TSTP Solution File: SEU186+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU186+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 : Wed May 31 12:36:10 EDT 2023
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU186+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:16:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % Drodi V3.5.1
% 0.19/0.51 % Refutation found
% 0.19/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.51 fof(f8,axiom,(
% 0.19/0.51 (! [A] :( relation(A)<=> (! [B] :~ ( in(B,A)& (! [C,D] : B != ordered_pair(C,D) )) )) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f9,axiom,(
% 0.19/0.51 (! [A,B] :( ( A != empty_set=> ( B = set_meet(A)<=> (! [C] :( in(C,B)<=> (! [D] :( in(D,A)=> in(C,D) ) )) )) )& ( A = empty_set=> ( B = set_meet(A)<=> B = empty_set ) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f11,axiom,(
% 0.19/0.51 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f12,axiom,(
% 0.19/0.51 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f13,axiom,(
% 0.19/0.51 (! [A,B] :( ( ~ empty(A)=> ( element(B,A)<=> in(B,A) ) )& ( empty(A)=> ( element(B,A)<=> empty(B) ) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f55,axiom,(
% 0.19/0.51 (! [A] :(? [B] : element(B,A) ))),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f57,axiom,(
% 0.19/0.51 empty(empty_set) ),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f72,lemma,(
% 0.19/0.51 (! [A] : singleton(A) != empty_set )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f87,axiom,(
% 0.19/0.51 (? [A] :( ~ empty(A)& relation(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f106,lemma,(
% 0.19/0.51 powerset(empty_set) = singleton(empty_set) ),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f115,lemma,(
% 0.19/0.51 (! [A] : subset(empty_set,A) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f147,conjecture,(
% 0.19/0.51 (! [A] :( relation(A)=> ( (! [B,C] : ~ in(ordered_pair(B,C),A))=> A = empty_set ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f148,negated_conjecture,(
% 0.19/0.51 ~((! [A] :( relation(A)=> ( (! [B,C] : ~ in(ordered_pair(B,C),A))=> A = empty_set ) ) ))),
% 0.19/0.51 inference(negated_conjecture,[status(cth)],[f147])).
% 0.19/0.51 fof(f154,axiom,(
% 0.19/0.51 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f180,plain,(
% 0.19/0.51 ![A]: (relation(A)<=>(![B]: (~in(B,A)|(?[C,D]: B=ordered_pair(C,D)))))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 0.19/0.51 fof(f181,plain,(
% 0.19/0.51 ![A]: ((~relation(A)|(![B]: (~in(B,A)|(?[C,D]: B=ordered_pair(C,D)))))&(relation(A)|(?[B]: (in(B,A)&(![C,D]: ~B=ordered_pair(C,D))))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f180])).
% 0.19/0.51 fof(f182,plain,(
% 0.19/0.51 (![A]: (~relation(A)|(![B]: (~in(B,A)|(?[C,D]: B=ordered_pair(C,D))))))&(![A]: (relation(A)|(?[B]: (in(B,A)&(![C,D]: ~B=ordered_pair(C,D))))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f181])).
% 0.19/0.51 fof(f183,plain,(
% 0.19/0.51 (![A]: (~relation(A)|(![B]: (~in(B,A)|B=ordered_pair(sk0_0(B,A),sk0_1(B,A))))))&(![A]: (relation(A)|(in(sk0_2(A),A)&(![C,D]: ~sk0_2(A)=ordered_pair(C,D)))))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f182])).
% 0.19/0.51 fof(f184,plain,(
% 0.19/0.51 ![X0,X1]: (~relation(X0)|~in(X1,X0)|X1=ordered_pair(sk0_0(X1,X0),sk0_1(X1,X0)))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f183])).
% 0.19/0.51 fof(f187,plain,(
% 0.19/0.51 ![A,B]: ((A=empty_set|(B=set_meet(A)<=>(![C]: (in(C,B)<=>(![D]: (~in(D,A)|in(C,D)))))))&(~A=empty_set|(B=set_meet(A)<=>B=empty_set)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 0.19/0.51 fof(f188,plain,(
% 0.19/0.51 ![A,B]: ((A=empty_set|((~B=set_meet(A)|(![C]: ((~in(C,B)|(![D]: (~in(D,A)|in(C,D))))&(in(C,B)|(?[D]: (in(D,A)&~in(C,D)))))))&(B=set_meet(A)|(?[C]: ((~in(C,B)|(?[D]: (in(D,A)&~in(C,D))))&(in(C,B)|(![D]: (~in(D,A)|in(C,D)))))))))&(~A=empty_set|((~B=set_meet(A)|B=empty_set)&(B=set_meet(A)|~B=empty_set))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f187])).
