%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 02:21:53 PM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:56:00 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.40 fof(f2,axiom,(
% 0.15/0.40 (! [A,B] :( ( ~ empty(A)=> ( element(B,A)<=> in(B,A) ) )& ( empty(A)=> ( element(B,A)<=> empty(B) ) ) ) )),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f3,axiom,(
% 0.15/0.40 (! [A,B,C] :( C = set_difference(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& ~ in(D,B) ) ) )) )),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f4,axiom,(
% 0.15/0.40 (! [A,B] :( element(B,powerset(A))=> subset_complement(A,B) = set_difference(A,B) ) )),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f15,axiom,(
% 0.15/0.40 (? [A] : empty(A) )),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f20,conjecture,(
% 0.15/0.40 (! [A] :( A != empty_set=> (! [B] :( element(B,powerset(A))=> (! [C] :( element(C,A)=> ( ~ in(C,B)=> in(C,subset_complement(A,B)) ) ) )) )) )),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f21,negated_conjecture,(
% 0.15/0.40 ~((! [A] :( A != empty_set=> (! [B] :( element(B,powerset(A))=> (! [C] :( element(C,A)=> ( ~ in(C,B)=> in(C,subset_complement(A,B)) ) ) )) )) ))),
% 0.15/0.40 inference(negated_conjecture,[status(cth)],[f20])).
% 0.15/0.40 fof(f22,axiom,(
% 0.15/0.40 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f27,plain,(
% 0.15/0.40 ![A,B]: ((empty(A)|(element(B,A)<=>in(B,A)))&(~empty(A)|(element(B,A)<=>empty(B))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.15/0.40 fof(f28,plain,(
% 0.15/0.40 ![A,B]: ((empty(A)|((~element(B,A)|in(B,A))&(element(B,A)|~in(B,A))))&(~empty(A)|((~element(B,A)|empty(B))&(element(B,A)|~empty(B)))))),
% 0.15/0.40 inference(NNF_transformation,[status(thm)],[f27])).
% 0.15/0.40 fof(f29,plain,(
% 0.15/0.40 (![A]: (empty(A)|((![B]: (~element(B,A)|in(B,A)))&(![B]: (element(B,A)|~in(B,A))))))&(![A]: (~empty(A)|((![B]: (~element(B,A)|empty(B)))&(![B]: (element(B,A)|~empty(B))))))),
% 0.15/0.40 inference(miniscoping,[status(thm)],[f28])).
% 0.15/0.40 fof(f30,plain,(
% 0.15/0.40 ![X0,X1]: (empty(X0)|~element(X1,X0)|in(X1,X0))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f29])).
% 0.15/0.40 fof(f34,plain,(
% 0.15/0.40 ![A,B,C]: ((~C=set_difference(A,B)|(![D]: ((~in(D,C)|(in(D,A)&~in(D,B)))&(in(D,C)|(~in(D,A)|in(D,B))))))&(C=set_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 0.15/0.40 inference(NNF_transformation,[status(thm)],[f3])).
% 0.15/0.40 fof(f35,plain,(
% 0.15/0.40 (![A,B,C]: (~C=set_difference(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_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 0.15/0.40 inference(miniscoping,[status(thm)],[f34])).
% 0.15/0.40 fof(f36,plain,(
% 0.15/0.40 (![A,B,C]: (~C=set_difference(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_difference(A,B)|((~in(sK0_skl(C,B,A),C)|(~in(sK0_skl(C,B,A),A)|in(sK0_skl(C,B,A),B)))&(in(sK0_skl(C,B,A),C)|(in(sK0_skl(C,B,A),A)&~in(sK0_skl(C,B,A),B))))))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f35])).
% 0.15/0.40 fof(f39,plain,(
% 0.15/0.40 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|in(X3,X0)|~in(X3,X1)|in(X3,X2))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f36])).
% 0.15/0.40 fof(f43,plain,(
% 0.15/0.40 ![A,B]: (~element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.15/0.40 fof(f44,plain,(
% 0.15/0.40 ![X0,X1]: (~element(X0,powerset(X1))|subset_complement(X1,X0)=set_difference(X1,X0))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f43])).
% 0.15/0.40 fof(f57,plain,(
% 0.15/0.40 empty(sK3_skl)),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f15])).
% 0.15/0.40 fof(f58,plain,(
% 0.15/0.40 empty(sK3_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f57])).
