%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU154+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 : 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 02:21:49 PM UTC 2026
% Result : Theorem 3.82s 0.92s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU154+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % 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
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:55:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 3.82/0.92 % Refutation found
% 3.82/0.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.82/0.92 % SZS output start CNFRefutation for theBenchmark
% 3.82/0.92 fof(f2,axiom,(
% 3.82/0.92 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 3.82/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.82/0.92 fof(f3,axiom,(
% 3.82/0.92 (! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
% 3.82/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.82/0.92 fof(f4,axiom,(
% 3.82/0.92 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 3.82/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.82/0.92 fof(f5,axiom,(
% 3.82/0.92 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 3.82/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.82/0.92 fof(f6,axiom,(
% 3.82/0.92 (! [A,B,C] :( C = set_intersection2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& in(D,B) ) ) )) )),
% 3.82/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.82/0.92 fof(f7,axiom,(
% 3.82/0.92 (! [A,B] :( disjoint(A,B)<=> set_intersection2(A,B) = empty_set ) )),
% 3.82/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.82/0.92 fof(f13,conjecture,(
% 3.82/0.92 (! [A,B] :( ~ in(A,B)=> disjoint(singleton(A),B) ) )),
% 3.82/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.82/0.92 fof(f14,negated_conjecture,(
% 3.82/0.92 ~((! [A,B] :( ~ in(A,B)=> disjoint(singleton(A),B) ) ))),
% 3.82/0.92 inference(negated_conjecture,[status(cth)],[f13])).
% 3.82/0.92 fof(f19,axiom,(
% 3.82/0.92 (! [A] : subset(empty_set,A) )),
% 3.82/0.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.82/0.92 fof(f22,plain,(
% 3.82/0.92 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 3.82/0.92 inference(cnf_transformation,[status(thm)],[f2])).
% 3.82/0.92 fof(f23,plain,(
% 3.82/0.92 ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
% 3.82/0.92 inference(NNF_transformation,[status(thm)],[f3])).
% 3.82/0.92 fof(f24,plain,(
% 3.82/0.92 (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
% 3.82/0.92 inference(miniscoping,[status(thm)],[f23])).
% 3.82/0.92 fof(f27,plain,(
% 3.82/0.92 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 3.82/0.92 inference(cnf_transformation,[status(thm)],[f24])).
% 3.82/0.92 fof(f28,plain,(
% 3.82/0.92 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 3.82/0.92 inference(NNF_transformation,[status(thm)],[f4])).
% 3.82/0.92 fof(f29,plain,(
% 3.82/0.92 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 3.82/0.92 inference(miniscoping,[status(thm)],[f28])).
% 3.82/0.92 fof(f30,plain,(
% 3.82/0.92 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sK0_skl(B,A),B)|~sK0_skl(B,A)=A)&(in(sK0_skl(B,A),B)|sK0_skl(B,A)=A))))),
% 3.82/0.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f29])).
% 3.82/0.92 fof(f31,plain,(
% 3.82/0.92 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 3.82/0.92 inference(cnf_transformation,[status(thm)],[f30])).
% 3.82/0.92 fof(f35,plain,(
% 3.82/0.92 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 3.82/0.92 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 3.82/0.92 fof(f36,plain,(
% 3.82/0.92 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 3.82/0.92 inference(NNF_transformation,[status(thm)],[f35])).
% 3.82/0.92 fof(f37,plain,(
% 3.82/0.92 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 3.82/0.92 inference(miniscoping,[status(thm)],[f36])).
% 3.82/0.92 fof(f38,plain,(
% 3.82/0.92 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK1_skl(B,A),A)&~in(sK1_skl(B,A),B))))),
% 3.82/0.92 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f37])).
% 3.82/0.92 fof(f40,plain,(
% 3.82/0.92 ![X0,X1]: (subset(X0,X1)|in(sK1_skl(X1,X0),X0))),
% 3.82/0.92 inference(cnf_transformation,[status(thm)],[f38])).
% 3.82/0.92 fof(f42,plain,(
% 3.82/0.92 ![A,B,C]: ((~C=set_intersection2(A,B)|(![D]: ((~in(D,C)|(in(D,A)&in(D,B)))&(in(D,C)|(~in(D,A)|~in(D,B))))))&(C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 3.82/0.92 inference(NNF_transformation,[status(thm)],[f6])).
% 3.82/0.92 fof(f43,plain,(
% 3.82/0.92 (![A,B,C]: (~C=set_intersection2(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_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 3.82/0.93 inference(miniscoping,[status(thm)],[f42])).
% 3.82/0.93 fof(f44,plain,(
% 3.82/0.93 (![A,B,C]: (~C=set_intersection2(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_intersection2(A,B)|((~in(sK2_skl(C,B,A),C)|(~in(sK2_skl(C,B,A),A)|~in(sK2_skl(C,B,A),B)))&(in(sK2_skl(C,B,A),C)|(in(sK2_skl(C,B,A),A)&in(sK2_skl(C,B,A),B))))))),
% 3.82/0.93 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f43])).
% 3.82/0.93 fof(f45,plain,(
% 3.82/0.93 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X1))),
% 3.82/0.93 inference(cnf_transformation,[status(thm)],[f44])).
% 3.82/0.93 fof(f46,plain,(
% 3.82/0.93 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X2))),
% 3.82/0.93 inference(cnf_transformation,[status(thm)],[f44])).
% 3.82/0.93 fof(f51,plain,(
% 3.82/0.93 ![A,B]: ((~disjoint(A,B)|set_intersection2(A,B)=empty_set)&(disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 3.82/0.93 inference(NNF_transformation,[status(thm)],[f7])).