% 0.19/0.51 fof(f189,plain,(
% 0.19/0.51 (![A]: (A=empty_set|((![B]: (~B=set_meet(A)|((![C]: (~in(C,B)|(![D]: (~in(D,A)|in(C,D)))))&(![C]: (in(C,B)|(?[D]: (in(D,A)&~in(C,D))))))))&(![B]: (B=set_meet(A)|(?[C]: ((~in(C,B)|(?[D]: (in(D,A)&~in(C,D))))&(in(C,B)|(![D]: (~in(D,A)|in(C,D)))))))))))&(![A]: (~A=empty_set|((![B]: (~B=set_meet(A)|B=empty_set))&(![B]: (B=set_meet(A)|~B=empty_set)))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f188])).
% 0.19/0.51 fof(f190,plain,(
% 0.19/0.51 (![A]: (A=empty_set|((![B]: (~B=set_meet(A)|((![C]: (~in(C,B)|(![D]: (~in(D,A)|in(C,D)))))&(![C]: (in(C,B)|(in(sk0_3(C,B,A),A)&~in(C,sk0_3(C,B,A))))))))&(![B]: (B=set_meet(A)|((~in(sk0_4(B,A),B)|(in(sk0_5(B,A),A)&~in(sk0_4(B,A),sk0_5(B,A))))&(in(sk0_4(B,A),B)|(![D]: (~in(D,A)|in(sk0_4(B,A),D))))))))))&(![A]: (~A=empty_set|((![B]: (~B=set_meet(A)|B=empty_set))&(![B]: (B=set_meet(A)|~B=empty_set)))))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f189])).
% 0.19/0.51 fof(f196,plain,(
% 0.19/0.51 ![X0,X1,X2]: (X0=empty_set|X1=set_meet(X0)|in(sk0_4(X1,X0),X1)|~in(X2,X0)|in(sk0_4(X1,X0),X2))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f190])).
% 0.19/0.51 fof(f206,plain,(
% 0.19/0.51 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f11])).
% 0.19/0.51 fof(f207,plain,(
% 0.19/0.51 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f206])).
% 0.19/0.51 fof(f208,plain,(
% 0.19/0.51 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_7(A),A)))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f207])).
% 0.19/0.51 fof(f209,plain,(
% 0.19/0.51 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f208])).
% 0.19/0.51 fof(f211,plain,(
% 0.19/0.51 ![A,B]: ((~B=powerset(A)|(![C]: ((~in(C,B)|subset(C,A))&(in(C,B)|~subset(C,A)))))&(B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f12])).
% 0.19/0.51 fof(f212,plain,(
% 0.19/0.51 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f211])).
% 0.19/0.51 fof(f213,plain,(
% 0.19/0.51 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|((~in(sk0_8(B,A),B)|~subset(sk0_8(B,A),A))&(in(sk0_8(B,A),B)|subset(sk0_8(B,A),A)))))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f212])).
% 0.19/0.51 fof(f215,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f213])).
% 0.19/0.51 fof(f218,plain,(
% 0.19/0.51 ![A,B]: ((empty(A)|(element(B,A)<=>in(B,A)))&(~empty(A)|(element(B,A)<=>empty(B))))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.19/0.51 fof(f219,plain,(
% 0.19/0.51 ![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)))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f218])).
% 0.19/0.51 fof(f220,plain,(
% 0.19/0.51 (![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))))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f219])).
% 0.19/0.51 fof(f223,plain,(
% 0.19/0.51 ![X0,X1]: (~empty(X0)|~element(X1,X0)|empty(X1))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f220])).
% 0.19/0.51 fof(f358,plain,(
% 0.19/0.51 ![A]: element(sk0_35(A),A)),
% 0.19/0.51 inference(skolemization,[status(esa)],[f55])).
% 0.19/0.51 fof(f359,plain,(
% 0.19/0.51 ![X0]: (element(sk0_35(X0),X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f358])).
% 0.19/0.51 fof(f361,plain,(
% 0.19/0.51 empty(empty_set)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f57])).
% 0.19/0.51 fof(f389,plain,(
% 0.19/0.51 ![X0]: (~singleton(X0)=empty_set)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f72])).
% 0.19/0.51 fof(f434,plain,(
% 0.19/0.51 (~empty(sk0_40)&relation(sk0_40))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f87])).
% 0.19/0.51 fof(f435,plain,(
% 0.19/0.51 ~empty(sk0_40)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f434])).
% 0.19/0.51 fof(f484,plain,(
% 0.19/0.51 powerset(empty_set)=singleton(empty_set)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f106])).
