%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET702+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 : n006.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 02:12:29 PM UTC 2026
% Result : Theorem 10.21s 1.76s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET702+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
% 0.10/0.37 % Computer : n006.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 05:33:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 10.21/1.76 % Refutation found
% 10.21/1.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.21/1.76 % SZS output start CNFRefutation for theBenchmark
% 10.21/1.76 fof(f1,axiom,(
% 10.21/1.76 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 10.21/1.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 10.21/1.76 fof(f4,axiom,(
% 10.21/1.76 (! [X,A,B] :( member(X,intersection(A,B))<=> ( member(X,A)& member(X,B) ) ) )),
% 10.21/1.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 10.21/1.76 fof(f11,axiom,(
% 10.21/1.76 (! [X,A] :( member(X,product(A))<=> (! [Y] :( member(Y,A)=> member(X,Y) ) )) )),
% 10.21/1.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 10.21/1.76 fof(f12,conjecture,(
% 10.21/1.76 (! [A,B] : subset(intersection(product(A),product(B)),product(intersection(A,B))) )),
% 10.21/1.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 10.21/1.76 fof(f13,negated_conjecture,(
% 10.21/1.76 ~((! [A,B] : subset(intersection(product(A),product(B)),product(intersection(A,B))) ))),
% 10.21/1.76 inference(negated_conjecture,[status(cth)],[f12])).
% 10.21/1.76 fof(f14,plain,(
% 10.21/1.76 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 10.21/1.76 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 10.21/1.76 fof(f15,plain,(
% 10.21/1.76 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 10.21/1.76 inference(NNF_transformation,[status(thm)],[f14])).
% 10.21/1.76 fof(f16,plain,(
% 10.21/1.76 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 10.21/1.76 inference(miniscoping,[status(thm)],[f15])).
% 10.21/1.76 fof(f17,plain,(
% 10.21/1.76 (![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))))),
% 10.21/1.76 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16])).
% 10.21/1.76 fof(f19,plain,(
% 10.21/1.76 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 10.21/1.76 inference(cnf_transformation,[status(thm)],[f17])).
% 10.21/1.76 fof(f20,plain,(
% 10.21/1.76 ![X0,X1]: (subset(X0,X1)|~member(sK0_skl(X1,X0),X1))),
% 10.21/1.76 inference(cnf_transformation,[status(thm)],[f17])).
% 10.21/1.76 fof(f30,plain,(
% 10.21/1.76 ![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))))),
% 10.21/1.76 inference(NNF_transformation,[status(thm)],[f4])).
% 10.21/1.76 fof(f31,plain,(
% 10.21/1.76 (![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))))),
% 10.21/1.76 inference(miniscoping,[status(thm)],[f30])).
% 10.21/1.76 fof(f33,plain,(
% 10.21/1.76 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 10.21/1.76 inference(cnf_transformation,[status(thm)],[f31])).
% 10.21/1.76 fof(f61,plain,(
% 10.21/1.76 ![X,A]: (member(X,product(A))<=>(![Y]: (~member(Y,A)|member(X,Y))))),
% 10.21/1.76 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 10.21/1.76 fof(f62,plain,(
% 10.21/1.76 ![X,A]: ((~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y))))&(member(X,product(A))|(?[Y]: (member(Y,A)&~member(X,Y)))))),
% 10.21/1.76 inference(NNF_transformation,[status(thm)],[f61])).
% 10.21/1.76 fof(f63,plain,(
% 10.21/1.76 (![X,A]: (~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y)))))&(![X,A]: (member(X,product(A))|(?[Y]: (member(Y,A)&~member(X,Y)))))),
% 10.21/1.76 inference(miniscoping,[status(thm)],[f62])).
% 10.21/1.76 fof(f64,plain,(
% 10.21/1.76 (![X,A]: (~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y)))))&(![X,A]: (member(X,product(A))|(member(sK2_skl(A,X),A)&~member(X,sK2_skl(A,X)))))),
% 10.21/1.76 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(A,X))],[f63])).
% 10.21/1.76 fof(f65,plain,(
% 10.21/1.76 ![X0,X1,X2]: (~member(X0,product(X1))|~member(X2,X1)|member(X0,X2))),
% 10.21/1.76 inference(cnf_transformation,[status(thm)],[f64])).
% 10.21/1.76 fof(f66,plain,(
% 10.21/1.76 ![X0,X1]: (member(X0,product(X1))|member(sK2_skl(X1,X0),X1))),
% 10.21/1.76 inference(cnf_transformation,[status(thm)],[f64])).
