%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 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 02:12:16 PM UTC 2026
% Result : Theorem 13.43s 2.22s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.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 05:30:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 13.43/2.22 % Refutation found
% 13.43/2.22 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.43/2.22 % SZS output start CNFRefutation for theBenchmark
% 13.43/2.22 fof(f1,axiom,(
% 13.43/2.22 (! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)) )),
% 13.43/2.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.43/2.22 fof(f2,axiom,(
% 13.43/2.22 (! [B] : intersection(B,B) = B )),
% 13.43/2.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.43/2.22 fof(f3,axiom,(
% 13.43/2.22 (! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)) )),
% 13.43/2.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.43/2.22 fof(f4,axiom,(
% 13.43/2.22 (! [B,C] : union(B,intersection(B,C)) = B )),
% 13.43/2.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.43/2.22 fof(f5,axiom,(
% 13.43/2.22 (! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)) )),
% 13.43/2.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.43/2.22 fof(f9,axiom,(
% 13.43/2.22 (! [B,C] : union(B,C) = union(C,B) )),
% 13.43/2.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.43/2.22 fof(f10,axiom,(
% 13.43/2.22 (! [B,C] : intersection(B,C) = intersection(C,B) )),
% 13.43/2.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.43/2.22 fof(f14,conjecture,(
% 13.43/2.22 (! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)) )),
% 13.43/2.22 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.43/2.22 fof(f15,negated_conjecture,(
% 13.43/2.22 ~((! [B,C,D] : union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B)) ))),
% 13.43/2.22 inference(negated_conjecture,[status(cth)],[f14])).
% 13.43/2.22 fof(f16,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(union(X0,X1),X2)=union(X0,union(X1,X2)))),
% 13.43/2.22 inference(cnf_transformation,[status(thm)],[f1])).
% 13.43/2.22 fof(f17,plain,(
% 13.43/2.22 ![X0]: (intersection(X0,X0)=X0)),
% 13.43/2.22 inference(cnf_transformation,[status(thm)],[f2])).
% 13.43/2.22 fof(f18,plain,(
% 13.43/2.22 ![X0,X1,X2]: (intersection(intersection(X0,X1),X2)=intersection(X0,intersection(X1,X2)))),
% 13.43/2.22 inference(cnf_transformation,[status(thm)],[f3])).
% 13.43/2.22 fof(f19,plain,(
% 13.43/2.22 ![X0,X1]: (union(X0,intersection(X0,X1))=X0)),
% 13.43/2.22 inference(cnf_transformation,[status(thm)],[f4])).
% 13.43/2.22 fof(f20,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(X0,intersection(X1,X2))=intersection(union(X0,X1),union(X0,X2)))),
% 13.43/2.22 inference(cnf_transformation,[status(thm)],[f5])).
% 13.43/2.22 fof(f36,plain,(
% 13.43/2.22 ![X0,X1]: (union(X0,X1)=union(X1,X0))),
% 13.43/2.22 inference(cnf_transformation,[status(thm)],[f9])).
% 13.43/2.22 fof(f37,plain,(
% 13.43/2.22 ![X0,X1]: (intersection(X0,X1)=intersection(X1,X0))),
% 13.43/2.22 inference(cnf_transformation,[status(thm)],[f10])).
% 13.43/2.22 fof(f53,plain,(
% 13.43/2.22 (?[B,C,D]: ~union(union(intersection(B,C),intersection(C,D)),intersection(D,B))=intersection(intersection(union(B,C),union(C,D)),union(D,B)))),
% 13.43/2.22 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 13.43/2.22 fof(f54,plain,(
% 13.43/2.22 ~union(union(intersection(sK2_skl,sK3_skl),intersection(sK3_skl,sK4_skl)),intersection(sK4_skl,sK2_skl))=intersection(intersection(union(sK2_skl,sK3_skl),union(sK3_skl,sK4_skl)),union(sK4_skl,sK2_skl))),
% 13.43/2.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f53])).
% 13.43/2.22 fof(f55,plain,(
% 13.43/2.22 ~union(union(intersection(sK2_skl,sK3_skl),intersection(sK3_skl,sK4_skl)),intersection(sK4_skl,sK2_skl))=intersection(intersection(union(sK2_skl,sK3_skl),union(sK3_skl,sK4_skl)),union(sK4_skl,sK2_skl))),
% 13.43/2.22 inference(cnf_transformation,[status(thm)],[f54])).
% 13.43/2.22 fof(f58,plain,(
% 13.43/2.22 ~union(intersection(sK2_skl,sK3_skl),union(intersection(sK3_skl,sK4_skl),intersection(sK4_skl,sK2_skl)))=intersection(intersection(union(sK2_skl,sK3_skl),union(sK3_skl,sK4_skl)),union(sK4_skl,sK2_skl))),
% 13.43/2.22 inference(forward_demodulation,[status(thm)],[f16,f55])).
