,(
% 0.14/0.50 $false),
% 0.14/0.50 inference(backward_subsumption_resolution,[status(thm)],[f110,f225])).
% 0.14/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.51 % Elapsed time: 0.130640 seconds
% 0.14/0.51 % CPU time: 0.732574 seconds
% 0.14/0.51 % Total memory used: 115.573 MB
% 0.14/0.51 % Net memory used: 113.883 MB
%------------------------------------------------------------------------------