TSTP Solution File: SEU131+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU131+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:41:07 EDT 2024
% Result : Theorem 0.10s 0.35s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SEU131+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33 % Computer : n021.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 19:47:40 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.34 % Drodi V3.6.0
% 0.10/0.35 % Refutation found
% 0.10/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.35 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.35 fof(f2,axiom,(
% 0.10/0.35 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.10/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.35 fof(f3,axiom,(
% 0.10/0.35 (! [A,B,C] :( C = set_difference(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& ~ in(D,B) ) ) )) )),
% 0.10/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.35 fof(f6,axiom,(
% 0.10/0.35 empty(empty_set) ),
% 0.10/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.35 fof(f7,conjecture,(
% 0.10/0.35 (! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) )),
% 0.10/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.35 fof(f8,negated_conjecture,(
% 0.10/0.35 ~((! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) ))),
% 0.10/0.35 inference(negated_conjecture,[status(cth)],[f7])).
% 0.10/0.35 fof(f14,axiom,(
% 0.10/0.35 (! [A] : set_difference(empty_set,A) = empty_set )),
% 0.10/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.35 fof(f16,axiom,(
% 0.10/0.35 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.10/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.35 fof(f20,plain,(
% 0.10/0.35 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.10/0.35 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.10/0.35 fof(f21,plain,(
% 0.10/0.35 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.10/0.35 inference(NNF_transformation,[status(esa)],[f20])).
% 0.10/0.35 fof(f22,plain,(
% 0.10/0.35 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.10/0.35 inference(miniscoping,[status(esa)],[f21])).
% 0.10/0.35 fof(f23,plain,(
% 0.10/0.35 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_0(B,A),A)&~in(sk0_0(B,A),B))))),
% 0.10/0.35 inference(skolemization,[status(esa)],[f22])).
% 0.10/0.35 fof(f24,plain,(
% 0.10/0.35 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f23])).
% 0.10/0.35 fof(f25,plain,(
% 0.10/0.35 ![X0,X1]: (subset(X0,X1)|in(sk0_0(X1,X0),X0))),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f23])).
% 0.10/0.35 fof(f26,plain,(
% 0.10/0.35 ![X0,X1]: (subset(X0,X1)|~in(sk0_0(X1,X0),X1))),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f23])).
% 0.10/0.35 fof(f27,plain,(
% 0.10/0.35 ![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)))))))),
% 0.10/0.35 inference(NNF_transformation,[status(esa)],[f3])).
% 0.10/0.35 fof(f28,plain,(
% 0.10/0.35 (![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)))))))),
% 0.10/0.35 inference(miniscoping,[status(esa)],[f27])).
% 0.10/0.35 fof(f29,plain,(
% 0.10/0.35 (![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_1(C,B,A),C)|(~in(sk0_1(C,B,A),A)|in(sk0_1(C,B,A),B)))&(in(sk0_1(C,B,A),C)|(in(sk0_1(C,B,A),A)&~in(sk0_1(C,B,A),B))))))),
% 0.10/0.35 inference(skolemization,[status(esa)],[f28])).
% 0.10/0.35 fof(f31,plain,(
% 0.10/0.35 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|~in(X3,X0)|~in(X3,X2))),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f29])).
% 0.10/0.35 fof(f32,plain,(
% 0.10/0.35 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|in(X3,X0)|~in(X3,X1)|in(X3,X2))),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f29])).
% 0.10/0.35 fof(f34,plain,(
% 0.10/0.35 ![X0,X1,X2]: (X0=set_difference(X1,X2)|in(sk0_1(X0,X2,X1),X0)|in(sk0_1(X0,X2,X1),X1))),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f29])).
% 0.10/0.35 fof(f35,plain,(
% 0.10/0.35 ![X0,X1,X2]: (X0=set_difference(X1,X2)|in(sk0_1(X0,X2,X1),X0)|~in(sk0_1(X0,X2,X1),X2))),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f29])).
% 0.10/0.35 fof(f36,plain,(
% 0.10/0.35 empty(empty_set)),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f6])).
% 0.10/0.35 fof(f37,plain,(
% 0.10/0.35 (?[A,B]: (set_difference(A,B)=empty_set<~>subset(A,B)))),
% 0.10/0.35 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 0.10/0.35 fof(f38,plain,(
% 0.10/0.35 ?[A,B]: ((set_difference(A,B)=empty_set|subset(A,B))&(~set_difference(A,B)=empty_set|~subset(A,B)))),
% 0.10/0.35 inference(NNF_transformation,[status(esa)],[f37])).
% 0.10/0.35 fof(f39,plain,(
% 0.10/0.35 ((set_difference(sk0_2,sk0_3)=empty_set|subset(sk0_2,sk0_3))&(~set_difference(sk0_2,sk0_3)=empty_set|~subset(sk0_2,sk0_3)))),
% 0.10/0.35 inference(skolemization,[status(esa)],[f38])).
% 0.10/0.35 fof(f40,plain,(
% 0.10/0.35 set_difference(sk0_2,sk0_3)=empty_set|subset(sk0_2,sk0_3)),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f39])).
