%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 02:12:22 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:36:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.41 fof(f1,axiom,(
% 0.10/0.41 (! [B,C] : subset(intersection(B,C),B) )),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f2,axiom,(
% 0.10/0.41 (! [B,C] :( difference(B,C) = empty_set<=> subset(B,C) ) )),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f3,axiom,(
% 0.10/0.41 (! [B] : union(B,empty_set) = B )),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f4,axiom,(
% 0.10/0.41 (! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)) )),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f5,axiom,(
% 0.10/0.41 (! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),D) )),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f9,axiom,(
% 0.10/0.41 (! [B,C] : union(B,C) = union(C,B) )),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f16,conjecture,(
% 0.10/0.41 (! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)) )),
% 0.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f17,negated_conjecture,(
% 0.10/0.41 ~((! [B,C,D] : intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D)) ))),
% 0.10/0.41 inference(negated_conjecture,[status(cth)],[f16])).
% 0.10/0.41 fof(f18,plain,(
% 0.10/0.41 ![X0,X1]: (subset(intersection(X0,X1),X0))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.41 fof(f19,plain,(
% 0.10/0.41 ![B,C]: ((~difference(B,C)=empty_set|subset(B,C))&(difference(B,C)=empty_set|~subset(B,C)))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f2])).
% 0.10/0.41 fof(f20,plain,(
% 0.10/0.41 (![B,C]: (~difference(B,C)=empty_set|subset(B,C)))&(![B,C]: (difference(B,C)=empty_set|~subset(B,C)))),
% 0.10/0.41 inference(miniscoping,[status(thm)],[f19])).
% 0.10/0.41 fof(f22,plain,(
% 0.10/0.41 ![X0,X1]: (difference(X0,X1)=empty_set|~subset(X0,X1))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f20])).
% 0.10/0.41 fof(f23,plain,(
% 0.10/0.41 ![X0]: (union(X0,empty_set)=X0)),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.41 fof(f24,plain,(
% 0.10/0.41 ![X0,X1,X2]: (difference(X0,intersection(X1,X2))=union(difference(X0,X1),difference(X0,X2)))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.41 fof(f25,plain,(
% 0.10/0.41 ![X0,X1,X2]: (intersection(X0,difference(X1,X2))=difference(intersection(X0,X1),X2))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f5])).
% 0.10/0.41 fof(f41,plain,(
% 0.10/0.41 ![X0,X1]: (union(X0,X1)=union(X1,X0))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.10/0.41 fof(f64,plain,(
% 0.10/0.41 (?[B,C,D]: ~intersection(B,difference(C,D))=difference(intersection(B,C),intersection(B,D)))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.10/0.41 fof(f65,plain,(
% 0.10/0.41 ~intersection(sK3_skl,difference(sK4_skl,sK5_skl))=difference(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f64])).
% 0.10/0.41 fof(f66,plain,(
% 0.10/0.41 ~intersection(sK3_skl,difference(sK4_skl,sK5_skl))=difference(intersection(sK3_skl,sK4_skl),intersection(sK3_skl,sK5_skl))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f65])).
% 0.10/0.41 fof(f69,plain,(
% 0.10/0.41 ~intersection(sK3_skl,difference(sK4_skl,sK5_skl))=intersection(sK3_skl,difference(sK4_skl,intersection(sK3_skl,sK5_skl)))),
% 0.10/0.41 inference(forward_demodulation,[status(thm)],[f25,f66])).
% 0.10/0.41 fof(f86,plain,(
% 0.10/0.41 ![X0,X1]: (difference(intersection(X0,X1),X0)=empty_set)),
% 0.10/0.41 inference(resolution,[status(thm)],[f22,f18])).
% 0.10/0.41 fof(f90,plain,(
% 0.10/0.41 ![X0,X1]: (intersection(X0,difference(X1,X0))=empty_set)),
% 0.10/0.41 inference(forward_demodulation,[status(thm)],[f25,f86])).
% 0.10/0.41 fof(f92,plain,(
% 0.10/0.41 ![X0,X1,X2,X3]: (difference(intersection(X0,X1),intersection(X2,X3))=union(intersection(X0,difference(X1,X2)),difference(intersection(X0,X1),X3)))),
% 0.10/0.41 inference(paramodulation,[status(thm)],[f25,f24])).
% 0.10/0.41 fof(f94,plain,(
% 0.10/0.41 ![X0,X1,X2,X3]: (intersection(X0,difference(X1,intersection(X2,X3)))=union(intersection(X0,difference(X1,X2)),difference(intersection(X0,X1),X3)))),
% 0.10/0.41 inference(forward_demodulation,[status(thm)],[f25,f92])).
% 0.10/0.41 fof(f95,plain,(
% 0.10/0.41 ![X0,X1,X2,X3]: (intersection(X0,difference(X1,intersection(X2,X3)))=union(intersection(X0,difference(X1,X2)),intersection(X0,difference(X1,X3))))),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f25,f94])).
% 0.14/0.42 fof(f185,plain,(
% 0.14/0.42 ![X0,X1,X2]: (intersection(X0,difference(X1,intersection(X0,X2)))=union(empty_set,intersection(X0,difference(X1,X2))))),
% 0.14/0.42 inference(paramodulation,[status(thm)],[f90,f95])).
% 0.14/0.42 fof(f249,plain,(
% 0.14/0.42 ![X0]: (X0=union(empty_set,X0))),
% 0.14/0.42 inference(paramodulation,[status(thm)],[f23,f41])).
% 0.14/0.42 fof(f265,plain,(
% 0.14/0.42 ![X0,X1,X2]: (intersection(X0,difference(X1,intersection(X0,X2)))=intersection(X0,difference(X1,X2)))),
% 0.14/0.42 inference(backward_demodulation,[status(thm)],[f249,f185])).
% 0.14/0.42 fof(f266,plain,(
% 0.14/0.42 ~intersection(sK3_skl,difference(sK4_skl,sK5_skl))=intersection(sK3_skl,difference(sK4_skl,sK5_skl))),
% 0.14/0.42 inference(backward_demodulation,[status(thm)],[f265,f69])).
% 0.14/0.42 fof(f267,plain,(
% 0.14/0.42 $false),
% 0.14/0.42 inference(trivial_equality_resolution,[status(thm)],[f266])).
% 0.14/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.47 % Elapsed time: 0.089678 seconds
% 0.14/0.47 % CPU time: 0.210950 seconds
% 0.14/0.47 % Total memory used: 39.523 MB
% 0.14/0.47 % Net memory used: 39.395 MB
%------------------------------------------------------------------------------