% 0.19/0.51 fof(f507,plain,(
% 0.19/0.51 ![X0]: (subset(empty_set,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f115])).
% 0.19/0.51 fof(f592,plain,(
% 0.19/0.51 (?[A]: (relation(A)&((![B,C]: ~in(ordered_pair(B,C),A))&~A=empty_set)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f148])).
% 0.19/0.51 fof(f593,plain,(
% 0.19/0.51 (relation(sk0_47)&((![B,C]: ~in(ordered_pair(B,C),sk0_47))&~sk0_47=empty_set))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f592])).
% 0.19/0.51 fof(f594,plain,(
% 0.19/0.51 relation(sk0_47)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f593])).
% 0.19/0.53 fof(f595,plain,(
% 0.19/0.53 ![X0,X1]: (~in(ordered_pair(X0,X1),sk0_47))),
% 0.19/0.53 inference(cnf_transformation,[status(esa)],[f593])).
% 0.19/0.53 fof(f596,plain,(
% 0.19/0.53 ~sk0_47=empty_set),
% 0.19/0.53 inference(cnf_transformation,[status(esa)],[f593])).
% 0.19/0.53 fof(f610,plain,(
% 0.19/0.53 ![A]: (~empty(A)|A=empty_set)),
% 0.19/0.53 inference(pre_NNF_transformation,[status(esa)],[f154])).
% 0.19/0.53 fof(f611,plain,(
% 0.19/0.53 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.19/0.53 inference(cnf_transformation,[status(esa)],[f610])).
% 0.19/0.53 fof(f659,plain,(
% 0.19/0.53 ![X0]: (~in(X0,empty_set))),
% 0.19/0.53 inference(destructive_equality_resolution,[status(esa)],[f209])).
% 0.19/0.53 fof(f661,plain,(
% 0.19/0.53 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 0.19/0.53 inference(destructive_equality_resolution,[status(esa)],[f215])).
% 0.19/0.53 fof(f1008,plain,(
% 0.19/0.53 ![X0]: (in(empty_set,powerset(X0)))),
% 0.19/0.53 inference(resolution,[status(thm)],[f661,f507])).
% 0.19/0.53 fof(f1013,plain,(
% 0.19/0.53 ![X0,X1]: (powerset(X0)=empty_set|X1=set_meet(powerset(X0))|in(sk0_4(X1,powerset(X0)),X1)|in(sk0_4(X1,powerset(X0)),empty_set))),
% 0.19/0.53 inference(resolution,[status(thm)],[f1008,f196])).
% 0.19/0.53 fof(f1014,plain,(
% 0.19/0.53 ![X0,X1]: (powerset(X0)=empty_set|X1=set_meet(powerset(X0))|in(sk0_4(X1,powerset(X0)),X1))),
% 0.19/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1013,f659])).
% 0.19/0.53 fof(f1023,plain,(
% 0.19/0.53 ![X0]: (powerset(X0)=empty_set|empty_set=set_meet(powerset(X0)))),
% 0.19/0.53 inference(resolution,[status(thm)],[f1014,f659])).
% 0.19/0.53 fof(f1027,plain,(
% 0.19/0.53 spl0_14 <=> powerset(empty_set)=empty_set),
% 0.19/0.53 introduced(split_symbol_definition)).
% 0.19/0.53 fof(f1028,plain,(
% 0.19/0.53 powerset(empty_set)=empty_set|~spl0_14),
% 0.19/0.53 inference(component_clause,[status(thm)],[f1027])).
% 0.19/0.53 fof(f1030,plain,(
% 0.19/0.53 spl0_15 <=> X0=set_meet(powerset(empty_set))|in(sk0_4(X0,singleton(empty_set)),X0)),
% 0.19/0.53 introduced(split_symbol_definition)).
% 0.19/0.53 fof(f1031,plain,(
% 0.19/0.53 ![X0]: (X0=set_meet(powerset(empty_set))|in(sk0_4(X0,singleton(empty_set)),X0)|~spl0_15)),
% 0.19/0.53 inference(component_clause,[status(thm)],[f1030])).
% 0.19/0.53 fof(f1033,plain,(
% 0.19/0.53 ![X0]: (powerset(empty_set)=empty_set|X0=set_meet(powerset(empty_set))|in(sk0_4(X0,singleton(empty_set)),X0))),
% 0.19/0.53 inference(paramodulation,[status(thm)],[f484,f1014])).
% 0.19/0.53 fof(f1034,plain,(
% 0.19/0.53 spl0_14|spl0_15),
% 0.19/0.53 inference(split_clause,[status(thm)],[f1033,f1027,f1030])).
