%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET974+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 : n018.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 02:12:56 PM UTC 2026
% Result : Theorem 0.17s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:47:14 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.52 % Refutation found
% 0.17/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.52 fof(f3,axiom,(
% 0.17/0.52 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f9,axiom,(
% 0.17/0.52 (! [A,B] :( disjoint(A,B)=> disjoint(B,A) ) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f10,axiom,(
% 0.17/0.52 (! [A,B,C,D,E] :~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))& (! [F,G] :~ ( A = ordered_pair(F,G)& in(F,set_intersection2(B,D))& in(G,set_intersection2(C,E)) ) )) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f11,conjecture,(
% 0.17/0.52 (! [A,B,C,D] :( ( disjoint(A,B)| disjoint(C,D) )=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f12,negated_conjecture,(
% 0.17/0.52 ~((! [A,B,C,D] :( ( disjoint(A,B)| disjoint(C,D) )=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ) ))),
% 0.17/0.52 inference(negated_conjecture,[status(cth)],[f11])).
% 0.17/0.52 fof(f13,axiom,(
% 0.17/0.52 (! [A,B] :( ~ ( ~ disjoint(A,B)& (! [C] : ~ in(C,set_intersection2(A,B)) ))& ~ ( (? [C] : in(C,set_intersection2(A,B)))& disjoint(A,B) ) ) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f17,plain,(
% 0.17/0.52 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f3])).
% 0.17/0.52 fof(f26,plain,(
% 0.17/0.52 ![A,B]: (~disjoint(A,B)|disjoint(B,A))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.17/0.52 fof(f27,plain,(
% 0.17/0.52 ![X0,X1]: (~disjoint(X0,X1)|disjoint(X1,X0))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f26])).
% 0.17/0.52 fof(f28,plain,(
% 0.17/0.52 ![A,B,C,D,E]: (~in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|(?[F,G]: ((A=ordered_pair(F,G)&in(F,set_intersection2(B,D)))&in(G,set_intersection2(C,E)))))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.17/0.52 fof(f29,plain,(
% 0.17/0.52 ![A,B,C,D,E]: (~in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|(?[G]: ((?[F]: (A=ordered_pair(F,G)&in(F,set_intersection2(B,D))))&in(G,set_intersection2(C,E)))))),
% 0.17/0.52 inference(miniscoping,[status(thm)],[f28])).
% 0.17/0.52 fof(f30,plain,(
% 0.17/0.52 ![A,B,C,D,E]: (~in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|((A=ordered_pair(sK3_skl(E,D,C,B,A),sK2_skl(E,D,C,B,A))&in(sK3_skl(E,D,C,B,A),set_intersection2(B,D)))&in(sK2_skl(E,D,C,B,A),set_intersection2(C,E))))),
% 0.17/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(G,sK2_skl(E,D,C,B,A)),skolemize(F,sK3_skl(E,D,C,B,A))],[f29])).
% 0.17/0.52 fof(f32,plain,(
% 0.17/0.52 ![X0,X1,X2,X3,X4]: (~in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))|in(sK3_skl(X4,X3,X2,X1,X0),set_intersection2(X1,X3)))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f30])).
% 0.17/0.52 fof(f33,plain,(
% 0.17/0.52 ![X0,X1,X2,X3,X4]: (~in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))|in(sK2_skl(X4,X3,X2,X1,X0),set_intersection2(X2,X4)))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f30])).
% 0.17/0.52 fof(f34,plain,(
% 0.17/0.52 (?[A,B,C,D]: ((disjoint(A,B)|disjoint(C,D))&~disjoint(cartesian_product2(A,C),cartesian_product2(B,D))))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.17/0.52 fof(f35,plain,(
% 0.17/0.52 ((disjoint(sK4_skl,sK5_skl)|disjoint(sK6_skl,sK7_skl))&~disjoint(cartesian_product2(sK4_skl,sK6_skl),cartesian_product2(sK5_skl,sK7_skl)))),
% 0.17/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl),skolemize(D,sK7_skl)],[f34])).
% 0.17/0.52 fof(f36,plain,(
% 0.17/0.52 disjoint(sK4_skl,sK5_skl)|disjoint(sK6_skl,sK7_skl)),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f35])).
% 0.17/0.52 fof(f37,plain,(
% 0.17/0.52 ~disjoint(cartesian_product2(sK4_skl,sK6_skl),cartesian_product2(sK5_skl,sK7_skl))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f35])).
% 0.17/0.52 fof(f38,plain,(
% 0.17/0.52 ![A,B]: ((disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B))))&((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.17/0.52 fof(f39,plain,(
% 0.17/0.52 (![A,B]: (disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B)))))&(![A,B]: ((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 0.17/0.54 inference(miniscoping,[status(thm)],[f38])).
% 0.17/0.54 fof(f40,plain,(
% 0.17/0.54 (![A,B]: (disjoint(A,B)|in(sK8_skl(B,A),set_intersection2(A,B))))&(![A,B]: ((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 0.17/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(C,sK8_skl(B,A))],[f39])).
% 0.17/0.54 fof(f41,plain,(
% 0.17/0.54 ![X0,X1]: (disjoint(X0,X1)|in(sK8_skl(X1,X0),set_intersection2(X0,X1)))),
% 0.17/0.54 inference(cnf_transformation,[status(thm)],[f40])).