% 0.10/0.35 fof(f41,plain,(
% 0.10/0.35 ~set_difference(sk0_2,sk0_3)=empty_set|~subset(sk0_2,sk0_3)),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f39])).
% 0.10/0.35 fof(f54,plain,(
% 0.10/0.35 ![X0]: (set_difference(empty_set,X0)=empty_set)),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f14])).
% 0.10/0.35 fof(f57,plain,(
% 0.10/0.35 ![A,B]: (~in(A,B)|~empty(B))),
% 0.10/0.35 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.10/0.35 fof(f58,plain,(
% 0.10/0.35 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.10/0.35 inference(miniscoping,[status(esa)],[f57])).
% 0.10/0.35 fof(f59,plain,(
% 0.10/0.35 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.10/0.35 inference(cnf_transformation,[status(esa)],[f58])).
% 0.10/0.35 fof(f63,plain,(
% 0.10/0.35 spl0_0 <=> set_difference(sk0_2,sk0_3)=empty_set),
% 0.10/0.35 introduced(split_symbol_definition)).
% 0.10/0.35 fof(f64,plain,(
% 0.10/0.35 set_difference(sk0_2,sk0_3)=empty_set|~spl0_0),
% 0.10/0.35 inference(component_clause,[status(thm)],[f63])).
% 0.10/0.35 fof(f66,plain,(
% 0.10/0.35 spl0_1 <=> subset(sk0_2,sk0_3)),
% 0.10/0.35 introduced(split_symbol_definition)).
% 0.10/0.35 fof(f67,plain,(
% 0.10/0.35 subset(sk0_2,sk0_3)|~spl0_1),
% 0.10/0.35 inference(component_clause,[status(thm)],[f66])).
% 0.10/0.35 fof(f69,plain,(
% 0.10/0.35 spl0_0|spl0_1),
% 0.10/0.35 inference(split_clause,[status(thm)],[f40,f63,f66])).
% 0.10/0.35 fof(f70,plain,(
% 0.10/0.35 ~spl0_0|~spl0_1),
% 0.10/0.35 inference(split_clause,[status(thm)],[f41,f63,f66])).
% 0.10/0.35 fof(f72,plain,(
% 0.10/0.35 ![X0,X1,X2]: (~in(X0,set_difference(X1,X2))|~in(X0,X2))),
% 0.10/0.35 inference(destructive_equality_resolution,[status(esa)],[f31])).
% 0.10/0.35 fof(f73,plain,(
% 0.10/0.35 ![X0,X1,X2]: (in(X0,set_difference(X1,X2))|~in(X0,X1)|in(X0,X2))),
% 0.10/0.35 inference(destructive_equality_resolution,[status(esa)],[f32])).
% 0.10/0.35 fof(f74,plain,(
% 0.10/0.35 ![X0,X1]: (~in(X0,empty_set)|~in(X0,X1))),
% 0.10/0.35 inference(paramodulation,[status(thm)],[f54,f72])).
% 0.10/0.35 fof(f78,plain,(
% 0.10/0.35 ![X0,X1,X2]: (~empty(set_difference(X0,X1))|~in(X2,X0)|in(X2,X1))),
% 0.10/0.35 inference(resolution,[status(thm)],[f59,f73])).
% 0.10/0.35 fof(f79,plain,(
% 0.10/0.35 spl0_2 <=> empty(empty_set)),
% 0.10/0.35 introduced(split_symbol_definition)).
% 0.10/0.35 fof(f81,plain,(
% 0.10/0.35 ~empty(empty_set)|spl0_2),
% 0.10/0.35 inference(component_clause,[status(thm)],[f79])).
% 0.10/0.35 fof(f82,plain,(
% 0.10/0.35 spl0_3 <=> ~in(X0,empty_set)|in(X0,X1)),
% 0.10/0.35 introduced(split_symbol_definition)).
% 0.10/0.35 fof(f85,plain,(
% 0.10/0.35 ![X0,X1]: (~empty(empty_set)|~in(X0,empty_set)|in(X0,X1))),
% 0.10/0.35 inference(paramodulation,[status(thm)],[f54,f78])).
% 0.10/0.35 fof(f86,plain,(
% 0.10/0.35 ~spl0_2|spl0_3),
% 0.10/0.35 inference(split_clause,[status(thm)],[f85,f79,f82])).
% 0.10/0.35 fof(f88,plain,(
% 0.10/0.35 $false|spl0_2),
% 0.10/0.35 inference(forward_subsumption_resolution,[status(thm)],[f81,f36])).
% 0.10/0.35 fof(f89,plain,(
% 0.10/0.35 spl0_2),
% 0.10/0.35 inference(contradiction_clause,[status(thm)],[f88])).
% 0.10/0.35 fof(f96,plain,(
% 0.10/0.35 ![X0,X1]: (subset(empty_set,X0)|~in(sk0_0(X0,empty_set),X1))),
% 0.10/0.35 inference(resolution,[status(thm)],[f25,f74])).
