%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET881+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 : n008.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 0.11s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n008.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 05:43:09 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.38 fof(f2,axiom,(
% 0.11/0.38 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f3,axiom,(
% 0.11/0.38 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f5,axiom,(
% 0.11/0.38 (! [A,B] :( set_difference(singleton(A),B) = empty_set<=> in(A,B) ) )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f8,conjecture,(
% 0.11/0.38 (! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set )),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f9,negated_conjecture,(
% 0.11/0.38 ~((! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set ))),
% 0.11/0.38 inference(negated_conjecture,[status(cth)],[f8])).
% 0.11/0.38 fof(f12,plain,(
% 0.11/0.38 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f2])).
% 0.11/0.38 fof(f13,plain,(
% 0.11/0.38 ![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))))))),
% 0.11/0.38 inference(NNF_transformation,[status(thm)],[f3])).
% 0.11/0.38 fof(f14,plain,(
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(miniscoping,[status(thm)],[f13])).
% 0.11/0.38 fof(f15,plain,(
% 0.11/0.38 (![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)))))),
% 0.11/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f14])).
% 0.11/0.38 fof(f18,plain,(
% 0.11/0.38 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f15])).
% 0.11/0.38 fof(f23,plain,(
% 0.11/0.38 ![A,B]: ((~set_difference(singleton(A),B)=empty_set|in(A,B))&(set_difference(singleton(A),B)=empty_set|~in(A,B)))),
% 0.11/0.38 inference(NNF_transformation,[status(thm)],[f5])).
% 0.11/0.38 fof(f24,plain,(
% 0.11/0.38 (![A,B]: (~set_difference(singleton(A),B)=empty_set|in(A,B)))&(![A,B]: (set_difference(singleton(A),B)=empty_set|~in(A,B)))),
% 0.11/0.38 inference(miniscoping,[status(thm)],[f23])).
% 0.11/0.38 fof(f26,plain,(
% 0.11/0.38 ![X0,X1]: (set_difference(singleton(X0),X1)=empty_set|~in(X0,X1))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f24])).
% 0.11/0.38 fof(f31,plain,(
% 0.11/0.38 (?[A,B]: ~set_difference(singleton(A),unordered_pair(A,B))=empty_set)),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.11/0.38 fof(f32,plain,(
% 0.11/0.38 ~set_difference(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl))=empty_set),
% 0.11/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f31])).
% 0.11/0.38 fof(f33,plain,(
% 0.11/0.38 ~set_difference(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl))=empty_set),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f32])).
% 0.11/0.38 fof(f36,plain,(
% 0.11/0.38 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.11/0.38 inference(destructive_equality_resolution,[status(thm)],[f18])).
% 0.11/0.38 fof(f41,plain,(
% 0.11/0.38 ~set_difference(singleton(sK3_skl),unordered_pair(sK4_skl,sK3_skl))=empty_set),
% 0.11/0.38 inference(paramodulation,[status(thm)],[f12,f33])).
% 0.11/0.38 fof(f51,plain,(
% 0.11/0.38 ![X0,X1]: (set_difference(singleton(X0),unordered_pair(X1,X0))=empty_set)),
% 0.11/0.38 inference(resolution,[status(thm)],[f26,f36])).
% 0.11/0.38 fof(f53,plain,(
% 0.11/0.38 ~empty_set=empty_set),
% 0.11/0.38 inference(backward_demodulation,[status(thm)],[f51,f41])).
% 0.11/0.38 fof(f58,plain,(
% 0.11/0.38 $false),
% 0.11/0.38 inference(trivial_equality_resolution,[status(thm)],[f53])).
% 0.11/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.40 % Elapsed time: 0.050197 seconds
% 0.11/0.40 % CPU time: 0.147994 seconds
% 0.11/0.40 % Total memory used: 101.414 MB
% 0.11/0.40 % Net memory used: 100.985 MB
%------------------------------------------------------------------------------