%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:12:57 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n006.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:45:57 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.48 fof(f1,axiom,(
% 0.17/0.48 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f7,axiom,(
% 0.17/0.48 (! [A,B] :( cartesian_product2(A,B) = empty_set<=> ( A = empty_set| B = empty_set ) ) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f8,axiom,(
% 0.17/0.48 (! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f9,axiom,(
% 0.17/0.48 (! [A,B,C,D] :( cartesian_product2(A,B) = cartesian_product2(C,D)=> ( A = empty_set| B = empty_set| ( A = C& B = D ) ) ) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f10,conjecture,(
% 0.17/0.48 (! [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) ) ) ) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f11,negated_conjecture,(
% 0.17/0.48 ~((! [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) ) ) ) ))),
% 0.17/0.48 inference(negated_conjecture,[status(cth)],[f10])).
% 0.17/0.48 fof(f12,axiom,(
% 0.17/0.48 (! [A,B] : subset(set_intersection2(A,B),A) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f13,axiom,(
% 0.17/0.48 (! [A,B] :( subset(A,B)=> set_intersection2(A,B) = A ) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f14,plain,(
% 0.17/0.48 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f1])).
% 0.17/0.48 fof(f24,plain,(
% 0.17/0.48 ![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)))),
% 0.17/0.48 inference(NNF_transformation,[status(thm)],[f7])).
% 0.17/0.48 fof(f25,plain,(
% 0.17/0.48 (![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)))),
% 0.17/0.48 inference(miniscoping,[status(thm)],[f24])).
% 0.17/0.48 fof(f27,plain,(
% 0.17/0.48 ![X0,X1]: (cartesian_product2(X0,X1)=empty_set|~X0=empty_set)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f25])).
% 0.17/0.48 fof(f28,plain,(
% 0.17/0.48 ![X0,X1]: (cartesian_product2(X0,X1)=empty_set|~X1=empty_set)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f25])).
% 0.17/0.48 fof(f29,plain,(
% 0.17/0.48 ![X0,X1,X2,X3]: (cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3))=set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f8])).
% 0.17/0.48 fof(f30,plain,(
% 0.17/0.48 ![A,B,C,D]: (~cartesian_product2(A,B)=cartesian_product2(C,D)|((A=empty_set|B=empty_set)|(A=C&B=D)))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.17/0.48 fof(f31,plain,(
% 0.17/0.48 ![X0,X1,X2,X3]: (~cartesian_product2(X0,X1)=cartesian_product2(X2,X3)|X0=empty_set|X1=empty_set|X0=X2)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f30])).
% 0.17/0.48 fof(f32,plain,(
% 0.17/0.48 ![X0,X1,X2,X3]: (~cartesian_product2(X0,X1)=cartesian_product2(X2,X3)|X0=empty_set|X1=empty_set|X1=X3)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f30])).
% 0.17/0.48 fof(f33,plain,(
% 0.17/0.48 (?[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)))))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.17/0.48 fof(f34,plain,(
% 0.17/0.48 (subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))&(~cartesian_product2(sK2_skl,sK3_skl)=empty_set&(~subset(sK2_skl,sK4_skl)|~subset(sK3_skl,sK5_skl))))),
% 0.17/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f33])).
% 0.17/0.48 fof(f35,plain,(
% 0.17/0.48 subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f34])).
% 0.17/0.48 fof(f36,plain,(
% 0.17/0.48 ~cartesian_product2(sK2_skl,sK3_skl)=empty_set),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f34])).
% 0.17/0.48 fof(f37,plain,(
% 0.17/0.48 ~subset(sK2_skl,sK4_skl)|~subset(sK3_skl,sK5_skl)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f34])).
% 0.17/0.48 fof(f38,plain,(
% 0.17/0.48 ![X0,X1]: (subset(set_intersection2(X0,X1),X0))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.17/0.48 fof(f39,plain,(
% 0.17/0.48 ![A,B]: (~subset(A,B)|set_intersection2(A,B)=A)),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.17/0.48 fof(f40,plain,(
% 0.17/0.48 ![X0,X1]: (~subset(X0,X1)|set_intersection2(X0,X1)=X0)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f39])).
% 0.17/0.48 fof(f41,definition,(
% 0.17/0.48 sQ0_spl <=> (subset(sK2_skl,sK4_skl))),
% 0.17/0.48 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.17/0.48 fof(f43,plain,(
% 0.17/0.48 ~subset(sK2_skl,sK4_skl)|sQ0_spl),
% 0.17/0.48 inference(component_clause,[status(thm)],[f41])).
