%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET878+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 : n009.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 02:12:48 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET878+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
% 0.17/0.43 % Computer : n009.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
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:42:27 UTC 2026
% 0.17/0.44 % 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(f2,axiom,(
% 0.17/0.48 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f3,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(f4,axiom,(
% 0.17/0.48 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f6,axiom,(
% 0.17/0.48 (! [A,B] :( in(A,B)=> set_intersection2(B,singleton(A)) = singleton(A) ) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f9,conjecture,(
% 0.17/0.48 (! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A) )),
% 0.17/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.48 fof(f10,negated_conjecture,(
% 0.17/0.48 ~((! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A) ))),
% 0.17/0.48 inference(negated_conjecture,[status(cth)],[f9])).
% 0.17/0.48 fof(f13,plain,(
% 0.17/0.48 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f2])).
% 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)],[f3])).
% 0.17/0.48 fof(f15,plain,(
% 0.17/0.48 ![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))))))),
% 0.17/0.48 inference(NNF_transformation,[status(thm)],[f4])).
% 0.17/0.48 fof(f16,plain,(
% 0.17/0.48 (![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))))))),
% 0.17/0.48 inference(miniscoping,[status(thm)],[f15])).
% 0.17/0.48 fof(f17,plain,(
% 0.17/0.48 (![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)))))),
% 0.17/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f16])).
% 0.17/0.48 fof(f20,plain,(
% 0.17/0.48 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f17])).
% 0.17/0.48 fof(f26,plain,(
% 0.17/0.48 ![A,B]: (~in(A,B)|set_intersection2(B,singleton(A))=singleton(A))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.17/0.48 fof(f27,plain,(
% 0.17/0.48 ![X0,X1]: (~in(X0,X1)|set_intersection2(X1,singleton(X0))=singleton(X0))),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f26])).
% 0.17/0.48 fof(f32,plain,(
% 0.17/0.48 (?[A,B]: ~set_intersection2(singleton(A),unordered_pair(A,B))=singleton(A))),
% 0.17/0.48 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.17/0.48 fof(f33,plain,(
% 0.17/0.48 ~set_intersection2(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl))=singleton(sK3_skl)),
% 0.17/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f32])).
% 0.17/0.48 fof(f34,plain,(
% 0.17/0.48 ~set_intersection2(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl))=singleton(sK3_skl)),
% 0.17/0.48 inference(cnf_transformation,[status(thm)],[f33])).
% 0.17/0.48 fof(f37,plain,(
% 0.17/0.48 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.17/0.48 inference(destructive_equality_resolution,[status(thm)],[f20])).
% 0.17/0.48 fof(f42,plain,(
% 0.17/0.48 ~set_intersection2(singleton(sK3_skl),unordered_pair(sK4_skl,sK3_skl))=singleton(sK3_skl)),
% 0.17/0.48 inference(paramodulation,[status(thm)],[f13,f34])).
% 0.17/0.48 fof(f56,plain,(
% 0.17/0.48 ![X0,X1]: (set_intersection2(unordered_pair(X0,X1),singleton(X1))=singleton(X1))),
% 0.17/0.48 inference(resolution,[status(thm)],[f27,f37])).
% 0.17/0.48 fof(f58,plain,(
% 0.17/0.48 ![X0,X1]: (set_intersection2(singleton(X0),unordered_pair(X1,X0))=singleton(X0))),
% 0.17/0.48 inference(paramodulation,[status(thm)],[f14,f56])).
% 0.17/0.48 fof(f72,plain,(
% 0.17/0.48 ~singleton(sK3_skl)=singleton(sK3_skl)),
% 0.17/0.48 inference(backward_demodulation,[status(thm)],[f58,f42])).
% 0.17/0.48 fof(f75,plain,(
% 0.17/0.48 $false),
% 0.17/0.48 inference(trivial_equality_resolution,[status(thm)],[f72])).
% 0.17/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.53 % Elapsed time: 0.077281 seconds
% 0.17/0.53 % CPU time: 0.107187 seconds
% 0.17/0.53 % Total memory used: 6.364 MB
% 0.17/0.53 % Net memory used: 6.352 MB
%------------------------------------------------------------------------------