% 0.19/0.53 fof(f1035,plain,(
% 0.19/0.53 singleton(empty_set)=empty_set|~spl0_14),
% 0.19/0.53 inference(forward_demodulation,[status(thm)],[f484,f1028])).
% 0.19/0.53 fof(f1036,plain,(
% 0.19/0.53 $false|~spl0_14),
% 0.19/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1035,f389])).
% 0.19/0.53 fof(f1037,plain,(
% 0.19/0.53 ~spl0_14),
% 0.19/0.53 inference(contradiction_clause,[status(thm)],[f1036])).
% 0.19/0.53 fof(f1038,plain,(
% 0.19/0.53 ![X0]: (X0=set_meet(singleton(empty_set))|in(sk0_4(X0,singleton(empty_set)),X0)|~spl0_15)),
% 0.19/0.53 inference(forward_demodulation,[status(thm)],[f484,f1031])).
% 0.19/0.53 fof(f1040,plain,(
% 0.19/0.53 spl0_16 <=> empty_set=set_meet(singleton(empty_set))),
% 0.19/0.53 introduced(split_symbol_definition)).
% 0.19/0.53 fof(f1041,plain,(
% 0.19/0.53 empty_set=set_meet(singleton(empty_set))|~spl0_16),
% 0.19/0.53 inference(component_clause,[status(thm)],[f1040])).
% 0.19/0.53 fof(f1043,plain,(
% 0.19/0.53 powerset(empty_set)=empty_set|empty_set=set_meet(singleton(empty_set))),
% 0.19/0.53 inference(paramodulation,[status(thm)],[f484,f1023])).
% 0.19/0.53 fof(f1044,plain,(
% 0.19/0.53 spl0_14|spl0_16),
% 0.19/0.53 inference(split_clause,[status(thm)],[f1043,f1027,f1040])).
% 0.19/0.53 fof(f1243,plain,(
% 0.19/0.53 ![X0]: (X0=empty_set|in(sk0_4(X0,singleton(empty_set)),X0)|~spl0_16|~spl0_15)),
% 0.19/0.53 inference(forward_demodulation,[status(thm)],[f1041,f1038])).
% 0.19/0.53 fof(f1255,plain,(
% 0.19/0.53 ![X0]: (X0=empty_set|~relation(X0)|sk0_4(X0,singleton(empty_set))=ordered_pair(sk0_0(sk0_4(X0,singleton(empty_set)),X0),sk0_1(sk0_4(X0,singleton(empty_set)),X0))|~spl0_16|~spl0_15)),
% 0.19/0.53 inference(resolution,[status(thm)],[f1243,f184])).
% 0.19/0.53 fof(f1637,plain,(
% 0.19/0.53 spl0_75 <=> sk0_40=empty_set),
% 0.19/0.53 introduced(split_symbol_definition)).
% 0.19/0.53 fof(f1638,plain,(
% 0.19/0.53 sk0_40=empty_set|~spl0_75),
% 0.19/0.53 inference(component_clause,[status(thm)],[f1637])).
% 0.19/0.53 fof(f1650,plain,(
% 0.19/0.53 spl0_78 <=> sk0_47=empty_set),
% 0.19/0.53 introduced(split_symbol_definition)).
% 0.19/0.53 fof(f1651,plain,(
% 0.19/0.53 sk0_47=empty_set|~spl0_78),
% 0.19/0.53 inference(component_clause,[status(thm)],[f1650])).
% 0.19/0.53 fof(f1653,plain,(
% 0.19/0.53 spl0_79 <=> sk0_4(sk0_47,singleton(empty_set))=ordered_pair(sk0_0(sk0_4(sk0_47,singleton(empty_set)),sk0_47),sk0_1(sk0_4(sk0_47,singleton(empty_set)),sk0_47))),
% 0.19/0.53 introduced(split_symbol_definition)).
% 0.19/0.53 fof(f1654,plain,(
% 0.19/0.53 sk0_4(sk0_47,singleton(empty_set))=ordered_pair(sk0_0(sk0_4(sk0_47,singleton(empty_set)),sk0_47),sk0_1(sk0_4(sk0_47,singleton(empty_set)),sk0_47))|~spl0_79),
% 0.19/0.53 inference(component_clause,[status(thm)],[f1653])).