% 0.17/0.48 fof(f44,definition,(
% 0.17/0.48 sQ1_spl <=> (subset(sK3_skl,sK5_skl))),
% 0.17/0.48 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.17/0.48 fof(f46,plain,(
% 0.17/0.48 ~subset(sK3_skl,sK5_skl)|sQ1_spl),
% 0.17/0.48 inference(component_clause,[status(thm)],[f44])).
% 0.17/0.48 fof(f47,plain,(
% 0.17/0.48 ~sQ0_spl|~sQ1_spl),
% 0.17/0.48 inference(split_clause,[status(thm)],[f37,f41,f44])).
% 0.17/0.48 fof(f48,plain,(
% 0.17/0.48 ![X0]: (cartesian_product2(empty_set,X0)=empty_set)),
% 0.17/0.48 inference(destructive_equality_resolution,[status(thm)],[f27])).
% 0.17/0.48 fof(f49,plain,(
% 0.17/0.48 ![X0]: (cartesian_product2(X0,empty_set)=empty_set)),
% 0.17/0.48 inference(destructive_equality_resolution,[status(thm)],[f28])).
% 0.17/0.48 fof(f67,plain,(
% 0.17/0.48 set_intersection2(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))=cartesian_product2(sK2_skl,sK3_skl)),
% 0.17/0.48 inference(resolution,[status(thm)],[f40,f35])).
% 0.17/0.48 fof(f129,plain,(
% 0.17/0.48 ![X0,X1]: (subset(set_intersection2(X0,X1),X1))),
% 0.17/0.48 inference(paramodulation,[status(thm)],[f14,f38])).
% 0.17/0.48 fof(f257,plain,(
% 0.17/0.48 cartesian_product2(set_intersection2(sK2_skl,sK4_skl),set_intersection2(sK3_skl,sK5_skl))=cartesian_product2(sK2_skl,sK3_skl)),
% 0.17/0.48 inference(forward_demodulation,[status(thm)],[f29,f67])).
% 0.17/0.48 fof(f260,plain,(
% 0.17/0.48 sK2_skl=empty_set|sK3_skl=empty_set|sK2_skl=set_intersection2(sK2_skl,sK4_skl)),
% 0.17/0.48 inference(resolution,[status(thm)],[f257,f31])).
% 0.17/0.48 fof(f261,plain,(
% 0.17/0.48 sK2_skl=empty_set|sK3_skl=empty_set|sK3_skl=set_intersection2(sK3_skl,sK5_skl)),
% 0.17/0.48 inference(resolution,[status(thm)],[f257,f32])).
% 0.17/0.48 fof(f279,definition,(
% 0.17/0.48 sQ11_spl <=> (set_intersection2(sK2_skl,sK4_skl)=sK2_skl)),
% 0.17/0.48 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.17/0.48 fof(f280,plain,(
% 0.17/0.48 set_intersection2(sK2_skl,sK4_skl)=sK2_skl|~sQ11_spl),
% 0.17/0.48 inference(component_clause,[status(thm)],[f279])).
% 0.17/0.48 fof(f283,definition,(
% 0.17/0.48 sQ12_spl <=> (set_intersection2(sK3_skl,sK5_skl)=sK3_skl)),
% 0.17/0.48 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.17/0.48 fof(f284,plain,(
% 0.17/0.48 set_intersection2(sK3_skl,sK5_skl)=sK3_skl|~sQ12_spl),
% 0.17/0.48 inference(component_clause,[status(thm)],[f283])).
% 0.17/0.48 fof(f287,definition,(
% 0.17/0.48 sQ13_spl <=> (sK2_skl=empty_set)),
% 0.17/0.48 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.17/0.48 fof(f288,plain,(
% 0.17/0.48 sK2_skl=empty_set|~sQ13_spl),
% 0.17/0.48 inference(component_clause,[status(thm)],[f287])).
% 0.17/0.48 fof(f290,definition,(
% 0.17/0.48 sQ14_spl <=> (sK3_skl=empty_set)),
% 0.17/0.48 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.17/0.48 fof(f291,plain,(
% 0.17/0.48 sK3_skl=empty_set|~sQ14_spl),
% 0.17/0.48 inference(component_clause,[status(thm)],[f290])).
% 0.17/0.48 fof(f293,plain,(
% 0.17/0.48 sQ13_spl|sQ14_spl|sQ11_spl),
% 0.17/0.48 inference(split_clause,[status(thm)],[f260,f287,f290,f279])).
% 0.17/0.48 fof(f294,plain,(
% 0.17/0.48 sQ13_spl|sQ14_spl|sQ12_spl),
% 0.17/0.48 inference(split_clause,[status(thm)],[f261,f287,f290,f283])).
