%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET696+4 : 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 : n009.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 02:12:28 PM UTC 2026
% Result : Theorem 2.17s 0.88s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET696+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:32:58 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 2.17/0.88 % Refutation found
% 2.17/0.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.17/0.88 % SZS output start CNFRefutation for theBenchmark
% 2.17/0.88 fof(f1,axiom,(
% 2.17/0.88 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 2.17/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.17/0.88 fof(f2,axiom,(
% 2.17/0.88 (! [A,B] :( equal_set(A,B)<=> ( subset(A,B)& subset(B,A) ) ) )),
% 2.17/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.17/0.88 fof(f4,axiom,(
% 2.17/0.88 (! [X,A,B] :( member(X,intersection(A,B))<=> ( member(X,A)& member(X,B) ) ) )),
% 2.17/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.17/0.88 fof(f6,axiom,(
% 2.17/0.88 (! [X] : ~ member(X,empty_set) )),
% 2.17/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.17/0.88 fof(f7,axiom,(
% 2.17/0.88 (! [B,A,E] :( member(B,difference(E,A))<=> ( member(B,E)& ~ member(B,A) ) ) )),
% 2.17/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.17/0.88 fof(f12,conjecture,(
% 2.17/0.88 (! [A,E] :( subset(A,E)=> equal_set(intersection(difference(E,A),A),empty_set) ) )),
% 2.17/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.17/0.88 fof(f13,negated_conjecture,(
% 2.17/0.88 ~((! [A,E] :( subset(A,E)=> equal_set(intersection(difference(E,A),A),empty_set) ) ))),
% 2.17/0.88 inference(negated_conjecture,[status(cth)],[f12])).
% 2.17/0.88 fof(f14,plain,(
% 2.17/0.88 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 2.17/0.88 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 2.17/0.88 fof(f15,plain,(
% 2.17/0.88 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 2.17/0.88 inference(NNF_transformation,[status(thm)],[f14])).
% 2.17/0.88 fof(f16,plain,(
% 2.17/0.88 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 2.17/0.88 inference(miniscoping,[status(thm)],[f15])).
% 2.17/0.88 fof(f17,plain,(
% 2.17/0.88 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(member(sK0_skl(B,A),A)&~member(sK0_skl(B,A),B))))),
% 2.17/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16])).
% 2.17/0.88 fof(f19,plain,(
% 2.17/0.88 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 2.17/0.88 inference(cnf_transformation,[status(thm)],[f17])).
% 2.17/0.88 fof(f21,plain,(
% 2.17/0.88 ![A,B]: ((~equal_set(A,B)|(subset(A,B)&subset(B,A)))&(equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 2.17/0.88 inference(NNF_transformation,[status(thm)],[f2])).
% 2.17/0.88 fof(f22,plain,(
% 2.17/0.88 (![A,B]: (~equal_set(A,B)|(subset(A,B)&subset(B,A))))&(![A,B]: (equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 2.17/0.88 inference(miniscoping,[status(thm)],[f21])).
% 2.17/0.88 fof(f25,plain,(
% 2.17/0.88 ![X0,X1]: (equal_set(X0,X1)|~subset(X0,X1)|~subset(X1,X0))),
% 2.17/0.88 inference(cnf_transformation,[status(thm)],[f22])).
% 2.17/0.88 fof(f30,plain,(
% 2.17/0.88 ![X,A,B]: ((~member(X,intersection(A,B))|(member(X,A)&member(X,B)))&(member(X,intersection(A,B))|(~member(X,A)|~member(X,B))))),
% 2.17/0.88 inference(NNF_transformation,[status(thm)],[f4])).
% 2.17/0.88 fof(f31,plain,(
% 2.17/0.88 (![X,A,B]: (~member(X,intersection(A,B))|(member(X,A)&member(X,B))))&(![X,A,B]: (member(X,intersection(A,B))|(~member(X,A)|~member(X,B))))),
% 2.17/0.88 inference(miniscoping,[status(thm)],[f30])).
% 2.17/0.88 fof(f32,plain,(
% 2.17/0.88 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 2.17/0.88 inference(cnf_transformation,[status(thm)],[f31])).
% 2.17/0.88 fof(f33,plain,(
% 2.17/0.88 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 2.17/0.88 inference(cnf_transformation,[status(thm)],[f31])).
% 2.17/0.88 fof(f40,plain,(
% 2.17/0.88 ![X0]: (~member(X0,empty_set))),
% 2.17/0.88 inference(cnf_transformation,[status(thm)],[f6])).