% 0.10/0.35 fof(f105,plain,(
% 0.10/0.35 ![X0]: (subset(empty_set,X0)|subset(empty_set,X0))),
% 0.10/0.35 inference(resolution,[status(thm)],[f96,f25])).
% 0.10/0.35 fof(f106,plain,(
% 0.10/0.35 ![X0]: (subset(empty_set,X0))),
% 0.10/0.35 inference(duplicate_literals_removal,[status(esa)],[f105])).
% 0.10/0.35 fof(f108,plain,(
% 0.10/0.35 ![X0,X1]: (~in(X0,empty_set)|in(X0,X1))),
% 0.10/0.35 inference(resolution,[status(thm)],[f106,f24])).
% 0.10/0.35 fof(f109,plain,(
% 0.10/0.35 ![X0]: (~in(X0,empty_set))),
% 0.10/0.35 inference(forward_subsumption_resolution,[status(thm)],[f108,f74])).
% 0.10/0.35 fof(f146,plain,(
% 0.10/0.35 spl0_6 <=> ~in(X0,sk0_2)|in(X0,sk0_3)),
% 0.10/0.35 introduced(split_symbol_definition)).
% 0.10/0.35 fof(f147,plain,(
% 0.10/0.35 ![X0]: (~in(X0,sk0_2)|in(X0,sk0_3)|~spl0_6)),
% 0.10/0.35 inference(component_clause,[status(thm)],[f146])).
% 0.10/0.35 fof(f149,plain,(
% 0.10/0.35 ![X0]: (~empty(empty_set)|~in(X0,sk0_2)|in(X0,sk0_3)|~spl0_0)),
% 0.10/0.35 inference(paramodulation,[status(thm)],[f64,f78])).
% 0.10/0.35 fof(f150,plain,(
% 0.10/0.35 ~spl0_2|spl0_6|~spl0_0),
% 0.10/0.35 inference(split_clause,[status(thm)],[f149,f79,f146,f63])).
% 0.10/0.35 fof(f155,plain,(
% 0.10/0.35 ![X0]: (~in(X0,sk0_2)|in(X0,sk0_3)|~spl0_1)),
% 0.10/0.35 inference(resolution,[status(thm)],[f67,f24])).
% 0.10/0.35 fof(f156,plain,(
% 0.10/0.35 ![X0,X1]: (in(sk0_1(X0,X1,sk0_2),sk0_3)|X0=set_difference(sk0_2,X1)|in(sk0_1(X0,X1,sk0_2),X0)|~spl0_1)),
% 0.10/0.35 inference(resolution,[status(thm)],[f155,f34])).
% 0.10/0.35 fof(f201,plain,(
% 0.10/0.35 ![X0]: (X0=set_difference(sk0_2,sk0_3)|in(sk0_1(X0,sk0_3,sk0_2),X0)|X0=set_difference(sk0_2,sk0_3)|in(sk0_1(X0,sk0_3,sk0_2),X0)|~spl0_1)),
% 0.10/0.35 inference(resolution,[status(thm)],[f156,f35])).
% 0.10/0.35 fof(f202,plain,(
% 0.10/0.35 ![X0]: (X0=set_difference(sk0_2,sk0_3)|in(sk0_1(X0,sk0_3,sk0_2),X0)|~spl0_1)),
% 0.10/0.35 inference(duplicate_literals_removal,[status(esa)],[f201])).
% 0.10/0.35 fof(f230,plain,(
% 0.10/0.35 empty_set=set_difference(sk0_2,sk0_3)|~spl0_1),
% 0.10/0.35 inference(resolution,[status(thm)],[f202,f109])).
% 0.10/0.35 fof(f231,plain,(
% 0.10/0.35 spl0_0|~spl0_1),
% 0.10/0.35 inference(split_clause,[status(thm)],[f230,f63,f66])).
% 0.10/0.35 fof(f249,plain,(
% 0.10/0.35 ![X0]: (in(sk0_0(X0,sk0_2),sk0_3)|subset(sk0_2,X0)|~spl0_6)),
% 0.10/0.35 inference(resolution,[status(thm)],[f147,f25])).
% 0.10/0.35 fof(f252,plain,(
% 0.10/0.35 subset(sk0_2,sk0_3)|subset(sk0_2,sk0_3)|~spl0_6),
% 0.10/0.35 inference(resolution,[status(thm)],[f249,f26])).
% 0.10/0.35 fof(f253,plain,(
% 0.10/0.35 spl0_1|~spl0_6),
% 0.10/0.35 inference(split_clause,[status(thm)],[f252,f66,f146])).
% 0.10/0.35 fof(f257,plain,(
% 0.10/0.35 $false),
% 0.10/0.35 inference(sat_refutation,[status(thm)],[f69,f70,f86,f89,f150,f231,f253])).
% 0.10/0.35 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.37 % Elapsed time: 0.021648 seconds
% 0.16/0.37 % CPU time: 0.042163 seconds
% 0.16/0.37 % Total memory used: 14.978 MB
% 0.16/0.37 % Net memory used: 14.919 MB
%------------------------------------------------------------------------------