%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU212+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 : n001.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 02:22:00 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU212+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
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 06:03:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.38 fof(f5,axiom,(
% 0.08/0.38 (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( ( in(B,relation_dom(A))=> ( C = apply(A,B)<=> in(ordered_pair(B,C),A) ) )& ( ~ in(B,relation_dom(A))=> ( C = apply(A,B)<=> C = empty_set ) ) ) )) )),
% 0.08/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f6,axiom,(
% 0.08/0.38 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.08/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f35,conjecture,(
% 0.08/0.38 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(ordered_pair(A,B),C)<=> ( in(A,relation_dom(C))& B = apply(C,A) ) ) ) )),
% 0.08/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f36,negated_conjecture,(
% 0.08/0.38 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(ordered_pair(A,B),C)<=> ( in(A,relation_dom(C))& B = apply(C,A) ) ) ) ))),
% 0.08/0.38 inference(negated_conjecture,[status(cth)],[f35])).
% 0.08/0.38 fof(f44,plain,(
% 0.08/0.38 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|(C=apply(A,B)<=>in(ordered_pair(B,C),A)))&(in(B,relation_dom(A))|(C=apply(A,B)<=>C=empty_set)))))),
% 0.08/0.38 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.08/0.38 fof(f45,plain,(
% 0.08/0.38 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|((~C=apply(A,B)|in(ordered_pair(B,C),A))&(C=apply(A,B)|~in(ordered_pair(B,C),A))))&(in(B,relation_dom(A))|((~C=apply(A,B)|C=empty_set)&(C=apply(A,B)|~C=empty_set))))))),
% 0.08/0.38 inference(NNF_transformation,[status(thm)],[f44])).
% 0.08/0.38 fof(f46,plain,(
% 0.08/0.38 ![A]: ((~relation(A)|~function(A))|((![B]: (~in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|in(ordered_pair(B,C),A)))&(![C]: (C=apply(A,B)|~in(ordered_pair(B,C),A))))))&(![B]: (in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|C=empty_set))&(![C]: (C=apply(A,B)|~C=empty_set)))))))),
% 0.08/0.38 inference(miniscoping,[status(thm)],[f45])).
% 0.08/0.38 fof(f47,plain,(
% 0.08/0.38 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|~X2=apply(X0,X1)|in(ordered_pair(X1,X2),X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f46])).
% 0.08/0.38 fof(f48,plain,(
% 0.08/0.38 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X2=apply(X0,X1)|~in(ordered_pair(X1,X2),X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f46])).
% 0.08/0.38 fof(f51,plain,(
% 0.08/0.38 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.08/0.38 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.08/0.38 fof(f52,plain,(
% 0.08/0.38 ![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)))))))))),
% 0.08/0.38 inference(NNF_transformation,[status(thm)],[f51])).
% 0.08/0.38 fof(f53,plain,(
% 0.08/0.38 ![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)))))))))),
% 0.08/0.38 inference(miniscoping,[status(thm)],[f52])).
% 0.08/0.38 fof(f54,plain,(
% 0.08/0.38 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sK0_skl(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sK1_skl(B,A),B)|(![D]: ~in(ordered_pair(sK1_skl(B,A),D),A)))&(in(sK1_skl(B,A),B)|in(ordered_pair(sK1_skl(B,A),sK2_skl(B,A)),A)))))))),
% 0.08/0.38 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))],[f53])).
% 0.08/0.38 fof(f56,plain,(
% 0.08/0.38 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f54])).
% 0.08/0.38 fof(f104,plain,(
% 0.08/0.38 (?[A,B,C]: ((relation(C)&function(C))&(in(ordered_pair(A,B),C)<~>(in(A,relation_dom(C))&B=apply(C,A)))))),
% 0.08/0.38 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 0.08/0.38 fof(f105,plain,(
% 0.08/0.38 ?[A,B,C]: ((relation(C)&function(C))&((in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A)))&(~in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A)))))),
% 0.08/0.38 inference(NNF_transformation,[status(thm)],[f104])).
% 0.08/0.38 fof(f106,plain,(
% 0.08/0.38 ?[C]: ((relation(C)&function(C))&(?[A,B]: ((in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A)))&(~in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A))))))),
% 0.08/0.38 inference(miniscoping,[status(thm)],[f105])).
% 0.08/0.38 fof(f107,plain,(
% 0.08/0.38 ((relation(sK10_skl)&function(sK10_skl))&((in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)|(in(sK11_skl,relation_dom(sK10_skl))&sK12_skl=apply(sK10_skl,sK11_skl)))&(~in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)|(~in(sK11_skl,relation_dom(sK10_skl))|~sK12_skl=apply(sK10_skl,sK11_skl)))))),
% 0.08/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(C,sK10_skl),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f106])).
% 0.08/0.38 fof(f108,plain,(
% 0.08/0.38 relation(sK10_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f107])).
% 0.08/0.38 fof(f109,plain,(
% 0.08/0.38 function(sK10_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f107])).
% 0.08/0.38 fof(f110,plain,(
% 0.08/0.38 in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)|in(sK11_skl,relation_dom(sK10_skl))),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f107])).