% 0.17/0.54 fof(f42,plain,(
% 0.17/0.54 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|~disjoint(X1,X2))),
% 0.17/0.54 inference(cnf_transformation,[status(thm)],[f40])).
% 0.17/0.54 fof(f43,definition,(
% 0.17/0.54 sQ0_spl <=> (disjoint(sK4_skl,sK5_skl))),
% 0.17/0.54 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.17/0.54 fof(f44,plain,(
% 0.17/0.54 disjoint(sK4_skl,sK5_skl)|~sQ0_spl),
% 0.17/0.54 inference(component_clause,[status(thm)],[f43])).
% 0.17/0.54 fof(f46,definition,(
% 0.17/0.54 sQ1_spl <=> (disjoint(sK6_skl,sK7_skl))),
% 0.17/0.54 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.17/0.54 fof(f47,plain,(
% 0.17/0.54 disjoint(sK6_skl,sK7_skl)|~sQ1_spl),
% 0.17/0.54 inference(component_clause,[status(thm)],[f46])).
% 0.17/0.54 fof(f49,plain,(
% 0.17/0.54 sQ0_spl|sQ1_spl),
% 0.17/0.54 inference(split_clause,[status(thm)],[f36,f43,f46])).
% 0.17/0.54 fof(f50,plain,(
% 0.17/0.54 disjoint(sK5_skl,sK4_skl)|~sQ0_spl),
% 0.17/0.54 inference(resolution,[status(thm)],[f27,f44])).
% 0.17/0.54 fof(f61,plain,(
% 0.17/0.54 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|~disjoint(X2,X1))),
% 0.17/0.54 inference(paramodulation,[status(thm)],[f17,f42])).
% 0.17/0.54 fof(f109,plain,(
% 0.17/0.54 ![X0,X1,X2,X3]: (disjoint(cartesian_product2(X0,X1),cartesian_product2(X2,X3))|in(sK3_skl(X3,X2,X1,X0,sK8_skl(cartesian_product2(X2,X3),cartesian_product2(X0,X1))),set_intersection2(X0,X2)))),
% 0.17/0.54 inference(resolution,[status(thm)],[f41,f32])).
% 0.17/0.54 fof(f124,plain,(
% 0.17/0.54 ![X0,X1,X2,X3]: (in(sK2_skl(X0,X1,X2,X3,sK8_skl(cartesian_product2(X1,X0),cartesian_product2(X3,X2))),set_intersection2(X2,X0))|disjoint(cartesian_product2(X3,X2),cartesian_product2(X1,X0)))),
% 0.17/0.54 inference(resolution,[status(thm)],[f33,f41])).
% 0.17/0.54 fof(f594,plain,(
% 0.17/0.54 ![X0,X1,X2,X3]: (disjoint(cartesian_product2(X0,X1),cartesian_product2(X2,X3))|~disjoint(X2,X0))),
% 0.17/0.54 inference(resolution,[status(thm)],[f109,f61])).
% 0.17/0.54 fof(f658,plain,(
% 0.17/0.54 ![X0,X1]: (disjoint(cartesian_product2(sK4_skl,X0),cartesian_product2(sK5_skl,X1))|~sQ0_spl)),
% 0.17/0.54 inference(resolution,[status(thm)],[f594,f50])).
% 0.17/0.54 fof(f660,plain,(
% 0.17/0.54 $false|~sQ0_spl),
% 0.17/0.54 inference(backward_subsumption_resolution,[status(thm)],[f37,f658])).
% 0.17/0.54 fof(f665,plain,(
% 0.17/0.54 ~sQ0_spl),
% 0.17/0.54 inference(contradiction_clause,[status(thm)],[f660])).
% 0.17/0.54 fof(f669,plain,(
% 0.17/0.54 disjoint(sK7_skl,sK6_skl)|~sQ1_spl),
% 0.17/0.54 inference(resolution,[status(thm)],[f47,f27])).
% 0.17/0.54 fof(f833,plain,(
% 0.17/0.54 ![X0,X1,X2,X3]: (disjoint(cartesian_product2(X0,X1),cartesian_product2(X2,X3))|~disjoint(X3,X1))),
% 0.17/0.54 inference(resolution,[status(thm)],[f124,f61])).
% 0.17/0.54 fof(f910,plain,(
% 0.17/0.54 ![X0,X1]: (disjoint(cartesian_product2(X0,sK6_skl),cartesian_product2(X1,sK7_skl))|~sQ1_spl)),
% 0.17/0.54 inference(resolution,[status(thm)],[f833,f669])).
% 0.17/0.54 fof(f920,plain,(
% 0.17/0.54 $false|~sQ1_spl),
% 0.17/0.54 inference(backward_subsumption_resolution,[status(thm)],[f37,f910])).
% 0.17/0.54 fof(f927,plain,(
% 0.17/0.54 ~sQ1_spl),
% 0.17/0.54 inference(contradiction_clause,[status(thm)],[f920])).
% 0.17/0.54 fof(f928,plain,(
% 0.17/0.54 $false),
% 0.17/0.54 inference(sat_refutation,[status(thm)],[f49,f665,f927])).
% 0.17/0.54 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.56 % Elapsed time: 0.115612 seconds
% 0.17/0.56 % CPU time: 0.410976 seconds
% 0.17/0.56 % Total memory used: 71.730 MB
% 0.17/0.56 % Net memory used: 71.525 MB
%------------------------------------------------------------------------------