%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU187+2 : 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 : n018.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 02:21:56 PM UTC 2026
% Result : Theorem 0.10s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU187+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:58:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.53 % Refutation found
% 0.10/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.53 fof(f11,axiom,(
% 0.10/0.53 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f15,axiom,(
% 0.10/0.53 (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f19,axiom,(
% 0.10/0.53 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f22,axiom,(
% 0.10/0.53 (! [A,B,C] :( C = set_difference(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& ~ in(D,B) ) ) )) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f23,axiom,(
% 0.10/0.53 (! [A] :( relation(A)=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(D,C),A) )) )) )) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f64,axiom,(
% 0.10/0.53 ( empty(empty_set)& relation(empty_set) ) ),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f68,axiom,(
% 0.10/0.53 (! [A,B] : set_union2(A,A) = A )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f151,conjecture,(
% 0.10/0.53 ( relation_dom(empty_set) = empty_set& relation_rng(empty_set) = empty_set ) ),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f152,negated_conjecture,(
% 0.10/0.53 ~(( relation_dom(empty_set) = empty_set& relation_rng(empty_set) = empty_set ) )),
% 0.10/0.53 inference(negated_conjecture,[status(cth)],[f151])).
% 0.10/0.53 fof(f209,plain,(
% 0.10/0.53 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.10/0.53 inference(NNF_transformation,[status(thm)],[f11])).
% 0.10/0.53 fof(f210,plain,(
% 0.10/0.53 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f209])).
% 0.10/0.53 fof(f211,plain,(
% 0.10/0.53 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK7_skl(A),A)))),
% 0.10/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(B,sK7_skl(A))],[f210])).
% 0.10/0.53 fof(f212,plain,(
% 0.10/0.53 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f211])).
% 0.10/0.53 fof(f237,plain,(
% 0.10/0.53 ![A,B,C]: ((~C=set_union2(A,B)|(![D]: ((~in(D,C)|(in(D,A)|in(D,B)))&(in(D,C)|(~in(D,A)&~in(D,B))))))&(C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.10/0.53 inference(NNF_transformation,[status(thm)],[f15])).
% 0.10/0.53 fof(f238,plain,(
% 0.10/0.53 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f237])).
% 0.10/0.53 fof(f239,plain,(
% 0.10/0.53 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|((~in(sK10_skl(C,B,A),C)|(~in(sK10_skl(C,B,A),A)&~in(sK10_skl(C,B,A),B)))&(in(sK10_skl(C,B,A),C)|(in(sK10_skl(C,B,A),A)|in(sK10_skl(C,B,A),B))))))),
% 0.10/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(D,sK10_skl(C,B,A))],[f238])).
% 0.10/0.53 fof(f245,plain,(
% 0.10/0.53 ![X0,X1,X2]: (X0=set_union2(X1,X2)|in(sK10_skl(X0,X2,X1),X0)|in(sK10_skl(X0,X2,X1),X1)|in(sK10_skl(X0,X2,X1),X2))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f239])).
% 0.10/0.53 fof(f271,plain,(
% 0.10/0.53 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.10/0.53 fof(f272,plain,(
% 0.10/0.53 ![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)))))))))),
% 0.10/0.53 inference(NNF_transformation,[status(thm)],[f271])).
% 0.10/0.53 fof(f273,plain,(
% 0.10/0.53 ![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)))))))))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f272])).
% 0.10/0.53 fof(f274,plain,(
% 0.10/0.53 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sK18_skl(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sK19_skl(B,A),B)|(![D]: ~in(ordered_pair(sK19_skl(B,A),D),A)))&(in(sK19_skl(B,A),B)|in(ordered_pair(sK19_skl(B,A),sK20_skl(B,A)),A)))))))),
% 0.10/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl]),skolemize(D,sK18_skl(C,B,A)),skolemize(C,sK19_skl(B,A)),skolemize(D,sK20_skl(B,A))],[f273])).
% 0.10/0.53 fof(f275,plain,(
% 0.10/0.53 ![X0,X1,X2]: (~relation(X0)|~X1=relation_dom(X0)|~in(X2,X1)|in(ordered_pair(X2,sK18_skl(X2,X1,X0)),X0))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f274])).
