%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET916+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 : n010.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 02:12:51 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET916+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:43:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.42 fof(f2,axiom,(
% 0.13/0.42 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f4,axiom,(
% 0.13/0.42 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f5,axiom,(
% 0.13/0.42 (! [A,B,C] :( C = set_intersection2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& in(D,B) ) ) )) )),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f10,axiom,(
% 0.13/0.42 (! [A,B] :( ~ ( ~ disjoint(A,B)& (! [C] : ~ in(C,set_intersection2(A,B)) ))& ~ ( (? [C] : in(C,set_intersection2(A,B)))& disjoint(A,B) ) ) )),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f11,conjecture,(
% 0.13/0.42 (! [A,B,C] :~ ( ~ in(A,B)& ~ in(C,B)& ~ disjoint(unordered_pair(A,C),B) ) )),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f12,negated_conjecture,(
% 0.13/0.42 ~((! [A,B,C] :~ ( ~ in(A,B)& ~ in(C,B)& ~ disjoint(unordered_pair(A,C),B) ) ))),
% 0.13/0.42 inference(negated_conjecture,[status(cth)],[f11])).
% 0.13/0.42 fof(f15,plain,(
% 0.13/0.42 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.42 fof(f17,plain,(
% 0.13/0.42 ![A,B,C]: ((~C=unordered_pair(A,B)|(![D]: ((~in(D,C)|(D=A|D=B))&(in(D,C)|(~D=A&~D=B)))))&(C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f4])).
% 0.13/0.42 fof(f18,plain,(
% 0.13/0.42 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f17])).
% 0.13/0.42 fof(f19,plain,(
% 0.13/0.42 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|((~in(sK0_skl(C,B,A),C)|(~sK0_skl(C,B,A)=A&~sK0_skl(C,B,A)=B))&(in(sK0_skl(C,B,A),C)|(sK0_skl(C,B,A)=A|sK0_skl(C,B,A)=B)))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f18])).
% 0.13/0.42 fof(f20,plain,(
% 0.13/0.42 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|~in(X3,X0)|X3=X1|X3=X2)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.42 fof(f26,plain,(
% 0.13/0.42 ![A,B,C]: ((~C=set_intersection2(A,B)|(![D]: ((~in(D,C)|(in(D,A)&in(D,B)))&(in(D,C)|(~in(D,A)|~in(D,B))))))&(C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f5])).
% 0.13/0.42 fof(f27,plain,(
% 0.13/0.42 (![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f26])).
% 0.13/0.42 fof(f28,plain,(
% 0.13/0.42 (![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|((~in(sK1_skl(C,B,A),C)|(~in(sK1_skl(C,B,A),A)|~in(sK1_skl(C,B,A),B)))&(in(sK1_skl(C,B,A),C)|(in(sK1_skl(C,B,A),A)&in(sK1_skl(C,B,A),B))))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f27])).
% 0.13/0.42 fof(f29,plain,(
% 0.13/0.42 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X1))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f28])).
% 0.13/0.42 fof(f30,plain,(
% 0.13/0.42 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X2))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f28])).
% 0.13/0.42 fof(f43,plain,(
% 0.13/0.42 ![A,B]: ((disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B))))&((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/0.42 fof(f44,plain,(
% 0.13/0.42 (![A,B]: (disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B)))))&(![A,B]: ((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f43])).
% 0.13/0.42 fof(f45,plain,(
% 0.13/0.42 (![A,B]: (disjoint(A,B)|in(sK4_skl(B,A),set_intersection2(A,B))))&(![A,B]: ((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 0.13/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(C,sK4_skl(B,A))],[f44])).
% 0.13/0.43 fof(f46,plain,(
% 0.13/0.43 ![X0,X1]: (disjoint(X0,X1)|in(sK4_skl(X1,X0),set_intersection2(X0,X1)))),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f45])).
% 0.13/0.43 fof(f48,plain,(
% 0.13/0.43 (?[A,B,C]: ((~in(A,B)&~in(C,B))&~disjoint(unordered_pair(A,C),B)))),
% 0.13/0.43 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.13/0.43 fof(f49,plain,(
% 0.13/0.43 ((~in(sK5_skl,sK6_skl)&~in(sK7_skl,sK6_skl))&~disjoint(unordered_pair(sK5_skl,sK7_skl),sK6_skl))),
% 0.13/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(C,sK7_skl)],[f48])).
