%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU206+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 : 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 02:21:59 PM UTC 2026
% Result : Theorem 0.24s 0.78s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU206+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n002.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 06:00:19 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.50 % Drodi V4.1.1
% 0.24/0.78 % Refutation found
% 0.24/0.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.78 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.78 fof(f5,axiom,(
% 0.24/0.78 (! [A] :( relation(A)=> (! [B,C] :( C = relation_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(E,D),A)& in(E,B) ) )) )) )) )),
% 0.24/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.78 fof(f7,axiom,(
% 0.24/0.78 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.24/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.78 fof(f8,axiom,(
% 0.24/0.78 (! [A] :( relation(A)=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(D,C),A) )) )) )) )),
% 0.24/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.78 fof(f38,conjecture,(
% 0.24/0.78 (! [A] :( relation(A)=> relation_image(A,relation_dom(A)) = relation_rng(A) ) )),
% 0.24/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.78 fof(f39,negated_conjecture,(
% 0.24/0.78 ~((! [A] :( relation(A)=> relation_image(A,relation_dom(A)) = relation_rng(A) ) ))),
% 0.24/0.78 inference(negated_conjecture,[status(cth)],[f38])).
% 0.24/0.78 fof(f58,plain,(
% 0.24/0.78 ![A]: (~relation(A)|(![B,C]: (C=relation_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))),
% 0.24/0.78 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.24/0.78 fof(f59,plain,(
% 0.24/0.78 ![A]: (~relation(A)|(![B,C]: ((~C=relation_image(A,B)|(![D]: ((~in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))&(in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B)))))))&(C=relation_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))))),
% 0.24/0.78 inference(NNF_transformation,[status(thm)],[f58])).
% 0.24/0.78 fof(f60,plain,(
% 0.24/0.78 ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B)))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))))))&(![B,C]: (C=relation_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))))),
% 0.24/0.78 inference(miniscoping,[status(thm)],[f59])).
% 0.24/0.78 fof(f61,plain,(
% 0.24/0.78 ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(sK0_skl(D,C,B,A),D),A)&in(sK0_skl(D,C,B,A),B))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))))))&(![B,C]: (C=relation_image(A,B)|((~in(sK1_skl(C,B,A),C)|(![E]: (~in(ordered_pair(E,sK1_skl(C,B,A)),A)|~in(E,B))))&(in(sK1_skl(C,B,A),C)|(in(ordered_pair(sK2_skl(C,B,A),sK1_skl(C,B,A)),A)&in(sK2_skl(C,B,A),B))))))))),
% 0.24/0.78 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))],[f60])).
% 0.24/0.78 fof(f65,plain,(
% 0.24/0.78 ![X0,X1,X2,X3]: (~relation(X0)|X1=relation_image(X0,X2)|~in(sK1_skl(X1,X2,X0),X1)|~in(ordered_pair(X3,sK1_skl(X1,X2,X0)),X0)|~in(X3,X2))),
% 0.24/0.78 inference(cnf_transformation,[status(thm)],[f61])).
% 0.24/0.78 fof(f66,plain,(
% 0.24/0.78 ![X0,X1,X2]: (~relation(X0)|X1=relation_image(X0,X2)|in(sK1_skl(X1,X2,X0),X1)|in(ordered_pair(sK2_skl(X1,X2,X0),sK1_skl(X1,X2,X0)),X0))),
% 0.24/0.78 inference(cnf_transformation,[status(thm)],[f61])).
% 0.24/0.78 fof(f75,plain,(
% 0.24/0.78 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.24/0.78 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.24/0.78 fof(f76,plain,(
% 0.24/0.78 ![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)))))))))),
% 0.24/0.78 inference(NNF_transformation,[status(thm)],[f75])).
% 0.24/0.78 fof(f77,plain,(
% 0.24/0.78 ![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)))))))))),
% 0.24/0.78 inference(miniscoping,[status(thm)],[f76])).
% 0.24/0.78 fof(f78,plain,(
% 0.24/0.78 ![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)))))))),
% 0.24/0.78 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))],[f77])).
% 0.24/0.78 fof(f80,plain,(
% 0.24/0.78 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.24/0.78 inference(cnf_transformation,[status(thm)],[f78])).
% 0.24/0.78 fof(f83,plain,(
% 0.24/0.78 ![A]: (~relation(A)|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(D,C),A)))))))),
% 0.24/0.78 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.24/0.78 fof(f84,plain,(
% 0.24/0.78 ![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)))))))))),
% 0.24/0.78 inference(NNF_transformation,[status(thm)],[f83])).