% 0.10/0.53 fof(f289,plain,(
% 0.10/0.53 ![A,B,C]: ((~C=set_difference(A,B)|(![D]: ((~in(D,C)|(in(D,A)&~in(D,B)))&(in(D,C)|(~in(D,A)|in(D,B))))))&(C=set_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 0.10/0.53 inference(NNF_transformation,[status(thm)],[f22])).
% 0.10/0.53 fof(f290,plain,(
% 0.10/0.53 (![A,B,C]: (~C=set_difference(A,B)|((![D]: (~in(D,C)|(in(D,A)&~in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|in(D,B)))))))&(![A,B,C]: (C=set_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f289])).
% 0.10/0.53 fof(f291,plain,(
% 0.10/0.53 (![A,B,C]: (~C=set_difference(A,B)|((![D]: (~in(D,C)|(in(D,A)&~in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|in(D,B)))))))&(![A,B,C]: (C=set_difference(A,B)|((~in(sK24_skl(C,B,A),C)|(~in(sK24_skl(C,B,A),A)|in(sK24_skl(C,B,A),B)))&(in(sK24_skl(C,B,A),C)|(in(sK24_skl(C,B,A),A)&~in(sK24_skl(C,B,A),B))))))),
% 0.10/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(D,sK24_skl(C,B,A))],[f290])).
% 0.10/0.53 fof(f296,plain,(
% 0.10/0.53 ![X0,X1,X2]: (X0=set_difference(X1,X2)|in(sK24_skl(X0,X2,X1),X0)|in(sK24_skl(X0,X2,X1),X1))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f291])).
% 0.10/0.53 fof(f298,plain,(
% 0.10/0.53 ![A]: (~relation(A)|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(D,C),A)))))))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.10/0.53 fof(f299,plain,(
% 0.10/0.53 ![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)))))))))),
% 0.10/0.53 inference(NNF_transformation,[status(thm)],[f298])).
% 0.10/0.53 fof(f300,plain,(
% 0.10/0.53 ![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)))))))))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f299])).
% 0.10/0.53 fof(f301,plain,(
% 0.10/0.53 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|in(ordered_pair(sK25_skl(C,B,A),C),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|((~in(sK26_skl(B,A),B)|(![D]: ~in(ordered_pair(D,sK26_skl(B,A)),A)))&(in(sK26_skl(B,A),B)|in(ordered_pair(sK27_skl(B,A),sK26_skl(B,A)),A)))))))),
% 0.10/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl,sK27_skl]),skolemize(D,sK25_skl(C,B,A)),skolemize(C,sK26_skl(B,A)),skolemize(D,sK27_skl(B,A))],[f300])).
% 0.10/0.53 fof(f302,plain,(
% 0.10/0.53 ![X0,X1,X2]: (~relation(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(ordered_pair(sK25_skl(X2,X1,X0),X2),X0))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f301])).
% 0.10/0.53 fof(f377,plain,(
% 0.10/0.53 relation(empty_set)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f64])).
% 0.10/0.53 fof(f384,plain,(
% 0.10/0.53 ![A]: set_union2(A,A)=A),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f68])).
% 0.10/0.53 fof(f385,plain,(
% 0.10/0.53 ![X0]: (set_union2(X0,X0)=X0)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f384])).
% 0.10/0.53 fof(f605,plain,(
% 0.10/0.53 (~relation_dom(empty_set)=empty_set|~relation_rng(empty_set)=empty_set)),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f152])).
% 0.10/0.53 fof(f606,plain,(
% 0.10/0.53 ~relation_dom(empty_set)=empty_set|~relation_rng(empty_set)=empty_set),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f605])).
% 0.10/0.53 fof(f666,plain,(
% 0.10/0.53 ![X0]: (~in(X0,empty_set))),
% 0.10/0.53 inference(destructive_equality_resolution,[status(thm)],[f212])).
% 0.10/0.53 fof(f680,plain,(
% 0.10/0.53 ![X0,X1]: (~relation(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,sK18_skl(X1,relation_dom(X0),X0)),X0))),
% 0.10/0.53 inference(destructive_equality_resolution,[status(thm)],[f275])).