% 10.21/1.76 fof(f67,plain,(
% 10.21/1.76 ![X0,X1]: (member(X0,product(X1))|~member(X0,sK2_skl(X1,X0)))),
% 10.21/1.76 inference(cnf_transformation,[status(thm)],[f64])).
% 10.21/1.76 fof(f68,plain,(
% 10.21/1.76 (?[A,B]: ~subset(intersection(product(A),product(B)),product(intersection(A,B))))),
% 10.21/1.76 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 10.21/1.76 fof(f69,plain,(
% 10.21/1.76 ~subset(intersection(product(sK3_skl),product(sK4_skl)),product(intersection(sK3_skl,sK4_skl)))),
% 10.21/1.76 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f68])).
% 10.21/1.77 fof(f70,plain,(
% 10.21/1.77 ~subset(intersection(product(sK3_skl),product(sK4_skl)),product(intersection(sK3_skl,sK4_skl)))),
% 10.21/1.77 inference(cnf_transformation,[status(thm)],[f69])).
% 10.21/1.77 fof(f75,plain,(
% 10.21/1.77 ![X0,X1,X2]: (subset(intersection(X0,X1),X2)|member(sK0_skl(X2,intersection(X0,X1)),X1))),
% 10.21/1.77 inference(resolution,[status(thm)],[f19,f33])).
% 10.21/1.77 fof(f79,plain,(
% 10.21/1.77 ![X0,X1,X2,X3]: (subset(intersection(X0,product(X1)),X2)|~member(X3,X1)|member(sK0_skl(X2,intersection(X0,product(X1))),X3))),
% 10.21/1.77 inference(resolution,[status(thm)],[f75,f65])).
% 10.21/1.77 fof(f170,plain,(
% 10.21/1.77 ![X0,X1,X2]: (member(X0,product(intersection(X1,X2)))|member(sK2_skl(intersection(X1,X2),X0),X2))),
% 10.21/1.77 inference(resolution,[status(thm)],[f66,f33])).
% 10.21/1.77 fof(f185,plain,(
% 10.21/1.77 ![X0,X1,X2,X3,X4]: (member(X0,product(intersection(X1,X2)))|subset(intersection(X3,product(X2)),X4)|member(sK0_skl(X4,intersection(X3,product(X2))),sK2_skl(intersection(X1,X2),X0)))),
% 10.21/1.77 inference(resolution,[status(thm)],[f170,f79])).
% 10.21/1.77 fof(f973,plain,(
% 10.21/1.77 ![X0,X1,X2,X3]: (member(sK0_skl(X0,intersection(X1,product(X2))),product(intersection(X3,X2)))|subset(intersection(X1,product(X2)),X0)|member(sK0_skl(X0,intersection(X1,product(X2))),product(intersection(X3,X2))))),
% 10.21/1.77 inference(resolution,[status(thm)],[f185,f67])).
% 10.21/1.77 fof(f979,plain,(
% 10.21/1.77 ![X0,X1,X2,X3]: (member(sK0_skl(X0,intersection(X1,product(X2))),product(intersection(X3,X2)))|subset(intersection(X1,product(X2)),X0))),
% 10.21/1.77 inference(duplicate_literals_removal,[status(thm)],[f973])).
% 10.21/1.77 fof(f980,plain,(
% 10.21/1.77 ![X0,X1,X2]: (subset(intersection(X0,product(X1)),product(intersection(X2,X1)))|subset(intersection(X0,product(X1)),product(intersection(X2,X1))))),
% 10.21/1.77 inference(resolution,[status(thm)],[f979,f20])).
% 10.21/1.77 fof(f987,plain,(
% 10.21/1.77 ![X0,X1,X2]: (subset(intersection(X0,product(X1)),product(intersection(X2,X1))))),
% 10.21/1.77 inference(duplicate_literals_removal,[status(thm)],[f980])).
% 10.21/1.77 fof(f988,plain,(
% 10.21/1.77 $false),
% 10.21/1.77 inference(backward_subsumption_resolution,[status(thm)],[f70,f987])).
% 10.21/1.77 % SZS output end CNFRefutation for theBenchmark.p
% 10.21/1.78 % Elapsed time: 1.396918 seconds
% 10.21/1.78 % CPU time: 10.773404 seconds
% 10.21/1.78 % Total memory used: 173.425 MB
% 10.21/1.78 % Net memory used: 156.011 MB
%------------------------------------------------------------------------------