% 13.43/2.22 fof(f59,plain,(
% 13.43/2.22 ~union(intersection(sK2_skl,sK3_skl),union(intersection(sK3_skl,sK4_skl),intersection(sK4_skl,sK2_skl)))=intersection(union(sK2_skl,sK3_skl),intersection(union(sK3_skl,sK4_skl),union(sK4_skl,sK2_skl)))),
% 13.43/2.22 inference(forward_demodulation,[status(thm)],[f18,f58])).
% 13.43/2.22 fof(f60,plain,(
% 13.43/2.22 ![X0]: (union(X0,X0)=X0)),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f17,f19])).
% 13.43/2.22 fof(f64,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(X0,X1)=union(X0,union(intersection(X0,X2),X1)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f19,f16])).
% 13.43/2.22 fof(f70,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(X0,union(X1,X2))=union(X2,union(X0,X1)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f16,f36])).
% 13.43/2.22 fof(f87,plain,(
% 13.43/2.22 ~union(intersection(sK3_skl,sK2_skl),union(intersection(sK3_skl,sK4_skl),intersection(sK4_skl,sK2_skl)))=intersection(union(sK2_skl,sK3_skl),intersection(union(sK3_skl,sK4_skl),union(sK4_skl,sK2_skl)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f37,f59])).
% 13.43/2.22 fof(f88,plain,(
% 13.43/2.22 ![X0,X1]: (union(X0,intersection(X1,X0))=X0)),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f37,f19])).
% 13.43/2.22 fof(f127,plain,(
% 13.43/2.22 ![X0,X1,X2]: (intersection(X0,intersection(X1,X2))=intersection(X1,intersection(X2,X0)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f37,f18])).
% 13.43/2.22 fof(f149,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(X0,intersection(intersection(X0,X1),X2))=intersection(X0,union(X0,X2)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f19,f20])).
% 13.43/2.22 fof(f150,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(X0,intersection(X1,X2))=intersection(union(X1,X0),union(X0,X2)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f36,f20])).
% 13.43/2.22 fof(f157,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(X0,intersection(X1,X2))=intersection(union(X0,X1),union(X2,X0)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f36,f20])).
% 13.43/2.22 fof(f173,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(X0,intersection(X0,intersection(X1,X2)))=intersection(X0,union(X0,X2)))),
% 13.43/2.22 inference(forward_demodulation,[status(thm)],[f18,f149])).
% 13.43/2.22 fof(f175,plain,(
% 13.43/2.22 ![X0,X1]: (X0=intersection(X0,union(X0,X1)))),
% 13.43/2.22 inference(forward_demodulation,[status(thm)],[f19,f173])).
% 13.43/2.22 fof(f177,plain,(
% 13.43/2.22 ~union(intersection(sK3_skl,sK2_skl),union(intersection(sK3_skl,sK4_skl),intersection(sK4_skl,sK2_skl)))=intersection(union(sK2_skl,sK3_skl),union(sK4_skl,intersection(sK3_skl,sK2_skl)))),
% 13.43/2.22 inference(backward_demodulation,[status(thm)],[f150,f87])).
% 13.43/2.22 fof(f195,plain,(
% 13.43/2.22 ![X0,X1]: (X0=intersection(X0,union(X1,X0)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f36,f175])).
% 13.43/2.22 fof(f237,plain,(
% 13.43/2.22 ![X0,X1,X2]: (intersection(X0,X1)=intersection(X0,intersection(union(X2,X0),X1)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f195,f18])).
% 13.43/2.22 fof(f462,plain,(
% 13.43/2.22 ~union(intersection(sK3_skl,sK2_skl),union(intersection(sK4_skl,sK2_skl),intersection(sK3_skl,sK4_skl)))=intersection(union(sK2_skl,sK3_skl),union(sK4_skl,intersection(sK3_skl,sK2_skl)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f36,f177])).
% 13.43/2.22 fof(f472,plain,(
% 13.43/2.22 ~union(intersection(sK3_skl,sK2_skl),union(intersection(sK4_skl,sK2_skl),intersection(sK4_skl,sK3_skl)))=intersection(union(sK2_skl,sK3_skl),union(sK4_skl,intersection(sK3_skl,sK2_skl)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f37,f462])).
% 13.43/2.22 fof(f935,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(X0,X1)=union(intersection(X2,X1),union(X0,X1)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f88,f70])).
% 13.43/2.22 fof(f939,plain,(
% 13.43/2.22 ![X0,X1]: (union(X0,X1)=union(X1,union(X0,X1)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f60,f70])).
% 13.43/2.22 fof(f1199,plain,(
% 13.43/2.22 ![X0,X1]: (union(intersection(X0,X1),X0)=union(X0,X0))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f64,f939])).
% 13.43/2.22 fof(f1250,plain,(
% 13.43/2.22 ![X0,X1]: (union(intersection(X0,X1),X0)=X0)),
% 13.43/2.22 inference(forward_demodulation,[status(thm)],[f60,f1199])).