% 0.10/0.53 fof(f688,plain,(
% 0.10/0.53 ![X0,X1]: (~relation(X0)|~in(X1,relation_rng(X0))|in(ordered_pair(sK25_skl(X1,relation_rng(X0),X0),X1),X0))),
% 0.10/0.53 inference(destructive_equality_resolution,[status(thm)],[f302])).
% 0.10/0.53 fof(f1037,plain,(
% 0.10/0.53 ![X0,X1]: (empty_set=set_union2(X0,X1)|in(sK10_skl(empty_set,X1,X0),X0)|in(sK10_skl(empty_set,X1,X0),X1))),
% 0.10/0.53 inference(resolution,[status(thm)],[f245,f666])).
% 0.10/0.53 fof(f1607,plain,(
% 0.10/0.53 ![X0]: (~in(X0,relation_dom(empty_set))|in(ordered_pair(X0,sK18_skl(X0,relation_dom(empty_set),empty_set)),empty_set))),
% 0.10/0.53 inference(resolution,[status(thm)],[f680,f377])).
% 0.10/0.53 fof(f1608,plain,(
% 0.10/0.53 ![X0]: (~in(X0,relation_dom(empty_set)))),
% 0.10/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1607,f666])).
% 0.10/0.53 fof(f1692,plain,(
% 0.10/0.53 empty_set=set_union2(relation_dom(empty_set),relation_dom(empty_set))),
% 0.10/0.53 inference(resolution,[status(thm)],[f1608,f1037])).
% 0.10/0.53 fof(f1721,plain,(
% 0.10/0.53 empty_set=relation_dom(empty_set)),
% 0.10/0.53 inference(forward_demodulation,[status(thm)],[f385,f1692])).
% 0.10/0.53 fof(f1889,plain,(
% 0.10/0.53 ~empty_set=empty_set|~relation_rng(empty_set)=empty_set),
% 0.10/0.53 inference(backward_demodulation,[status(thm)],[f1721,f606])).
% 0.10/0.53 fof(f1896,plain,(
% 0.10/0.53 ~relation_rng(empty_set)=empty_set),
% 0.10/0.53 inference(trivial_equality_resolution,[status(thm)],[f1889])).
% 0.10/0.53 fof(f2225,plain,(
% 0.10/0.53 ![X0]: (empty_set=set_difference(empty_set,X0))),
% 0.10/0.53 inference(resolution,[status(thm)],[f296,f666])).
% 0.10/0.53 fof(f2244,plain,(
% 0.10/0.53 ![X0,X1]: (X0=set_difference(empty_set,X1)|in(sK24_skl(X0,X1,empty_set),X0))),
% 0.10/0.53 inference(resolution,[status(thm)],[f296,f666])).
% 0.10/0.53 fof(f2263,plain,(
% 0.10/0.53 ![X0]: (~in(X0,relation_rng(empty_set))|in(ordered_pair(sK25_skl(X0,relation_rng(empty_set),empty_set),X0),empty_set))),
% 0.10/0.53 inference(resolution,[status(thm)],[f688,f377])).
% 0.10/0.53 fof(f2264,plain,(
% 0.10/0.53 ![X0]: (~in(X0,relation_rng(empty_set)))),
% 0.10/0.53 inference(forward_subsumption_resolution,[status(thm)],[f2263,f666])).
% 0.10/0.53 fof(f2365,plain,(
% 0.10/0.53 ![X0,X1]: (X0=empty_set|in(sK24_skl(X0,X1,empty_set),X0))),
% 0.10/0.53 inference(forward_demodulation,[status(thm)],[f2225,f2244])).
% 0.10/0.53 fof(f2386,plain,(
% 0.10/0.53 relation_rng(empty_set)=empty_set),
% 0.10/0.53 inference(resolution,[status(thm)],[f2264,f2365])).
% 0.10/0.53 fof(f2438,plain,(
% 0.10/0.53 $false),
% 0.10/0.53 inference(forward_subsumption_resolution,[status(thm)],[f2386,f1896])).
% 0.10/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.45/0.55 % Elapsed time: 0.179784 seconds
% 0.45/0.55 % CPU time: 0.943764 seconds
% 0.45/0.55 % Total memory used: 125.786 MB
% 0.45/0.55 % Net memory used: 123.958 MB
%------------------------------------------------------------------------------