%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:12:57 PM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.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 05:45:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.38 fof(f1,axiom,(
% 0.10/0.38 empty(empty_set) ),
% 0.10/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.38 fof(f5,axiom,(
% 0.10/0.38 (! [A,B] :( cartesian_product2(A,B) = empty_set<=> ( A = empty_set| B = empty_set ) ) )),
% 0.10/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.38 fof(f6,axiom,(
% 0.10/0.38 (! [A,B,C,D] :( subset(cartesian_product2(A,B),cartesian_product2(C,D))=> ( cartesian_product2(A,B) = empty_set| ( subset(A,C)& subset(B,D) ) ) ) )),
% 0.10/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.38 fof(f7,conjecture,(
% 0.10/0.38 (! [A] :( ~ empty(A)=> (! [B,C,D] :( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))| subset(cartesian_product2(B,A),cartesian_product2(D,C)) )=> subset(B,D) ) )) )),
% 0.10/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.38 fof(f8,negated_conjecture,(
% 0.10/0.38 ~((! [A] :( ~ empty(A)=> (! [B,C,D] :( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))| subset(cartesian_product2(B,A),cartesian_product2(D,C)) )=> subset(B,D) ) )) ))),
% 0.10/0.38 inference(negated_conjecture,[status(cth)],[f7])).
% 0.10/0.38 fof(f9,axiom,(
% 0.10/0.38 (! [A] : subset(empty_set,A) )),
% 0.10/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.38 fof(f10,plain,(
% 0.10/0.38 empty(empty_set)),
% 0.10/0.38 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.38 fof(f17,plain,(
% 0.10/0.38 ![A,B]: ((~cartesian_product2(A,B)=empty_set|(A=empty_set|B=empty_set))&(cartesian_product2(A,B)=empty_set|(~A=empty_set&~B=empty_set)))),
% 0.10/0.38 inference(NNF_transformation,[status(thm)],[f5])).
% 0.10/0.38 fof(f18,plain,(
% 0.10/0.38 (![A,B]: (~cartesian_product2(A,B)=empty_set|(A=empty_set|B=empty_set)))&(![A,B]: (cartesian_product2(A,B)=empty_set|(~A=empty_set&~B=empty_set)))),
% 0.10/0.38 inference(miniscoping,[status(thm)],[f17])).
% 0.10/0.38 fof(f19,plain,(
% 0.10/0.38 ![X0,X1]: (~cartesian_product2(X0,X1)=empty_set|X0=empty_set|X1=empty_set)),
% 0.10/0.38 inference(cnf_transformation,[status(thm)],[f18])).
% 0.10/0.38 fof(f22,plain,(
% 0.10/0.38 ![A,B,C,D]: (~subset(cartesian_product2(A,B),cartesian_product2(C,D))|(cartesian_product2(A,B)=empty_set|(subset(A,C)&subset(B,D))))),
% 0.10/0.38 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.10/0.38 fof(f23,plain,(
% 0.10/0.38 ![X0,X1,X2,X3]: (~subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))|cartesian_product2(X0,X1)=empty_set|subset(X0,X2))),
% 0.10/0.38 inference(cnf_transformation,[status(thm)],[f22])).
% 0.10/0.38 fof(f24,plain,(
% 0.10/0.38 ![X0,X1,X2,X3]: (~subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))|cartesian_product2(X0,X1)=empty_set|subset(X1,X3))),
% 0.10/0.38 inference(cnf_transformation,[status(thm)],[f22])).
% 0.10/0.38 fof(f25,plain,(
% 0.10/0.38 (?[A]: (~empty(A)&(?[B,C,D]: ((subset(cartesian_product2(A,B),cartesian_product2(C,D))|subset(cartesian_product2(B,A),cartesian_product2(D,C)))&~subset(B,D)))))),
% 0.10/0.38 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.10/0.38 fof(f26,plain,(
% 0.10/0.38 ?[A]: (~empty(A)&(?[B,D]: (((?[C]: subset(cartesian_product2(A,B),cartesian_product2(C,D)))|(?[C]: subset(cartesian_product2(B,A),cartesian_product2(D,C))))&~subset(B,D))))),
% 0.10/0.38 inference(miniscoping,[status(thm)],[f25])).