% 13.43/2.22 fof(f1337,plain,(
% 13.43/2.22 ![X0,X1,X2]: (union(intersection(X0,X1),intersection(X0,X2))=intersection(X0,union(intersection(X0,X1),X2)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f1250,f20])).
% 13.43/2.22 fof(f1359,plain,(
% 13.43/2.22 ~union(intersection(sK3_skl,sK2_skl),intersection(sK4_skl,union(intersection(sK4_skl,sK2_skl),sK3_skl)))=intersection(union(sK2_skl,sK3_skl),union(sK4_skl,intersection(sK3_skl,sK2_skl)))),
% 13.43/2.22 inference(backward_demodulation,[status(thm)],[f1337,f472])).
% 13.43/2.22 fof(f2588,plain,(
% 13.43/2.22 ![X0,X1,X2]: (intersection(X0,union(X1,X2))=intersection(X0,union(X1,intersection(X0,X2))))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f20,f237])).
% 13.43/2.22 fof(f2617,plain,(
% 13.43/2.22 ![X0,X1,X2,X3]: (intersection(union(X0,X1),X2)=intersection(union(X0,X1),intersection(union(X1,union(X3,X0)),X2)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f70,f237])).
% 13.43/2.22 fof(f4052,plain,(
% 13.43/2.22 ![X0,X1,X2,X3]: (intersection(X0,union(X1,intersection(X2,X3)))=intersection(union(X2,X1),intersection(union(X1,X3),X0)))),
% 13.43/2.22 inference(paramodulation,[status(thm)],[f150,f127])).
% 14.25/2.25 fof(f4180,plain,(
% 14.25/2.25 ![X0,X1,X2,X3]: (intersection(union(X0,X1),X2)=intersection(X2,union(X1,intersection(X0,union(X3,X0)))))),
% 14.25/2.25 inference(backward_demodulation,[status(thm)],[f4052,f2617])).
% 14.25/2.25 fof(f4232,plain,(
% 14.25/2.25 ![X0,X1,X2]: (intersection(union(X0,X1),X2)=intersection(X2,union(X1,X0)))),
% 14.25/2.25 inference(forward_demodulation,[status(thm)],[f195,f4180])).
% 14.25/2.25 fof(f4247,plain,(
% 14.25/2.25 ![X0,X1,X2]: (union(intersection(X0,X1),intersection(X0,X2))=intersection(X0,union(X2,intersection(X0,X1))))),
% 14.25/2.25 inference(paramodulation,[status(thm)],[f1250,f157])).
% 14.25/2.25 fof(f4347,plain,(
% 14.25/2.25 ![X0,X1,X2]: (intersection(X0,union(X1,X2))=intersection(X0,union(intersection(X0,X2),X1)))),
% 14.25/2.25 inference(backward_demodulation,[status(thm)],[f4348,f1337])).
% 14.25/2.25 fof(f4348,plain,(
% 14.25/2.25 ![X0,X1,X2]: (union(intersection(X0,X1),intersection(X0,X2))=intersection(X0,union(X2,X1)))),
% 14.25/2.25 inference(forward_demodulation,[status(thm)],[f2588,f4247])).
% 14.25/2.25 fof(f4487,plain,(
% 14.25/2.25 ~union(intersection(sK3_skl,sK2_skl),intersection(sK4_skl,union(sK3_skl,sK2_skl)))=intersection(union(sK2_skl,sK3_skl),union(sK4_skl,intersection(sK3_skl,sK2_skl)))),
% 14.25/2.25 inference(backward_demodulation,[status(thm)],[f4347,f1359])).
% 14.25/2.25 fof(f17737,plain,(
% 14.25/2.25 ![X0,X1,X2,X3]: (union(intersection(X0,X1),intersection(X2,union(X3,X1)))=intersection(union(X2,intersection(X0,X1)),union(X3,X1)))),
% 14.25/2.25 inference(paramodulation,[status(thm)],[f935,f150])).
% 14.25/2.25 fof(f17943,plain,(
% 14.25/2.25 ~intersection(union(sK4_skl,intersection(sK3_skl,sK2_skl)),union(sK3_skl,sK2_skl))=intersection(union(sK2_skl,sK3_skl),union(sK4_skl,intersection(sK3_skl,sK2_skl)))),
% 14.25/2.25 inference(backward_demodulation,[status(thm)],[f17737,f4487])).
% 14.25/2.25 fof(f17995,plain,(
% 14.25/2.25 $false),
% 14.25/2.25 inference(forward_subsumption_resolution,[status(thm)],[f17943,f4232])).
% 14.25/2.25 % SZS output end CNFRefutation for theBenchmark.p
% 14.25/2.27 % Elapsed time: 1.905836 seconds
% 14.25/2.27 % CPU time: 14.648777 seconds
% 14.25/2.27 % Total memory used: 198.529 MB
% 14.25/2.27 % Net memory used: 192.495 MB
%------------------------------------------------------------------------------