%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU131+1 : 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 : n011.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 02:21:44 PM UTC 2026
% Result : Theorem 1.24s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:51:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 1.24/0.57 % Refutation found
% 1.24/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.24/0.57 % SZS output start CNFRefutation for theBenchmark
% 1.24/0.57 fof(f2,axiom,(
% 1.24/0.57 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 1.24/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.24/0.57 fof(f3,axiom,(
% 1.24/0.57 (! [A,B,C] :( C = set_difference(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& ~ in(D,B) ) ) )) )),
% 1.24/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.24/0.57 fof(f6,axiom,(
% 1.24/0.57 empty(empty_set) ),
% 1.24/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.24/0.57 fof(f7,conjecture,(
% 1.24/0.57 (! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) )),
% 1.24/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.24/0.57 fof(f8,negated_conjecture,(
% 1.24/0.57 ~((! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) ))),
% 1.24/0.57 inference(negated_conjecture,[status(cth)],[f7])).
% 1.24/0.57 fof(f16,axiom,(
% 1.24/0.57 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 1.24/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.24/0.57 fof(f20,plain,(
% 1.24/0.57 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 1.24/0.57 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 1.24/0.57 fof(f21,plain,(
% 1.24/0.57 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 1.24/0.57 inference(NNF_transformation,[status(thm)],[f20])).
% 1.24/0.57 fof(f22,plain,(
% 1.24/0.57 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 1.24/0.57 inference(miniscoping,[status(thm)],[f21])).
% 1.24/0.57 fof(f23,plain,(
% 1.24/0.57 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK0_skl(B,A),A)&~in(sK0_skl(B,A),B))))),
% 1.24/0.57 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f22])).
% 1.24/0.57 fof(f24,plain,(
% 1.24/0.57 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f23])).
% 1.24/0.57 fof(f25,plain,(
% 1.24/0.57 ![X0,X1]: (subset(X0,X1)|in(sK0_skl(X1,X0),X0))),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f23])).
% 1.24/0.57 fof(f26,plain,(
% 1.24/0.57 ![X0,X1]: (subset(X0,X1)|~in(sK0_skl(X1,X0),X1))),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f23])).
% 1.24/0.57 fof(f27,plain,(
% 1.24/0.57 ![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)))))))),
% 1.24/0.57 inference(NNF_transformation,[status(thm)],[f3])).
% 1.24/0.57 fof(f28,plain,(
% 1.24/0.57 (![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)))))))),
% 1.24/0.57 inference(miniscoping,[status(thm)],[f27])).
% 1.24/0.57 fof(f29,plain,(
% 1.24/0.57 (![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(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))))))),
% 1.24/0.57 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f28])).
% 1.24/0.57 fof(f32,plain,(
% 1.24/0.57 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|in(X3,X0)|~in(X3,X1)|in(X3,X2))),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f29])).
% 1.24/0.57 fof(f34,plain,(
% 1.24/0.57 ![X0,X1,X2]: (X0=set_difference(X1,X2)|in(sK1_skl(X0,X2,X1),X0)|in(sK1_skl(X0,X2,X1),X1))),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f29])).
% 1.24/0.57 fof(f35,plain,(
% 1.24/0.57 ![X0,X1,X2]: (X0=set_difference(X1,X2)|in(sK1_skl(X0,X2,X1),X0)|~in(sK1_skl(X0,X2,X1),X2))),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f29])).
% 1.24/0.57 fof(f36,plain,(
% 1.24/0.57 empty(empty_set)),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f6])).
% 1.24/0.57 fof(f37,plain,(
% 1.24/0.57 (?[A,B]: (set_difference(A,B)=empty_set<~>subset(A,B)))),
% 1.24/0.57 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 1.24/0.57 fof(f38,plain,(
% 1.24/0.57 ?[A,B]: ((set_difference(A,B)=empty_set|subset(A,B))&(~set_difference(A,B)=empty_set|~subset(A,B)))),
% 1.24/0.57 inference(NNF_transformation,[status(thm)],[f37])).
% 1.24/0.57 fof(f39,plain,(
% 1.24/0.57 ((set_difference(sK2_skl,sK3_skl)=empty_set|subset(sK2_skl,sK3_skl))&(~set_difference(sK2_skl,sK3_skl)=empty_set|~subset(sK2_skl,sK3_skl)))),
% 1.24/0.57 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f38])).
