%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU131+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 : n026.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 02:21:44 PM UTC 2026
% Result : Theorem 6.36s 1.24s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU131+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 : n026.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
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:54:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 6.36/1.24 % Refutation found
% 6.36/1.24 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.36/1.24 % SZS output start CNFRefutation for theBenchmark
% 6.36/1.24 fof(f5,axiom,(
% 6.36/1.24 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 6.36/1.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.36/1.24 fof(f7,axiom,(
% 6.36/1.24 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 6.36/1.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.36/1.24 fof(f9,axiom,(
% 6.36/1.24 (! [A,B,C] :( C = set_difference(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& ~ in(D,B) ) ) )) )),
% 6.36/1.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.36/1.24 fof(f15,axiom,(
% 6.36/1.24 empty(empty_set) ),
% 6.36/1.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.36/1.24 fof(f20,conjecture,(
% 6.36/1.24 (! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) )),
% 6.36/1.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.36/1.24 fof(f21,negated_conjecture,(
% 6.36/1.24 ~((! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) ))),
% 6.36/1.24 inference(negated_conjecture,[status(cth)],[f20])).
% 6.36/1.24 fof(f42,axiom,(
% 6.36/1.24 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 6.36/1.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 6.36/1.24 fof(f55,plain,(
% 6.36/1.24 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 6.36/1.24 inference(NNF_transformation,[status(thm)],[f5])).
% 6.36/1.24 fof(f56,plain,(
% 6.36/1.24 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 6.36/1.24 inference(miniscoping,[status(thm)],[f55])).
% 6.36/1.24 fof(f57,plain,(
% 6.36/1.24 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK0_skl(A),A)))),
% 6.36/1.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f56])).
% 6.36/1.24 fof(f59,plain,(
% 6.36/1.24 ![X0]: (X0=empty_set|in(sK0_skl(X0),X0))),
% 6.36/1.24 inference(cnf_transformation,[status(thm)],[f57])).
% 6.36/1.24 fof(f69,plain,(
% 6.36/1.24 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 6.36/1.24 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 6.36/1.24 fof(f70,plain,(
% 6.36/1.24 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 6.36/1.24 inference(NNF_transformation,[status(thm)],[f69])).
% 6.36/1.24 fof(f71,plain,(
% 6.36/1.24 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 6.36/1.24 inference(miniscoping,[status(thm)],[f70])).
% 6.36/1.24 fof(f72,plain,(
% 6.36/1.24 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK2_skl(B,A),A)&~in(sK2_skl(B,A),B))))),
% 6.36/1.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f71])).
% 6.36/1.24 fof(f73,plain,(
% 6.36/1.24 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 6.36/1.24 inference(cnf_transformation,[status(thm)],[f72])).
% 6.36/1.24 fof(f74,plain,(
% 6.36/1.24 ![X0,X1]: (subset(X0,X1)|in(sK2_skl(X1,X0),X0))),
% 6.36/1.24 inference(cnf_transformation,[status(thm)],[f72])).
% 6.36/1.24 fof(f75,plain,(
% 6.36/1.24 ![X0,X1]: (subset(X0,X1)|~in(sK2_skl(X1,X0),X1))),
% 6.36/1.24 inference(cnf_transformation,[status(thm)],[f72])).
% 6.36/1.24 fof(f85,plain,(
% 6.36/1.24 ![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)))))))),
% 6.36/1.24 inference(NNF_transformation,[status(thm)],[f9])).
% 6.36/1.24 fof(f86,plain,(
% 6.36/1.24 (![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)))))))),
% 6.36/1.24 inference(miniscoping,[status(thm)],[f85])).
% 6.36/1.24 fof(f87,plain,(
% 6.36/1.24 (![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(sK4_skl(C,B,A),C)|(~in(sK4_skl(C,B,A),A)|in(sK4_skl(C,B,A),B)))&(in(sK4_skl(C,B,A),C)|(in(sK4_skl(C,B,A),A)&~in(sK4_skl(C,B,A),B))))))),
% 6.36/1.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f86])).