% 0.15/0.40 fof(f66,plain,(
% 0.15/0.40 (?[A]: (~A=empty_set&(?[B]: (element(B,powerset(A))&(?[C]: (element(C,A)&(~in(C,B)&~in(C,subset_complement(A,B)))))))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.15/0.40 fof(f67,plain,(
% 0.15/0.40 (~sK6_skl=empty_set&(element(sK7_skl,powerset(sK6_skl))&(element(sK8_skl,sK6_skl)&(~in(sK8_skl,sK7_skl)&~in(sK8_skl,subset_complement(sK6_skl,sK7_skl))))))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl),skolemize(C,sK8_skl)],[f66])).
% 0.15/0.40 fof(f68,plain,(
% 0.15/0.40 ~sK6_skl=empty_set),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f67])).
% 0.15/0.40 fof(f69,plain,(
% 0.15/0.40 element(sK7_skl,powerset(sK6_skl))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f67])).
% 0.15/0.40 fof(f70,plain,(
% 0.15/0.40 element(sK8_skl,sK6_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f67])).
% 0.15/0.40 fof(f71,plain,(
% 0.15/0.40 ~in(sK8_skl,sK7_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f67])).
% 0.15/0.40 fof(f72,plain,(
% 0.15/0.40 ~in(sK8_skl,subset_complement(sK6_skl,sK7_skl))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f67])).
% 0.15/0.40 fof(f73,plain,(
% 0.15/0.40 ![A]: (~empty(A)|A=empty_set)),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.15/0.40 fof(f74,plain,(
% 0.15/0.40 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f73])).
% 0.15/0.40 fof(f83,plain,(
% 0.15/0.40 ![X0,X1,X2]: (in(X0,set_difference(X1,X2))|~in(X0,X1)|in(X0,X2))),
% 0.15/0.40 inference(destructive_equality_resolution,[status(thm)],[f39])).
% 0.15/0.40 fof(f84,plain,(
% 0.15/0.40 empty(sK6_skl)|in(sK8_skl,sK6_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f30,f70])).
% 0.15/0.40 fof(f110,plain,(
% 0.15/0.40 ![X0]: (empty(sK6_skl)|in(sK8_skl,set_difference(sK6_skl,X0))|in(sK8_skl,X0))),
% 0.15/0.40 inference(resolution,[status(thm)],[f84,f83])).
% 0.15/0.40 fof(f117,plain,(
% 0.15/0.40 sK3_skl=empty_set),
% 0.15/0.40 inference(resolution,[status(thm)],[f74,f58])).
% 0.15/0.40 fof(f119,plain,(
% 0.15/0.40 subset_complement(sK6_skl,sK7_skl)=set_difference(sK6_skl,sK7_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f44,f69])).
% 0.15/0.40 fof(f132,plain,(
% 0.15/0.40 ![X0]: (~empty(X0)|X0=sK3_skl)),
% 0.15/0.40 inference(backward_demodulation,[status(thm)],[f117,f74])).
% 0.15/0.40 fof(f135,plain,(
% 0.15/0.40 ~sK6_skl=sK3_skl),
% 0.15/0.40 inference(backward_demodulation,[status(thm)],[f117,f68])).
% 0.15/0.40 fof(f163,plain,(
% 0.15/0.40 ~in(sK8_skl,set_difference(sK6_skl,sK7_skl))),
% 0.15/0.40 inference(backward_demodulation,[status(thm)],[f119,f72])).
% 0.15/0.40 fof(f253,plain,(
% 0.15/0.40 empty(sK6_skl)|in(sK8_skl,sK7_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f110,f163])).
% 0.15/0.40 fof(f259,plain,(
% 0.15/0.40 empty(sK6_skl)),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f253,f71])).
% 0.15/0.40 fof(f261,plain,(
% 0.15/0.40 sK6_skl=sK3_skl),
% 0.15/0.40 inference(resolution,[status(thm)],[f259,f132])).
% 0.15/0.40 fof(f264,plain,(
% 0.15/0.40 $false),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f261,f135])).
% 0.15/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.43 % Elapsed time: 0.067773 seconds
% 0.15/0.43 % CPU time: 0.181895 seconds
% 0.15/0.43 % Total memory used: 102.703 MB
% 0.15/0.43 % Net memory used: 102.473 MB
%------------------------------------------------------------------------------