% 0.24/0.78 fof(f85,plain,(
% 0.24/0.78 ![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)))))))))),
% 0.24/0.78 inference(miniscoping,[status(thm)],[f84])).
% 0.24/0.78 fof(f86,plain,(
% 0.24/0.78 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|in(ordered_pair(sK7_skl(C,B,A),C),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|((~in(sK8_skl(B,A),B)|(![D]: ~in(ordered_pair(D,sK8_skl(B,A)),A)))&(in(sK8_skl(B,A),B)|in(ordered_pair(sK9_skl(B,A),sK8_skl(B,A)),A)))))))),
% 0.24/0.78 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(D,sK7_skl(C,B,A)),skolemize(C,sK8_skl(B,A)),skolemize(D,sK9_skl(B,A))],[f85])).
% 0.24/0.78 fof(f87,plain,(
% 0.24/0.78 ![X0,X1,X2]: (~relation(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(ordered_pair(sK7_skl(X2,X1,X0),X2),X0))),
% 0.24/0.78 inference(cnf_transformation,[status(thm)],[f86])).
% 0.24/0.78 fof(f88,plain,(
% 0.24/0.78 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_rng(X0)|in(X2,X1)|~in(ordered_pair(X3,X2),X0))),
% 0.24/0.78 inference(cnf_transformation,[status(thm)],[f86])).
% 0.24/0.78 fof(f133,plain,(
% 0.24/0.78 (?[A]: (relation(A)&~relation_image(A,relation_dom(A))=relation_rng(A)))),
% 0.24/0.78 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 0.24/0.78 fof(f134,plain,(
% 0.24/0.78 (relation(sK17_skl)&~relation_image(sK17_skl,relation_dom(sK17_skl))=relation_rng(sK17_skl))),
% 0.24/0.78 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(A,sK17_skl)],[f133])).
% 0.24/0.78 fof(f135,plain,(
% 0.24/0.78 relation(sK17_skl)),
% 0.24/0.78 inference(cnf_transformation,[status(thm)],[f134])).
% 0.24/0.78 fof(f136,plain,(
% 0.24/0.78 ~relation_image(sK17_skl,relation_dom(sK17_skl))=relation_rng(sK17_skl)),
% 0.24/0.78 inference(cnf_transformation,[status(thm)],[f134])).
% 0.24/0.78 fof(f165,plain,(
% 0.24/0.78 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.24/0.78 inference(destructive_equality_resolution,[status(thm)],[f80])).
% 0.24/0.78 fof(f166,plain,(
% 0.24/0.78 ![X0,X1]: (~relation(X0)|~in(X1,relation_rng(X0))|in(ordered_pair(sK7_skl(X1,relation_rng(X0),X0),X1),X0))),
% 0.24/0.78 inference(destructive_equality_resolution,[status(thm)],[f87])).
% 0.24/0.78 fof(f167,plain,(
% 0.24/0.78 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_rng(X0))|~in(ordered_pair(X2,X1),X0))),
% 0.24/0.78 inference(destructive_equality_resolution,[status(thm)],[f88])).
% 0.24/0.78 fof(f180,plain,(
% 0.24/0.78 ![X0,X1]: (X0=relation_image(sK17_skl,X1)|in(sK1_skl(X0,X1,sK17_skl),X0)|in(ordered_pair(sK2_skl(X0,X1,sK17_skl),sK1_skl(X0,X1,sK17_skl)),sK17_skl))),
% 0.24/0.78 inference(resolution,[status(thm)],[f66,f135])).
% 0.24/0.78 fof(f181,plain,(
% 0.24/0.78 ![X0,X1]: (X0=relation_image(sK17_skl,X1)|in(sK1_skl(X0,X1,sK17_skl),X0)|~relation(sK17_skl)|in(sK1_skl(X0,X1,sK17_skl),relation_rng(sK17_skl)))),
% 0.24/0.78 inference(resolution,[status(thm)],[f180,f167])).
% 0.24/0.78 fof(f187,plain,(
% 0.24/0.78 ![X0,X1]: (X0=relation_image(sK17_skl,X1)|in(sK1_skl(X0,X1,sK17_skl),X0)|in(sK1_skl(X0,X1,sK17_skl),relation_rng(sK17_skl)))),
% 0.24/0.78 inference(forward_subsumption_resolution,[status(thm)],[f181,f135])).
% 0.24/0.78 fof(f190,plain,(
% 0.24/0.80 ![X0,X1]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|~relation(sK17_skl)|relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|~in(ordered_pair(X1,sK1_skl(relation_rng(sK17_skl),X0,sK17_skl)),sK17_skl)|~in(X1,X0))),
% 0.24/0.80 inference(resolution,[status(thm)],[f187,f65])).
