%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% 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 02:21:43 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:51:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % 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] : set_union2(A,B) = set_union2(B,A) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f6,axiom,(
% 0.13/0.42 (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f7,axiom,(
% 0.13/0.42 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f30,conjecture,(
% 0.13/0.42 (! [A,B] : subset(A,set_union2(A,B)) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f31,negated_conjecture,(
% 0.13/0.42 ~((! [A,B] : subset(A,set_union2(A,B)) ))),
% 0.13/0.42 inference(negated_conjecture,[status(cth)],[f30])).
% 0.13/0.42 fof(f35,plain,(
% 0.13/0.42 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.42 fof(f47,plain,(
% 0.13/0.42 ![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)))))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f6])).
% 0.13/0.42 fof(f48,plain,(
% 0.13/0.42 (![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)))))))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f47])).
% 0.13/0.42 fof(f49,plain,(
% 0.13/0.42 (![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))))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f48])).
% 0.13/0.42 fof(f52,plain,(
% 0.13/0.42 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X2))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.42 fof(f56,plain,(
% 0.13/0.42 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.13/0.42 fof(f57,plain,(
% 0.13/0.42 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f56])).
% 0.13/0.42 fof(f58,plain,(
% 0.13/0.42 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f57])).
% 0.13/0.42 fof(f59,plain,(
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f58])).
% 0.13/0.42 fof(f61,plain,(
% 0.13/0.42 ![X0,X1]: (subset(X0,X1)|in(sK2_skl(X1,X0),X0))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f59])).
% 0.13/0.42 fof(f62,plain,(
% 0.13/0.42 ![X0,X1]: (subset(X0,X1)|~in(sK2_skl(X1,X0),X1))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f59])).
% 0.13/0.42 fof(f118,plain,(
% 0.13/0.42 (?[A,B]: ~subset(A,set_union2(A,B)))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 0.13/0.42 fof(f119,plain,(
% 0.13/0.42 ~subset(sK8_skl,set_union2(sK8_skl,sK9_skl))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f118])).
% 0.13/0.42 fof(f120,plain,(
% 0.13/0.42 ~subset(sK8_skl,set_union2(sK8_skl,sK9_skl))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f119])).
% 0.13/0.42 fof(f129,plain,(
% 0.13/0.42 ![X0,X1,X2]: (in(X0,set_union2(X1,X2))|~in(X0,X2))),
% 0.13/0.42 inference(destructive_equality_resolution,[status(thm)],[f52])).
% 0.13/0.42 fof(f383,plain,(
% 0.13/0.42 ![X0,X1,X2]: (subset(X0,X1)|in(sK2_skl(X1,X0),set_union2(X2,X0)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f61,f129])).
% 0.13/0.42 fof(f419,plain,(
% 0.13/0.42 ![X0,X1]: (subset(X0,set_union2(X1,X0))|subset(X0,set_union2(X1,X0)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f383,f62])).
% 0.13/0.42 fof(f430,plain,(
% 0.13/0.42 ![X0,X1]: (subset(X0,set_union2(X1,X0)))),
% 0.13/0.42 inference(duplicate_literals_removal,[status(thm)],[f419])).
% 0.13/0.42 fof(f449,plain,(
% 0.13/0.42 ![X0,X1]: (subset(X0,set_union2(X0,X1)))),
% 0.13/0.42 inference(paramodulation,[status(thm)],[f35,f430])).
% 0.13/0.42 fof(f452,plain,(
% 0.13/0.42 $false),
% 0.13/0.42 inference(backward_subsumption_resolution,[status(thm)],[f120,f449])).
% 0.13/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.45 % Elapsed time: 0.083184 seconds
% 0.13/0.45 % CPU time: 0.372554 seconds
% 0.13/0.45 % Total memory used: 106.016 MB
% 0.13/0.45 % Net memory used: 105.320 MB
%------------------------------------------------------------------------------