% 6.36/1.24 fof(f88,plain,(
% 6.36/1.24 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|~in(X3,X0)|in(X3,X1))),
% 6.36/1.24 inference(cnf_transformation,[status(thm)],[f87])).
% 6.36/1.24 fof(f89,plain,(
% 6.36/1.24 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|~in(X3,X0)|~in(X3,X2))),
% 6.36/1.24 inference(cnf_transformation,[status(thm)],[f87])).
% 6.36/1.24 fof(f90,plain,(
% 6.36/1.24 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|in(X3,X0)|~in(X3,X1)|in(X3,X2))),
% 6.36/1.26 inference(cnf_transformation,[status(thm)],[f87])).
% 6.36/1.26 fof(f98,plain,(
% 6.36/1.26 empty(empty_set)),
% 6.36/1.26 inference(cnf_transformation,[status(thm)],[f15])).
% 6.36/1.26 fof(f109,plain,(
% 6.36/1.26 (?[A,B]: (set_difference(A,B)=empty_set<~>subset(A,B)))),
% 6.36/1.26 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 6.36/1.26 fof(f110,plain,(
% 6.36/1.26 ?[A,B]: ((set_difference(A,B)=empty_set|subset(A,B))&(~set_difference(A,B)=empty_set|~subset(A,B)))),
% 6.36/1.26 inference(NNF_transformation,[status(thm)],[f109])).
% 6.36/1.26 fof(f111,plain,(
% 6.36/1.26 ((set_difference(sK5_skl,sK6_skl)=empty_set|subset(sK5_skl,sK6_skl))&(~set_difference(sK5_skl,sK6_skl)=empty_set|~subset(sK5_skl,sK6_skl)))),
% 6.36/1.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f110])).
% 6.36/1.26 fof(f112,plain,(
% 6.36/1.26 set_difference(sK5_skl,sK6_skl)=empty_set|subset(sK5_skl,sK6_skl)),
% 6.36/1.26 inference(cnf_transformation,[status(thm)],[f111])).
% 6.36/1.26 fof(f113,plain,(
% 6.36/1.26 ~set_difference(sK5_skl,sK6_skl)=empty_set|~subset(sK5_skl,sK6_skl)),
% 6.36/1.26 inference(cnf_transformation,[status(thm)],[f111])).
% 6.36/1.26 fof(f160,plain,(
% 6.36/1.26 ![A,B]: (~in(A,B)|~empty(B))),
% 6.36/1.26 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 6.36/1.26 fof(f161,plain,(
% 6.36/1.26 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 6.36/1.26 inference(miniscoping,[status(thm)],[f160])).
% 6.36/1.26 fof(f162,plain,(
% 6.36/1.26 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 6.36/1.26 inference(cnf_transformation,[status(thm)],[f161])).
% 6.36/1.26 fof(f178,plain,(
% 6.36/1.26 ![X0,X1,X2]: (~in(X0,set_difference(X1,X2))|in(X0,X1))),
% 6.36/1.26 inference(destructive_equality_resolution,[status(thm)],[f88])).
% 6.36/1.26 fof(f179,plain,(
% 6.36/1.26 ![X0,X1,X2]: (~in(X0,set_difference(X1,X2))|~in(X0,X2))),
% 6.36/1.26 inference(destructive_equality_resolution,[status(thm)],[f89])).
% 6.36/1.26 fof(f180,plain,(
% 6.36/1.26 ![X0,X1,X2]: (in(X0,set_difference(X1,X2))|~in(X0,X1)|in(X0,X2))),
% 6.36/1.26 inference(destructive_equality_resolution,[status(thm)],[f90])).
% 6.36/1.26 fof(f238,plain,(
% 6.36/1.26 ![X0]: (set_difference(sK5_skl,sK6_skl)=empty_set|~in(X0,sK5_skl)|in(X0,sK6_skl))),
% 6.36/1.26 inference(resolution,[status(thm)],[f112,f73])).
% 6.36/1.26 fof(f241,plain,(
% 6.36/1.26 ![X0,X1]: (set_difference(X0,X1)=empty_set|~in(sK0_skl(set_difference(X0,X1)),X1))),
% 6.36/1.26 inference(resolution,[status(thm)],[f59,f179])).
