%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:21:42 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU120+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:53:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.41 fof(f3,axiom,(
% 0.09/0.41 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f5,axiom,(
% 0.09/0.41 (! [A,B] :( disjoint(A,B)<=> set_intersection2(A,B) = empty_set ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f14,conjecture,(
% 0.09/0.41 (! [A,B] :( ~ ( ~ disjoint(A,B)& (! [C] : ~ in(C,set_intersection2(A,B)) ))& ~ ( (? [C] : in(C,set_intersection2(A,B)))& disjoint(A,B) ) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f15,negated_conjecture,(
% 0.09/0.41 ~((! [A,B] :( ~ ( ~ disjoint(A,B)& (! [C] : ~ in(C,set_intersection2(A,B)) ))& ~ ( (? [C] : in(C,set_intersection2(A,B)))& disjoint(A,B) ) ) ))),
% 0.09/0.41 inference(negated_conjecture,[status(cth)],[f14])).
% 0.09/0.41 fof(f19,plain,(
% 0.09/0.41 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f3])).
% 0.09/0.41 fof(f20,plain,(
% 0.09/0.41 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f19])).
% 0.09/0.41 fof(f21,plain,(
% 0.09/0.41 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK0_skl(A),A)))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f20])).
% 0.09/0.41 fof(f22,plain,(
% 0.09/0.41 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f21])).
% 0.09/0.41 fof(f23,plain,(
% 0.09/0.41 ![X0]: (X0=empty_set|in(sK0_skl(X0),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f21])).
% 0.09/0.41 fof(f33,plain,(
% 0.09/0.41 ![A,B]: ((~disjoint(A,B)|set_intersection2(A,B)=empty_set)&(disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f5])).
% 0.09/0.41 fof(f34,plain,(
% 0.09/0.41 (![A,B]: (~disjoint(A,B)|set_intersection2(A,B)=empty_set))&(![A,B]: (disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f33])).
% 0.09/0.41 fof(f35,plain,(
% 0.09/0.41 ![X0,X1]: (~disjoint(X0,X1)|set_intersection2(X0,X1)=empty_set)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f34])).
% 0.09/0.41 fof(f36,plain,(
% 0.09/0.41 ![X0,X1]: (disjoint(X0,X1)|~set_intersection2(X0,X1)=empty_set)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f34])).
% 0.09/0.41 fof(f52,plain,(
% 0.09/0.41 (?[A,B]: ((~disjoint(A,B)&(![C]: ~in(C,set_intersection2(A,B))))|((?[C]: in(C,set_intersection2(A,B)))&disjoint(A,B))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.09/0.41 fof(f53,definition,(
% 0.09/0.41 ![A,B]: (sP0_prd(B,A)<=>(~disjoint(A,B)&(![C]: ~in(C,set_intersection2(A,B)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.41 fof(f54,plain,(
% 0.09/0.41 ?[A,B]: (sP0_prd(B,A)|((?[C]: in(C,set_intersection2(A,B)))&disjoint(A,B)))),
% 0.09/0.41 inference(formula_renaming,[status(thm)],[f52,f53])).
% 0.09/0.41 fof(f55,plain,(
% 0.09/0.41 (?[A,B]: sP0_prd(B,A))|(?[A,B]: ((?[C]: in(C,set_intersection2(A,B)))&disjoint(A,B)))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f54])).
% 0.09/0.41 fof(f56,plain,(
% 0.09/0.41 sP0_prd(sK6_skl,sK5_skl)|(in(sK9_skl,set_intersection2(sK7_skl,sK8_skl))&disjoint(sK7_skl,sK8_skl))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(A,sK7_skl),skolemize(B,sK8_skl),skolemize(C,sK9_skl)],[f55])).
% 0.09/0.41 fof(f57,plain,(
% 0.09/0.41 sP0_prd(sK6_skl,sK5_skl)|in(sK9_skl,set_intersection2(sK7_skl,sK8_skl))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f56])).
% 0.09/0.41 fof(f58,plain,(
% 0.09/0.41 sP0_prd(sK6_skl,sK5_skl)|disjoint(sK7_skl,sK8_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f56])).
% 0.09/0.41 fof(f59,plain,(
% 0.09/0.41 ![A,B]: ((~sP0_prd(B,A)|(~disjoint(A,B)&(![C]: ~in(C,set_intersection2(A,B)))))&(sP0_prd(B,A)|(disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B))))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f53])).
% 0.09/0.41 fof(f60,plain,(
% 0.09/0.41 (![A,B]: (~sP0_prd(B,A)|(~disjoint(A,B)&(![C]: ~in(C,set_intersection2(A,B))))))&(![A,B]: (sP0_prd(B,A)|(disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B))))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f59])).
% 0.09/0.41 fof(f61,plain,(
% 0.09/0.41 (![A,B]: (~sP0_prd(B,A)|(~disjoint(A,B)&(![C]: ~in(C,set_intersection2(A,B))))))&(![A,B]: (sP0_prd(B,A)|(disjoint(A,B)|in(sK10_skl(B,A),set_intersection2(A,B)))))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(B,A))],[f60])).
% 0.09/0.41 fof(f62,plain,(
% 0.09/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|~disjoint(X1,X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f61])).
% 0.09/0.41 fof(f63,plain,(
% 0.09/0.41 ![X0,X1,X2]: (~sP0_prd(X0,X1)|~in(X2,set_intersection2(X1,X0)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f61])).
% 0.09/0.41 fof(f65,plain,(
% 0.09/0.41 ![X0]: (~in(X0,empty_set))),
% 0.09/0.41 inference(destructive_equality_resolution,[status(thm)],[f22])).
% 0.09/0.41 fof(f96,plain,(
% 0.09/0.41 ![X0,X1]: (set_intersection2(X0,X1)=empty_set|~sP0_prd(X1,X0))),
% 0.09/0.41 inference(resolution,[status(thm)],[f23,f63])).
% 0.09/0.41 fof(f100,plain,(
% 0.09/0.41 set_intersection2(sK7_skl,sK8_skl)=empty_set|sP0_prd(sK6_skl,sK5_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f35,f58])).
% 0.09/0.41 fof(f103,plain,(
% 0.09/0.41 ![X0,X1]: (~set_intersection2(X0,X1)=empty_set|~sP0_prd(X1,X0))),
% 0.09/0.41 inference(resolution,[status(thm)],[f36,f62])).
% 0.09/0.41 fof(f104,plain,(
% 0.09/0.41 in(sK9_skl,set_intersection2(sK7_skl,sK8_skl))),
% 0.09/0.41 inference(backward_subsumption_resolution,[status(thm)],[f57,f114])).
% 0.09/0.41 fof(f106,plain,(
% 0.09/0.41 set_intersection2(sK7_skl,sK8_skl)=empty_set),
% 0.09/0.41 inference(backward_subsumption_resolution,[status(thm)],[f100,f114])).
% 0.09/0.41 fof(f114,plain,(
% 0.09/0.41 ![X0,X1]: (~sP0_prd(X0,X1))),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f103,f96])).
% 0.09/0.41 fof(f115,plain,(
% 0.09/0.41 in(sK9_skl,empty_set)),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f106,f104])).
% 0.09/0.41 fof(f119,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f115,f65])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.45 % Elapsed time: 0.059567 seconds
% 0.09/0.45 % CPU time: 0.167788 seconds
% 0.09/0.45 % Total memory used: 102.213 MB
% 0.09/0.45 % Net memory used: 101.845 MB
%------------------------------------------------------------------------------