% 2.17/0.88 fof(f41,plain,(
% 2.17/0.88 ![B,A,E]: ((~member(B,difference(E,A))|(member(B,E)&~member(B,A)))&(member(B,difference(E,A))|(~member(B,E)|member(B,A))))),
% 2.17/0.88 inference(NNF_transformation,[status(thm)],[f7])).
% 2.17/0.88 fof(f42,plain,(
% 2.17/0.88 (![B,A,E]: (~member(B,difference(E,A))|(member(B,E)&~member(B,A))))&(![B,A,E]: (member(B,difference(E,A))|(~member(B,E)|member(B,A))))),
% 2.17/0.88 inference(miniscoping,[status(thm)],[f41])).
% 2.17/0.88 fof(f44,plain,(
% 2.17/0.88 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|~member(X0,X2))),
% 2.17/0.88 inference(cnf_transformation,[status(thm)],[f42])).
% 2.17/0.88 fof(f68,plain,(
% 2.17/0.88 (?[A,E]: (subset(A,E)&~equal_set(intersection(difference(E,A),A),empty_set)))),
% 2.17/0.88 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 2.17/0.88 fof(f69,plain,(
% 2.17/0.88 (subset(sK3_skl,sK4_skl)&~equal_set(intersection(difference(sK4_skl,sK3_skl),sK3_skl),empty_set))),
% 2.17/0.89 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(E,sK4_skl)],[f68])).
% 2.17/0.89 fof(f71,plain,(
% 2.17/0.89 ~equal_set(intersection(difference(sK4_skl,sK3_skl),sK3_skl),empty_set)),
% 2.17/0.89 inference(cnf_transformation,[status(thm)],[f69])).
% 2.17/0.89 fof(f81,plain,(
% 2.17/0.89 ![X0,X1,X2]: (subset(intersection(X0,X1),X2)|member(sK0_skl(X2,intersection(X0,X1)),X0))),
% 2.17/0.89 inference(resolution,[status(thm)],[f19,f32])).
% 2.17/0.89 fof(f83,plain,(
% 2.17/0.89 ![X0]: (subset(empty_set,X0))),
% 2.17/0.89 inference(resolution,[status(thm)],[f19,f40])).
% 2.17/0.89 fof(f86,plain,(
% 2.17/0.89 ![X0,X1,X2]: (member(sK0_skl(X0,intersection(X1,X2)),X2)|subset(intersection(X1,X2),X0))),
% 2.17/0.89 inference(resolution,[status(thm)],[f33,f19])).
% 2.17/0.89 fof(f91,plain,(
% 2.17/0.89 ![X0]: (equal_set(X0,empty_set)|~subset(X0,empty_set))),
% 2.17/0.89 inference(resolution,[status(thm)],[f83,f25])).
% 2.17/0.89 fof(f203,plain,(
% 2.17/0.89 ![X0,X1,X2,X3]: (subset(intersection(difference(X0,X1),X2),X3)|~member(sK0_skl(X3,intersection(difference(X0,X1),X2)),X1))),
% 2.17/0.89 inference(resolution,[status(thm)],[f81,f44])).
% 2.17/0.89 fof(f3005,plain,(
% 2.17/0.89 ![X0,X1,X2]: (subset(intersection(difference(X0,X1),X1),X2)|subset(intersection(difference(X0,X1),X1),X2))),
% 2.17/0.89 inference(resolution,[status(thm)],[f203,f86])).
% 2.17/0.89 fof(f3024,plain,(
% 2.17/0.89 ![X0,X1,X2]: (subset(intersection(difference(X0,X1),X1),X2))),
% 2.17/0.89 inference(duplicate_literals_removal,[status(thm)],[f3005])).
% 2.17/0.89 fof(f3124,plain,(
% 2.17/0.89 ![X0,X1]: (equal_set(intersection(difference(X0,X1),X1),empty_set))),
% 2.17/0.89 inference(resolution,[status(thm)],[f3024,f91])).
% 2.17/0.89 fof(f3135,plain,(
% 2.17/0.89 $false),
% 2.17/0.89 inference(backward_subsumption_resolution,[status(thm)],[f71,f3124])).
% 2.17/0.89 % SZS output end CNFRefutation for theBenchmark.p
% 2.17/0.92 % Elapsed time: 0.565150 seconds
% 2.17/0.92 % CPU time: 4.137362 seconds
% 2.17/0.92 % Total memory used: 110.184 MB
% 2.17/0.92 % Net memory used: 105.680 MB
%------------------------------------------------------------------------------