% 0.17/0.48 fof(f373,plain,(
% 0.17/0.48 ![X0]: (cartesian_product2(sK2_skl,X0)=empty_set|~sQ13_spl)),
% 0.17/0.48 inference(forward_demodulation,[status(thm)],[f288,f48])).
% 0.17/0.48 fof(f375,plain,(
% 0.17/0.48 ![X0]: (cartesian_product2(sK2_skl,X0)=sK2_skl|~sQ13_spl)),
% 0.17/0.48 inference(forward_demodulation,[status(thm)],[f288,f373])).
% 0.17/0.48 fof(f380,plain,(
% 0.17/0.48 ~sK2_skl=empty_set|~sQ13_spl),
% 0.17/0.48 inference(forward_demodulation,[status(thm)],[f375,f36])).
% 0.17/0.48 fof(f381,plain,(
% 0.17/0.48 ~sK2_skl=sK2_skl|~sQ13_spl),
% 0.17/0.48 inference(forward_demodulation,[status(thm)],[f288,f380])).
% 0.17/0.48 fof(f382,plain,(
% 0.17/0.48 $false|~sQ13_spl),
% 0.17/0.48 inference(trivial_equality_resolution,[status(thm)],[f381])).
% 0.17/0.49 fof(f383,plain,(
% 0.17/0.49 ~sQ13_spl),
% 0.17/0.49 inference(contradiction_clause,[status(thm)],[f382])).
% 0.17/0.49 fof(f393,plain,(
% 0.17/0.49 subset(sK3_skl,sK5_skl)|~sQ12_spl),
% 0.17/0.49 inference(paramodulation,[status(thm)],[f284,f129])).
% 0.17/0.49 fof(f441,plain,(
% 0.17/0.49 ![X0]: (cartesian_product2(X0,sK3_skl)=empty_set|~sQ14_spl)),
% 0.17/0.49 inference(forward_demodulation,[status(thm)],[f291,f49])).
% 0.17/0.49 fof(f442,plain,(
% 0.17/0.49 ![X0]: (cartesian_product2(X0,sK3_skl)=sK3_skl|~sQ14_spl)),
% 0.17/0.49 inference(forward_demodulation,[status(thm)],[f291,f441])).
% 0.17/0.49 fof(f477,plain,(
% 0.17/0.49 subset(sK2_skl,sK4_skl)|~sQ11_spl),
% 0.17/0.49 inference(paramodulation,[status(thm)],[f280,f129])).
% 0.17/0.49 fof(f479,plain,(
% 0.17/0.49 $false|sQ0_spl|~sQ11_spl),
% 0.17/0.49 inference(forward_subsumption_resolution,[status(thm)],[f477,f43])).
% 0.17/0.49 fof(f480,plain,(
% 0.17/0.49 sQ0_spl|~sQ11_spl),
% 0.17/0.49 inference(contradiction_clause,[status(thm)],[f479])).
% 0.17/0.49 fof(f492,plain,(
% 0.17/0.49 ~sK3_skl=empty_set|~sQ14_spl),
% 0.17/0.49 inference(forward_demodulation,[status(thm)],[f442,f36])).
% 0.17/0.49 fof(f493,plain,(
% 0.17/0.49 ~sK3_skl=sK3_skl|~sQ14_spl),
% 0.17/0.49 inference(forward_demodulation,[status(thm)],[f291,f492])).
% 0.17/0.49 fof(f494,plain,(
% 0.17/0.49 $false|~sQ14_spl),
% 0.17/0.49 inference(trivial_equality_resolution,[status(thm)],[f493])).
% 0.17/0.49 fof(f495,plain,(
% 0.17/0.49 ~sQ14_spl),
% 0.17/0.49 inference(contradiction_clause,[status(thm)],[f494])).
% 0.17/0.49 fof(f496,plain,(
% 0.17/0.49 $false|sQ1_spl|~sQ12_spl),
% 0.17/0.49 inference(forward_subsumption_resolution,[status(thm)],[f393,f46])).
% 0.17/0.49 fof(f497,plain,(
% 0.17/0.49 sQ1_spl|~sQ12_spl),
% 0.17/0.49 inference(contradiction_clause,[status(thm)],[f496])).
% 0.17/0.49 fof(f498,plain,(
% 0.17/0.49 $false),
% 0.17/0.49 inference(sat_refutation,[status(thm)],[f47,f293,f294,f383,f480,f495,f497])).
% 0.17/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.25/0.56 % Elapsed time: 0.105963 seconds
% 0.25/0.56 % CPU time: 0.120411 seconds
% 0.25/0.56 % Total memory used: 16.249 MB
% 0.25/0.56 % Net memory used: 16.230 MB
%------------------------------------------------------------------------------