% 0.10/0.38 fof(f27,plain,(
% 0.10/0.38 (~empty(sK2_skl)&((subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK5_skl,sK4_skl))|subset(cartesian_product2(sK3_skl,sK2_skl),cartesian_product2(sK4_skl,sK6_skl)))&~subset(sK3_skl,sK4_skl)))),
% 0.10/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(D,sK4_skl),skolemize(C,sK5_skl),skolemize(C,sK6_skl)],[f26])).
% 0.10/0.38 fof(f28,plain,(
% 0.10/0.38 ~empty(sK2_skl)),
% 0.10/0.38 inference(cnf_transformation,[status(thm)],[f27])).
% 0.10/0.38 fof(f29,plain,(
% 0.10/0.38 subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK5_skl,sK4_skl))|subset(cartesian_product2(sK3_skl,sK2_skl),cartesian_product2(sK4_skl,sK6_skl))),
% 0.10/0.38 inference(cnf_transformation,[status(thm)],[f27])).
% 0.10/0.38 fof(f30,plain,(
% 0.10/0.38 ~subset(sK3_skl,sK4_skl)),
% 0.10/0.38 inference(cnf_transformation,[status(thm)],[f27])).
% 0.10/0.38 fof(f31,plain,(
% 0.10/0.38 ![X0]: (subset(empty_set,X0))),
% 0.10/0.38 inference(cnf_transformation,[status(thm)],[f9])).
% 0.10/0.38 fof(f34,plain,(
% 0.10/0.38 cartesian_product2(sK3_skl,sK2_skl)=empty_set|subset(sK3_skl,sK4_skl)|subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK5_skl,sK4_skl))),
% 0.10/0.38 inference(resolution,[status(thm)],[f23,f29])).
% 0.10/0.38 fof(f36,plain,(
% 0.10/0.38 cartesian_product2(sK3_skl,sK2_skl)=empty_set|subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK5_skl,sK4_skl))),
% 0.10/0.38 inference(forward_subsumption_resolution,[status(thm)],[f34,f30])).
% 0.10/0.38 fof(f39,plain,(
% 0.10/0.38 cartesian_product2(sK3_skl,sK2_skl)=empty_set|cartesian_product2(sK2_skl,sK3_skl)=empty_set|subset(sK3_skl,sK4_skl)),
% 0.10/0.38 inference(resolution,[status(thm)],[f36,f24])).
% 0.10/0.38 fof(f41,plain,(
% 0.10/0.38 cartesian_product2(sK3_skl,sK2_skl)=empty_set|cartesian_product2(sK2_skl,sK3_skl)=empty_set),
% 0.10/0.38 inference(forward_subsumption_resolution,[status(thm)],[f39,f30])).
% 0.10/0.38 fof(f60,plain,(
% 0.10/0.38 cartesian_product2(sK2_skl,sK3_skl)=empty_set|sK3_skl=empty_set|sK2_skl=empty_set),
% 0.10/0.38 inference(resolution,[status(thm)],[f41,f19])).
% 0.10/0.38 fof(f69,plain,(
% 0.10/0.38 sK3_skl=empty_set|sK2_skl=empty_set),
% 0.10/0.38 inference(forward_subsumption_resolution,[status(thm)],[f60,f19])).
% 0.10/0.38 fof(f76,plain,(
% 0.10/0.38 ![X0]: (subset(sK3_skl,X0)|sK2_skl=empty_set)),
% 0.10/0.38 inference(paramodulation,[status(thm)],[f69,f31])).
% 0.10/0.38 fof(f89,plain,(
% 0.10/0.38 sK2_skl=empty_set),
% 0.10/0.38 inference(resolution,[status(thm)],[f76,f30])).
% 0.10/0.38 fof(f106,plain,(
% 0.10/0.38 empty(sK2_skl)),
% 0.10/0.38 inference(backward_demodulation,[status(thm)],[f89,f10])).
% 0.10/0.38 fof(f114,plain,(
% 0.10/0.38 $false),
% 0.10/0.38 inference(forward_subsumption_resolution,[status(thm)],[f106,f28])).
% 0.10/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.41 % Elapsed time: 0.043165 seconds
% 0.15/0.41 % CPU time: 0.083510 seconds
% 0.15/0.41 % Total memory used: 15.162 MB
% 0.15/0.41 % Net memory used: 15.126 MB
%------------------------------------------------------------------------------