% 1.24/0.57 fof(f40,plain,(
% 1.24/0.57 set_difference(sK2_skl,sK3_skl)=empty_set|subset(sK2_skl,sK3_skl)),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f39])).
% 1.24/0.57 fof(f41,plain,(
% 1.24/0.57 ~set_difference(sK2_skl,sK3_skl)=empty_set|~subset(sK2_skl,sK3_skl)),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f39])).
% 1.24/0.57 fof(f57,plain,(
% 1.24/0.57 ![A,B]: (~in(A,B)|~empty(B))),
% 1.24/0.57 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 1.24/0.57 fof(f58,plain,(
% 1.24/0.57 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 1.24/0.57 inference(miniscoping,[status(thm)],[f57])).
% 1.24/0.57 fof(f59,plain,(
% 1.24/0.57 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 1.24/0.57 inference(cnf_transformation,[status(thm)],[f58])).
% 1.24/0.57 fof(f63,definition,(
% 1.24/0.57 sQ0_spl <=> (set_difference(sK2_skl,sK3_skl)=empty_set)),
% 1.24/0.57 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 1.24/0.57 fof(f64,plain,(
% 1.24/0.57 set_difference(sK2_skl,sK3_skl)=empty_set|~sQ0_spl),
% 1.24/0.57 inference(component_clause,[status(thm)],[f63])).
% 1.24/0.57 fof(f66,definition,(
% 1.24/0.57 sQ1_spl <=> (subset(sK2_skl,sK3_skl))),
% 1.24/0.57 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 1.24/0.57 fof(f67,plain,(
% 1.24/0.57 subset(sK2_skl,sK3_skl)|~sQ1_spl),
% 1.24/0.57 inference(component_clause,[status(thm)],[f66])).
% 1.24/0.57 fof(f69,plain,(
% 1.24/0.57 sQ0_spl|sQ1_spl),
% 1.24/0.57 inference(split_clause,[status(thm)],[f40,f63,f66])).
% 1.24/0.57 fof(f70,plain,(
% 1.24/0.57 ~sQ0_spl|~sQ1_spl),
% 1.24/0.57 inference(split_clause,[status(thm)],[f41,f63,f66])).
% 1.24/0.57 fof(f73,plain,(
% 1.24/0.57 ![X0,X1,X2]: (in(X0,set_difference(X1,X2))|~in(X0,X1)|in(X0,X2))),
% 1.24/0.57 inference(destructive_equality_resolution,[status(thm)],[f32])).
% 1.24/0.57 fof(f85,plain,(
% 1.24/0.57 ![X0]: (~in(X0,empty_set))),
% 1.24/0.57 inference(resolution,[status(thm)],[f59,f36])).
% 1.24/0.57 fof(f94,plain,(
% 1.24/0.57 ![X0,X1,X2]: (subset(X0,X1)|in(sK0_skl(X1,X0),set_difference(X0,X2))|in(sK0_skl(X1,X0),X2))),
% 1.24/0.57 inference(resolution,[status(thm)],[f25,f73])).
% 1.24/0.57 fof(f103,plain,(
% 1.24/0.57 ![X0,X1]: (empty_set=set_difference(X0,X1)|in(sK1_skl(empty_set,X1,X0),X0))),
% 1.24/0.57 inference(resolution,[status(thm)],[f34,f85])).
% 1.24/0.57 fof(f226,plain,(
% 1.24/0.57 ![X0,X1,X2,X3]: (X0=set_difference(X1,X2)|in(sK1_skl(X0,X2,X1),X0)|~subset(X3,X2)|~in(sK1_skl(X0,X2,X1),X3))),
% 1.24/0.57 inference(resolution,[status(thm)],[f35,f24])).
% 1.24/0.57 fof(f296,plain,(
% 1.24/0.57 ![X0]: (subset(sK2_skl,X0)|in(sK0_skl(X0,sK2_skl),empty_set)|in(sK0_skl(X0,sK2_skl),sK3_skl)|~sQ0_spl)),
% 1.24/0.57 inference(paramodulation,[status(thm)],[f64,f94])).