% 6.36/1.26 fof(f242,plain,(
% 6.36/1.26 ![X0,X1]: (set_difference(X0,X1)=empty_set|in(sK0_skl(set_difference(X0,X1)),X0))),
% 6.36/1.26 inference(resolution,[status(thm)],[f59,f178])).
% 6.36/1.26 fof(f306,plain,(
% 6.36/1.26 ![X0]: (set_difference(sK5_skl,X0)=empty_set|set_difference(sK5_skl,sK6_skl)=empty_set|in(sK0_skl(set_difference(sK5_skl,X0)),sK6_skl))),
% 6.36/1.26 inference(resolution,[status(thm)],[f242,f238])).
% 6.36/1.26 fof(f629,plain,(
% 6.36/1.26 ![X0,X1,X2]: (subset(X0,X1)|in(sK2_skl(X1,X0),set_difference(X0,X2))|in(sK2_skl(X1,X0),X2))),
% 6.36/1.26 inference(resolution,[status(thm)],[f74,f180])).
% 6.36/1.26 fof(f1030,plain,(
% 6.36/1.26 ![X0,X1,X2]: (subset(X0,X1)|in(sK2_skl(X1,X0),X2)|~empty(set_difference(X0,X2)))),
% 6.36/1.26 inference(resolution,[status(thm)],[f629,f162])).
% 6.36/1.26 fof(f4360,plain,(
% 6.36/1.26 set_difference(sK5_skl,sK6_skl)=empty_set|set_difference(sK5_skl,sK6_skl)=empty_set|set_difference(sK5_skl,sK6_skl)=empty_set),
% 6.36/1.26 inference(resolution,[status(thm)],[f241,f306])).
% 6.36/1.26 fof(f4379,plain,(
% 6.36/1.26 set_difference(sK5_skl,sK6_skl)=empty_set),
% 6.36/1.26 inference(duplicate_literals_removal,[status(thm)],[f4360])).
% 6.36/1.26 fof(f7232,plain,(
% 6.36/1.26 ~empty_set=empty_set|~subset(sK5_skl,sK6_skl)),
% 6.36/1.26 inference(backward_demodulation,[status(thm)],[f4379,f113])).
% 6.36/1.26 fof(f7281,plain,(
% 6.36/1.26 ![X0]: (subset(sK5_skl,X0)|in(sK2_skl(X0,sK5_skl),sK6_skl)|~empty(empty_set))),
% 6.36/1.26 inference(paramodulation,[status(thm)],[f4379,f1030])).
% 6.36/1.26 fof(f7328,plain,(
% 6.36/1.26 ~subset(sK5_skl,sK6_skl)),
% 6.36/1.26 inference(trivial_equality_resolution,[status(thm)],[f7232])).
% 6.36/1.26 fof(f7410,plain,(
% 6.36/1.26 ![X0]: (subset(sK5_skl,X0)|in(sK2_skl(X0,sK5_skl),sK6_skl))),
% 6.36/1.26 inference(forward_subsumption_resolution,[status(thm)],[f7281,f98])).
% 6.36/1.26 fof(f8619,plain,(
% 6.36/1.26 subset(sK5_skl,sK6_skl)|subset(sK5_skl,sK6_skl)),
% 6.36/1.26 inference(resolution,[status(thm)],[f7410,f75])).
% 6.36/1.26 fof(f8626,plain,(
% 6.36/1.26 subset(sK5_skl,sK6_skl)),
% 6.36/1.26 inference(duplicate_literals_removal,[status(thm)],[f8619])).
% 6.36/1.26 fof(f8627,plain,(
% 6.36/1.26 $false),
% 6.36/1.26 inference(forward_subsumption_resolution,[status(thm)],[f8626,f7328])).
% 6.36/1.26 % SZS output end CNFRefutation for theBenchmark.p
% 6.36/1.26 % Elapsed time: 0.886542 seconds
% 6.36/1.27 % CPU time: 6.783082 seconds
% 6.36/1.27 % Total memory used: 160.567 MB
% 6.36/1.27 % Net memory used: 150.595 MB
%------------------------------------------------------------------------------