%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET906+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 : n014.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 02:12:50 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET906+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
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:43:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.40 fof(f3,axiom,(
% 0.14/0.40 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f4,axiom,(
% 0.14/0.40 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f5,axiom,(
% 0.14/0.40 (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f6,axiom,(
% 0.14/0.40 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f13,conjecture,(
% 0.14/0.40 (! [A,B,C] :( subset(set_union2(unordered_pair(A,B),C),C)=> in(A,C) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f14,negated_conjecture,(
% 0.14/0.40 ~((! [A,B,C] :( subset(set_union2(unordered_pair(A,B),C),C)=> in(A,C) ) ))),
% 0.14/0.40 inference(negated_conjecture,[status(cth)],[f13])).
% 0.14/0.40 fof(f18,plain,(
% 0.14/0.40 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.40 fof(f19,plain,(
% 0.14/0.40 ![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))))))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f4])).
% 0.14/0.40 fof(f20,plain,(
% 0.14/0.40 (![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))))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f19])).
% 0.14/0.40 fof(f21,plain,(
% 0.14/0.40 (![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)))))),
% 0.14/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f20])).
% 0.14/0.40 fof(f23,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X1)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/0.40 fof(f28,plain,(
% 0.14/0.40 ![A,B,C]: ((~C=set_union2(A,B)|(![D]: ((~in(D,C)|(in(D,A)|in(D,B)))&(in(D,C)|(~in(D,A)&~in(D,B))))))&(C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f5])).
% 0.14/0.40 fof(f29,plain,(
% 0.14/0.40 (![A,B,C]: (~C=set_union2(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_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f28])).
% 0.14/0.40 fof(f30,plain,(
% 0.14/0.40 (![A,B,C]: (~C=set_union2(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_union2(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))))))),
% 0.14/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f29])).
% 0.14/0.40 fof(f32,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X1))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f30])).
% 0.14/0.40 fof(f37,plain,(
% 0.14/0.40 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.14/0.40 fof(f38,plain,(
% 0.14/0.40 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f37])).
% 0.14/0.40 fof(f39,plain,(
% 0.14/0.40 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f38])).
% 0.14/0.40 fof(f40,plain,(
% 0.14/0.40 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK2_skl(B,A),A)&~in(sK2_skl(B,A),B))))),
% 0.14/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f39])).
% 0.14/0.40 fof(f41,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.14/0.40 fof(f58,plain,(
% 0.14/0.40 (?[A,B,C]: (subset(set_union2(unordered_pair(A,B),C),C)&~in(A,C)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.14/0.40 fof(f59,plain,(
% 0.14/0.40 ?[A,C]: ((?[B]: subset(set_union2(unordered_pair(A,B),C),C))&~in(A,C))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f58])).
% 0.14/0.40 fof(f60,plain,(
% 0.14/0.40 (subset(set_union2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK6_skl)&~in(sK5_skl,sK6_skl))),
% 0.14/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK5_skl),skolemize(C,sK6_skl),skolemize(B,sK7_skl)],[f59])).
% 0.14/0.40 fof(f61,plain,(
% 0.14/0.40 subset(set_union2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK6_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f60])).
% 0.14/0.40 fof(f62,plain,(
% 0.14/0.40 ~in(sK5_skl,sK6_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f60])).
% 0.14/0.40 fof(f64,plain,(
% 0.14/0.40 ![X0,X1]: (in(X0,unordered_pair(X0,X1)))),
% 0.14/0.40 inference(destructive_equality_resolution,[status(thm)],[f23])).
% 0.14/0.40 fof(f67,plain,(
% 0.14/0.40 ![X0,X1,X2]: (in(X0,set_union2(X1,X2))|~in(X0,X1))),
% 0.14/0.40 inference(destructive_equality_resolution,[status(thm)],[f32])).
% 0.14/0.40 fof(f83,plain,(
% 0.14/0.40 subset(set_union2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK6_skl)),
% 0.14/0.40 inference(paramodulation,[status(thm)],[f18,f61])).
% 0.14/0.40 fof(f100,plain,(
% 0.14/0.40 ![X0,X1,X2]: (in(X0,set_union2(unordered_pair(X0,X1),X2)))),
% 0.14/0.40 inference(resolution,[status(thm)],[f67,f64])).
% 0.14/0.40 fof(f115,plain,(
% 0.14/0.40 ![X0,X1,X2]: (in(X0,set_union2(X1,unordered_pair(X0,X2))))),
% 0.14/0.40 inference(paramodulation,[status(thm)],[f18,f100])).
% 0.14/0.40 fof(f138,plain,(
% 0.14/0.40 ![X0]: (~in(X0,set_union2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)))|in(X0,sK6_skl))),
% 0.14/0.40 inference(resolution,[status(thm)],[f41,f83])).
% 0.14/0.40 fof(f181,plain,(
% 0.14/0.40 in(sK5_skl,sK6_skl)),
% 0.14/0.40 inference(resolution,[status(thm)],[f138,f115])).
% 0.14/0.40 fof(f183,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f181,f62])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.42 % Elapsed time: 0.055974 seconds
% 0.14/0.42 % CPU time: 0.171897 seconds
% 0.14/0.42 % Total memory used: 102.404 MB
% 0.14/0.42 % Net memory used: 102.094 MB
%------------------------------------------------------------------------------