% 0.24/0.80 fof(f194,plain,(
% 0.24/0.80 ![X0]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|~relation(sK17_skl)|in(ordered_pair(sK7_skl(sK1_skl(relation_rng(sK17_skl),X0,sK17_skl),relation_rng(sK17_skl),sK17_skl),sK1_skl(relation_rng(sK17_skl),X0,sK17_skl)),sK17_skl))),
% 0.24/0.80 inference(resolution,[status(thm)],[f187,f166])).
% 0.24/0.80 fof(f208,plain,(
% 0.24/0.80 ![X0,X1]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|~relation(sK17_skl)|~in(ordered_pair(X1,sK1_skl(relation_rng(sK17_skl),X0,sK17_skl)),sK17_skl)|~in(X1,X0))),
% 0.24/0.80 inference(duplicate_literals_removal,[status(thm)],[f190])).
% 0.24/0.80 fof(f209,plain,(
% 0.24/0.80 ![X0,X1]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|~in(ordered_pair(X1,sK1_skl(relation_rng(sK17_skl),X0,sK17_skl)),sK17_skl)|~in(X1,X0))),
% 0.24/0.80 inference(forward_subsumption_resolution,[status(thm)],[f208,f135])).
% 0.24/0.80 fof(f211,plain,(
% 0.24/0.80 ![X0]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|in(ordered_pair(sK7_skl(sK1_skl(relation_rng(sK17_skl),X0,sK17_skl),relation_rng(sK17_skl),sK17_skl),sK1_skl(relation_rng(sK17_skl),X0,sK17_skl)),sK17_skl))),
% 0.24/0.80 inference(forward_subsumption_resolution,[status(thm)],[f194,f135])).
% 0.24/0.80 fof(f244,plain,(
% 0.24/0.80 ![X0]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|~in(sK7_skl(sK1_skl(relation_rng(sK17_skl),X0,sK17_skl),relation_rng(sK17_skl),sK17_skl),X0))),
% 0.24/0.80 inference(resolution,[status(thm)],[f211,f209])).
% 0.24/0.80 fof(f247,plain,(
% 0.24/0.80 ![X0]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|~relation(sK17_skl)|in(sK7_skl(sK1_skl(relation_rng(sK17_skl),X0,sK17_skl),relation_rng(sK17_skl),sK17_skl),relation_dom(sK17_skl)))),
% 0.24/0.80 inference(resolution,[status(thm)],[f211,f165])).
% 0.24/0.80 fof(f251,plain,(
% 0.24/0.80 ![X0]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|~in(sK7_skl(sK1_skl(relation_rng(sK17_skl),X0,sK17_skl),relation_rng(sK17_skl),sK17_skl),X0))),
% 0.24/0.80 inference(duplicate_literals_removal,[status(thm)],[f244])).
% 0.24/0.80 fof(f254,plain,(
% 0.24/0.80 ![X0]: (relation_rng(sK17_skl)=relation_image(sK17_skl,X0)|in(sK7_skl(sK1_skl(relation_rng(sK17_skl),X0,sK17_skl),relation_rng(sK17_skl),sK17_skl),relation_dom(sK17_skl)))),
% 0.24/0.80 inference(forward_subsumption_resolution,[status(thm)],[f247,f135])).
% 0.24/0.80 fof(f701,plain,(
% 0.24/0.80 relation_rng(sK17_skl)=relation_image(sK17_skl,relation_dom(sK17_skl))|relation_rng(sK17_skl)=relation_image(sK17_skl,relation_dom(sK17_skl))),
% 0.24/0.80 inference(resolution,[status(thm)],[f254,f251])).
% 0.24/0.80 fof(f707,plain,(
% 0.24/0.80 relation_rng(sK17_skl)=relation_image(sK17_skl,relation_dom(sK17_skl))),
% 0.24/0.80 inference(duplicate_literals_removal,[status(thm)],[f701])).
% 0.24/0.80 fof(f708,plain,(
% 0.24/0.80 $false),
% 0.24/0.80 inference(forward_subsumption_resolution,[status(thm)],[f707,f136])).
% 0.24/0.80 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.82 % Elapsed time: 0.337013 seconds
% 0.24/0.82 % CPU time: 2.157296 seconds
% 0.24/0.82 % Total memory used: 128.245 MB
% 0.24/0.82 % Net memory used: 125.699 MB
%------------------------------------------------------------------------------