% 0.13/0.43 fof(f50,plain,(
% 0.13/0.43 ~in(sK5_skl,sK6_skl)),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.43 fof(f51,plain,(
% 0.13/0.43 ~in(sK7_skl,sK6_skl)),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.43 fof(f52,plain,(
% 0.13/0.43 ~disjoint(unordered_pair(sK5_skl,sK7_skl),sK6_skl)),
% 0.13/0.43 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.43 fof(f53,plain,(
% 0.13/0.43 ![X0,X1,X2]: (~in(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 0.13/0.43 inference(destructive_equality_resolution,[status(thm)],[f20])).
% 0.13/0.43 fof(f56,plain,(
% 0.13/0.43 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X1))),
% 0.13/0.43 inference(destructive_equality_resolution,[status(thm)],[f29])).
% 0.13/0.43 fof(f57,plain,(
% 0.13/0.43 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X2))),
% 0.13/0.43 inference(destructive_equality_resolution,[status(thm)],[f30])).
% 0.13/0.43 fof(f65,plain,(
% 0.13/0.43 ~disjoint(unordered_pair(sK7_skl,sK5_skl),sK6_skl)),
% 0.13/0.43 inference(paramodulation,[status(thm)],[f15,f52])).
% 0.13/0.43 fof(f92,plain,(
% 0.13/0.43 ![X0,X1]: (disjoint(X0,X1)|in(sK4_skl(X1,X0),X1))),
% 0.13/0.43 inference(resolution,[status(thm)],[f46,f57])).
% 0.13/0.43 fof(f93,plain,(
% 0.13/0.43 ![X0,X1]: (disjoint(X0,X1)|in(sK4_skl(X1,X0),X0))),
% 0.13/0.43 inference(resolution,[status(thm)],[f46,f56])).
% 0.13/0.43 fof(f107,plain,(
% 0.13/0.43 ![X0,X1,X2]: (disjoint(unordered_pair(X0,X1),X2)|sK4_skl(X2,unordered_pair(X0,X1))=X0|sK4_skl(X2,unordered_pair(X0,X1))=X1)),
% 0.13/0.43 inference(resolution,[status(thm)],[f93,f53])).
% 0.13/0.43 fof(f130,plain,(
% 0.13/0.43 sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl))=sK7_skl|sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl))=sK5_skl),
% 0.13/0.43 inference(resolution,[status(thm)],[f107,f65])).
% 0.13/0.43 fof(f199,plain,(
% 0.13/0.43 disjoint(unordered_pair(sK7_skl,sK5_skl),sK6_skl)|in(sK5_skl,sK6_skl)|sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl))=sK7_skl),
% 0.13/0.43 inference(paramodulation,[status(thm)],[f130,f92])).
% 0.13/0.43 fof(f205,plain,(
% 0.13/0.43 in(sK5_skl,sK6_skl)|sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl))=sK7_skl),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f199,f65])).
% 0.13/0.43 fof(f405,plain,(
% 0.13/0.43 sK4_skl(sK6_skl,unordered_pair(sK7_skl,sK5_skl))=sK7_skl),
% 0.13/0.43 inference(resolution,[status(thm)],[f205,f50])).
% 0.13/0.43 fof(f423,plain,(
% 0.13/0.43 disjoint(unordered_pair(sK7_skl,sK5_skl),sK6_skl)|in(sK7_skl,sK6_skl)),
% 0.13/0.43 inference(paramodulation,[status(thm)],[f405,f92])).
% 0.13/0.43 fof(f430,plain,(
% 0.13/0.43 in(sK7_skl,sK6_skl)),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f423,f65])).
% 0.13/0.43 fof(f431,plain,(
% 0.13/0.43 $false),
% 0.13/0.43 inference(backward_subsumption_resolution,[status(thm)],[f51,f430])).
% 0.13/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.45 % Elapsed time: 0.088719 seconds
% 0.13/0.45 % CPU time: 0.420823 seconds
% 0.13/0.45 % Total memory used: 58.727 MB
% 0.13/0.45 % Net memory used: 58.235 MB
%------------------------------------------------------------------------------