% 0.19/0.53 fof(f1656,plain,(
% 0.19/0.53 sk0_47=empty_set|sk0_4(sk0_47,singleton(empty_set))=ordered_pair(sk0_0(sk0_4(sk0_47,singleton(empty_set)),sk0_47),sk0_1(sk0_4(sk0_47,singleton(empty_set)),sk0_47))|~spl0_16|~spl0_15),
% 0.19/0.53 inference(resolution,[status(thm)],[f1255,f594])).
% 0.19/0.53 fof(f1657,plain,(
% 0.19/0.53 spl0_78|spl0_79|~spl0_16|~spl0_15),
% 0.19/0.53 inference(split_clause,[status(thm)],[f1656,f1650,f1653,f1040,f1030])).
% 0.19/0.53 fof(f1660,plain,(
% 0.19/0.53 $false|~spl0_78),
% 0.19/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1651,f596])).
% 0.19/0.53 fof(f1661,plain,(
% 0.19/0.53 ~spl0_78),
% 0.19/0.53 inference(contradiction_clause,[status(thm)],[f1660])).
% 0.19/0.53 fof(f1801,plain,(
% 0.19/0.53 ![X0]: (~element(X0,empty_set)|empty(X0))),
% 0.19/0.53 inference(resolution,[status(thm)],[f223,f361])).
% 0.19/0.53 fof(f1802,plain,(
% 0.19/0.53 empty(sk0_35(empty_set))),
% 0.19/0.53 inference(resolution,[status(thm)],[f1801,f359])).
% 0.19/0.53 fof(f1808,plain,(
% 0.19/0.53 spl0_86 <=> empty_set=powerset(sk0_35(empty_set))),
% 0.19/0.53 introduced(split_symbol_definition)).
% 0.19/0.53 fof(f1809,plain,(
% 0.19/0.53 empty_set=powerset(sk0_35(empty_set))|~spl0_86),
% 0.19/0.53 inference(component_clause,[status(thm)],[f1808])).
% 0.19/0.53 fof(f1824,plain,(
% 0.19/0.53 sk0_35(empty_set)=empty_set),
% 0.19/0.53 inference(resolution,[status(thm)],[f1802,f611])).
% 0.19/0.53 fof(f1874,plain,(
% 0.19/0.53 ~in(sk0_4(sk0_47,singleton(empty_set)),sk0_47)|~spl0_79),
% 0.19/0.53 inference(paramodulation,[status(thm)],[f1654,f595])).
% 0.19/0.53 fof(f1885,plain,(
% 0.19/0.53 ~empty(empty_set)|~spl0_75),
% 0.19/0.53 inference(backward_demodulation,[status(thm)],[f1638,f435])).
% 0.19/0.53 fof(f1886,plain,(
% 0.19/0.53 $false|~spl0_75),
% 0.19/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1885,f361])).
% 0.19/0.53 fof(f1887,plain,(
% 0.19/0.53 ~spl0_75),
% 0.19/0.53 inference(contradiction_clause,[status(thm)],[f1886])).
% 0.19/0.53 fof(f1943,plain,(
% 0.19/0.53 empty_set=powerset(empty_set)|~spl0_86),
% 0.19/0.53 inference(forward_demodulation,[status(thm)],[f1824,f1809])).
% 0.19/0.53 fof(f1944,plain,(
% 0.19/0.53 empty_set=singleton(empty_set)|~spl0_86),
% 0.19/0.53 inference(forward_demodulation,[status(thm)],[f484,f1943])).
% 0.19/0.53 fof(f1945,plain,(
% 0.19/0.53 $false|~spl0_86),
% 0.19/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1944,f389])).
% 0.19/0.53 fof(f1946,plain,(
% 0.19/0.53 ~spl0_86),
% 0.19/0.53 inference(contradiction_clause,[status(thm)],[f1945])).
% 0.19/0.53 fof(f1956,plain,(
% 0.19/0.53 sk0_47=empty_set|~spl0_79|~spl0_16|~spl0_15),
% 0.19/0.53 inference(resolution,[status(thm)],[f1874,f1243])).
% 0.19/0.53 fof(f1957,plain,(
% 0.19/0.53 spl0_78|~spl0_79|~spl0_16|~spl0_15),
% 0.19/0.53 inference(split_clause,[status(thm)],[f1956,f1650,f1653,f1040,f1030])).
% 0.19/0.53 fof(f1966,plain,(
% 0.19/0.53 $false),
% 0.19/0.53 inference(sat_refutation,[status(thm)],[f1034,f1037,f1044,f1657,f1661,f1887,f1946,f1957])).
% 0.19/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.54 % Elapsed time: 0.185248 seconds
% 0.19/0.54 % CPU time: 0.602232 seconds
% 0.19/0.54 % Memory used: 48.104 MB
%------------------------------------------------------------------------------