% 3.82/0.93 fof(f52,plain,(
% 3.82/0.93 (![A,B]: (~disjoint(A,B)|set_intersection2(A,B)=empty_set))&(![A,B]: (disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 3.82/0.93 inference(miniscoping,[status(thm)],[f51])).
% 3.82/0.93 fof(f54,plain,(
% 3.82/0.93 ![X0,X1]: (disjoint(X0,X1)|~set_intersection2(X0,X1)=empty_set)),
% 3.82/0.93 inference(cnf_transformation,[status(thm)],[f52])).
% 3.82/0.93 fof(f58,plain,(
% 3.82/0.93 (?[A,B]: (~in(A,B)&~disjoint(singleton(A),B)))),
% 3.82/0.93 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 3.82/0.93 fof(f59,plain,(
% 3.82/0.93 (~in(sK3_skl,sK4_skl)&~disjoint(singleton(sK3_skl),sK4_skl))),
% 3.82/0.93 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f58])).
% 3.82/0.93 fof(f60,plain,(
% 3.82/0.93 ~in(sK3_skl,sK4_skl)),
% 3.82/0.93 inference(cnf_transformation,[status(thm)],[f59])).
% 3.82/0.93 fof(f61,plain,(
% 3.82/0.93 ~disjoint(singleton(sK3_skl),sK4_skl)),
% 3.82/0.93 inference(cnf_transformation,[status(thm)],[f59])).
% 3.82/0.93 fof(f70,plain,(
% 3.82/0.93 ![X0]: (subset(empty_set,X0))),
% 3.82/0.93 inference(cnf_transformation,[status(thm)],[f19])).
% 3.82/0.93 fof(f73,plain,(
% 3.82/0.93 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 3.82/0.93 inference(destructive_equality_resolution,[status(thm)],[f31])).
% 3.82/0.93 fof(f75,plain,(
% 3.82/0.93 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X1))),
% 3.82/0.93 inference(destructive_equality_resolution,[status(thm)],[f45])).
% 3.82/0.93 fof(f76,plain,(
% 3.82/0.93 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X2))),
% 3.82/0.93 inference(destructive_equality_resolution,[status(thm)],[f46])).
% 3.82/0.93 fof(f85,plain,(
% 3.82/0.93 ![X0]: (X0=empty_set|~subset(X0,empty_set))),
% 3.82/0.93 inference(resolution,[status(thm)],[f70,f27])).
% 3.82/0.93 fof(f90,plain,(
% 3.82/0.93 ![X0,X1]: (disjoint(X0,X1)|~set_intersection2(X1,X0)=empty_set)),
% 3.82/0.93 inference(paramodulation,[status(thm)],[f22,f54])).
% 3.82/0.93 fof(f110,plain,(
% 3.82/0.93 ![X0,X1,X2]: (subset(set_intersection2(X0,X1),X2)|in(sK1_skl(X2,set_intersection2(X0,X1)),X1))),
% 3.82/0.93 inference(resolution,[status(thm)],[f40,f76])).
% 3.82/0.93 fof(f111,plain,(
% 3.82/0.93 ![X0,X1,X2]: (subset(set_intersection2(X0,X1),X2)|in(sK1_skl(X2,set_intersection2(X0,X1)),X0))),
% 3.82/0.93 inference(resolution,[status(thm)],[f40,f75])).
% 3.82/0.93 fof(f760,plain,(
% 3.82/0.93 ![X0,X1,X2]: (subset(set_intersection2(X0,singleton(X1)),X2)|sK1_skl(X2,set_intersection2(X0,singleton(X1)))=X1)),
% 3.82/0.93 inference(resolution,[status(thm)],[f110,f73])).
% 3.82/0.93 fof(f1099,plain,(
% 3.82/0.93 ![X0,X1]: (sK1_skl(empty_set,set_intersection2(X0,singleton(X1)))=X1|set_intersection2(X0,singleton(X1))=empty_set)),
% 3.82/0.93 inference(resolution,[status(thm)],[f760,f85])).
% 3.82/0.93 fof(f1267,plain,(
% 3.82/0.93 ![X0,X1]: (subset(set_intersection2(X0,singleton(X1)),empty_set)|in(X1,X0)|set_intersection2(X0,singleton(X1))=empty_set)),
% 3.82/0.93 inference(paramodulation,[status(thm)],[f1099,f111])).
% 3.82/0.93 fof(f1274,plain,(
% 3.82/0.93 ![X0,X1]: (in(X0,X1)|set_intersection2(X1,singleton(X0))=empty_set)),
% 3.82/0.93 inference(forward_subsumption_resolution,[status(thm)],[f1267,f85])).
% 3.82/0.93 fof(f1280,plain,(
% 3.82/0.93 set_intersection2(sK4_skl,singleton(sK3_skl))=empty_set),
% 3.82/0.93 inference(resolution,[status(thm)],[f1274,f60])).
% 3.82/0.93 fof(f1732,plain,(
% 3.82/0.93 disjoint(singleton(sK3_skl),sK4_skl)),
% 3.82/0.93 inference(resolution,[status(thm)],[f1280,f90])).
% 3.82/0.93 fof(f1763,plain,(
% 3.82/0.93 $false),
% 3.82/0.93 inference(forward_subsumption_resolution,[status(thm)],[f1732,f61])).
% 3.82/0.93 % SZS output end CNFRefutation for theBenchmark.p
% 3.82/0.94 % Elapsed time: 0.562561 seconds
% 3.82/0.94 % CPU time: 4.151754 seconds
% 3.82/0.94 % Total memory used: 140.112 MB
% 3.82/0.94 % Net memory used: 132.356 MB
%------------------------------------------------------------------------------