% 0.08/0.38 fof(f111,plain,(
% 0.08/0.38 in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)|sK12_skl=apply(sK10_skl,sK11_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f107])).
% 0.08/0.38 fof(f112,plain,(
% 0.08/0.38 ~in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)|~in(sK11_skl,relation_dom(sK10_skl))|~sK12_skl=apply(sK10_skl,sK11_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f107])).
% 0.08/0.38 fof(f113,plain,(
% 0.08/0.38 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,apply(X0,X1)),X0))),
% 0.08/0.38 inference(destructive_equality_resolution,[status(thm)],[f47])).
% 0.08/0.38 fof(f117,plain,(
% 0.08/0.38 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=apply(X0,X2)|~in(ordered_pair(X2,X1),X0))),
% 0.08/0.38 inference(backward_subsumption_resolution,[status(thm)],[f48,f118])).
% 0.08/0.38 fof(f118,plain,(
% 0.08/0.38 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.08/0.38 inference(destructive_equality_resolution,[status(thm)],[f56])).
% 0.08/0.38 fof(f131,plain,(
% 0.08/0.38 ~relation(sK10_skl)|in(sK11_skl,relation_dom(sK10_skl))|in(sK11_skl,relation_dom(sK10_skl))),
% 0.08/0.38 inference(resolution,[status(thm)],[f118,f110])).
% 0.08/0.38 fof(f132,plain,(
% 0.08/0.38 ~relation(sK10_skl)|in(sK11_skl,relation_dom(sK10_skl))),
% 0.08/0.38 inference(duplicate_literals_removal,[status(thm)],[f131])).
% 0.08/0.38 fof(f133,plain,(
% 0.08/0.38 ~in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)|~sK12_skl=apply(sK10_skl,sK11_skl)),
% 0.08/0.38 inference(backward_subsumption_resolution,[status(thm)],[f112,f134])).
% 0.08/0.38 fof(f134,plain,(
% 0.08/0.38 in(sK11_skl,relation_dom(sK10_skl))),
% 0.08/0.38 inference(forward_subsumption_resolution,[status(thm)],[f132,f108])).
% 0.08/0.38 fof(f136,plain,(
% 0.08/0.38 ~relation(sK10_skl)|~function(sK10_skl)|in(ordered_pair(sK11_skl,apply(sK10_skl,sK11_skl)),sK10_skl)),
% 0.08/0.38 inference(resolution,[status(thm)],[f134,f113])).
% 0.08/0.38 fof(f139,plain,(
% 0.08/0.38 ~function(sK10_skl)|in(ordered_pair(sK11_skl,apply(sK10_skl,sK11_skl)),sK10_skl)),
% 0.08/0.38 inference(forward_subsumption_resolution,[status(thm)],[f136,f108])).
% 0.08/0.38 fof(f150,plain,(
% 0.08/0.38 ~relation(sK10_skl)|~function(sK10_skl)|sK12_skl=apply(sK10_skl,sK11_skl)|sK12_skl=apply(sK10_skl,sK11_skl)),
% 0.08/0.38 inference(resolution,[status(thm)],[f117,f111])).
% 0.08/0.38 fof(f152,plain,(
% 0.08/0.38 ~relation(sK10_skl)|~function(sK10_skl)|sK12_skl=apply(sK10_skl,sK11_skl)),
% 0.08/0.38 inference(duplicate_literals_removal,[status(thm)],[f150])).
% 0.08/0.38 fof(f153,plain,(
% 0.08/0.38 ~function(sK10_skl)|sK12_skl=apply(sK10_skl,sK11_skl)),
% 0.08/0.38 inference(forward_subsumption_resolution,[status(thm)],[f152,f108])).
% 0.08/0.38 fof(f173,plain,(
% 0.08/0.38 sK12_skl=apply(sK10_skl,sK11_skl)),
% 0.08/0.38 inference(resolution,[status(thm)],[f153,f109])).
% 0.08/0.38 fof(f176,plain,(
% 0.08/0.38 ~in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)|~sK12_skl=sK12_skl),
% 0.08/0.38 inference(backward_demodulation,[status(thm)],[f173,f133])).
% 0.08/0.38 fof(f179,plain,(
% 0.08/0.38 ~function(sK10_skl)|in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)),
% 0.08/0.38 inference(backward_demodulation,[status(thm)],[f173,f139])).
% 0.08/0.38 fof(f180,plain,(
% 0.08/0.38 ~in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)),
% 0.08/0.38 inference(trivial_equality_resolution,[status(thm)],[f176])).
% 0.08/0.38 fof(f182,plain,(
% 0.08/0.38 in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)),
% 0.08/0.38 inference(forward_subsumption_resolution,[status(thm)],[f179,f109])).
% 0.08/0.38 fof(f183,plain,(
% 0.08/0.38 $false),
% 0.08/0.38 inference(backward_subsumption_resolution,[status(thm)],[f180,f182])).
% 0.08/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.41 % Elapsed time: 0.057607 seconds
% 0.12/0.41 % CPU time: 0.119838 seconds
% 0.12/0.41 % Total memory used: 51.572 MB
% 0.12/0.41 % Net memory used: 51.540 MB
%------------------------------------------------------------------------------