% 1.24/0.57 fof(f302,plain,(
% 1.24/0.57 ![X0]: (subset(sK2_skl,X0)|in(sK0_skl(X0,sK2_skl),sK3_skl)|~sQ0_spl)),
% 1.24/0.57 inference(forward_subsumption_resolution,[status(thm)],[f296,f85])).
% 1.24/0.57 fof(f511,plain,(
% 1.24/0.57 subset(sK2_skl,sK3_skl)|subset(sK2_skl,sK3_skl)|~sQ0_spl),
% 1.24/0.57 inference(resolution,[status(thm)],[f302,f26])).
% 1.24/0.57 fof(f519,plain,(
% 1.24/0.57 sQ1_spl|~sQ0_spl),
% 1.24/0.57 inference(split_clause,[status(thm)],[f511,f66,f63])).
% 1.24/0.57 fof(f1258,plain,(
% 1.24/0.57 ![X0,X1]: (X0=set_difference(X1,sK3_skl)|in(sK1_skl(X0,sK3_skl,X1),X0)|~in(sK1_skl(X0,sK3_skl,X1),sK2_skl)|~sQ1_spl)),
% 1.24/0.57 inference(resolution,[status(thm)],[f226,f67])).
% 1.24/0.57 fof(f1522,definition,(
% 1.24/0.57 sQ35_spl <=> (in(sK6_skl(empty_set,sK2_skl),empty_set))),
% 1.24/0.57 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 1.24/0.57 fof(f1523,plain,(
% 1.24/0.57 in(sK6_skl(empty_set,sK2_skl),empty_set)|~sQ35_spl),
% 1.24/0.57 inference(component_clause,[status(thm)],[f1522])).
% 1.24/0.57 fof(f1531,plain,(
% 1.24/0.57 $false|~sQ35_spl),
% 1.24/0.57 inference(forward_subsumption_resolution,[status(thm)],[f1523,f85])).
% 1.24/0.57 fof(f1532,plain,(
% 1.24/0.57 ~sQ35_spl),
% 1.24/0.57 inference(contradiction_clause,[status(thm)],[f1531])).
% 1.24/0.57 fof(f1582,plain,(
% 1.24/0.57 empty_set=set_difference(sK2_skl,sK3_skl)|in(sK1_skl(empty_set,sK3_skl,sK2_skl),empty_set)|empty_set=set_difference(sK2_skl,sK3_skl)|~sQ1_spl),
% 1.24/0.57 inference(resolution,[status(thm)],[f1258,f103])).
% 1.24/0.57 fof(f1603,definition,(
% 1.24/0.57 sQ37_spl <=> (in(sK1_skl(empty_set,sK3_skl,sK2_skl),empty_set))),
% 1.24/0.57 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 1.24/0.57 fof(f1604,plain,(
% 1.24/0.57 in(sK1_skl(empty_set,sK3_skl,sK2_skl),empty_set)|~sQ37_spl),
% 1.24/0.57 inference(component_clause,[status(thm)],[f1603])).
% 1.24/0.57 fof(f1606,plain,(
% 1.24/0.57 sQ0_spl|sQ37_spl|~sQ1_spl),
% 1.24/0.57 inference(split_clause,[status(thm)],[f1582,f63,f1603,f66])).
% 1.24/0.57 fof(f1646,plain,(
% 1.24/0.57 $false|~sQ37_spl),
% 1.24/0.57 inference(forward_subsumption_resolution,[status(thm)],[f1604,f85])).
% 1.24/0.57 fof(f1647,plain,(
% 1.24/0.57 ~sQ37_spl),
% 1.24/0.57 inference(contradiction_clause,[status(thm)],[f1646])).
% 1.24/0.57 fof(f1648,plain,(
% 1.24/0.57 $false),
% 1.24/0.57 inference(sat_refutation,[status(thm)],[f69,f70,f519,f1532,f1606,f1647])).
% 1.24/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 1.24/0.59 % Elapsed time: 0.222734 seconds
% 1.24/0.59 % CPU time: 1.523608 seconds
% 1.24/0.59 % Total memory used: 120.596 MB
% 1.24/0.59 % Net memory used: 117.013 MB
%------------------------------------------------------------------------------