%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU156+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 : n020.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 02:21:49 PM UTC 2026
% Result : Theorem 1.01s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+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
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:54:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.01/0.62 % Refutation found
% 1.01/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.01/0.62 % SZS output start CNFRefutation for theBenchmark
% 1.01/0.62 fof(f1,axiom,(
% 1.01/0.62 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f3,axiom,(
% 1.01/0.62 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f7,axiom,(
% 1.01/0.62 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f8,axiom,(
% 1.01/0.62 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f10,axiom,(
% 1.01/0.62 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f11,axiom,(
% 1.01/0.62 (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f16,axiom,(
% 1.01/0.62 (! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f35,lemma,(
% 1.01/0.62 (! [A] : singleton(A) != empty_set )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f44,axiom,(
% 1.01/0.62 (? [A] : empty(A) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f54,lemma,(
% 1.01/0.62 powerset(empty_set) = singleton(empty_set) ),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f61,conjecture,(
% 1.01/0.62 (! [A,B,C,D] :( ordered_pair(A,B) = ordered_pair(C,D)=> ( A = C& B = D ) ) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f62,negated_conjecture,(
% 1.01/0.62 ~((! [A,B,C,D] :( ordered_pair(A,B) = ordered_pair(C,D)=> ( A = C& B = D ) ) ))),
% 1.01/0.62 inference(negated_conjecture,[status(cth)],[f61])).
% 1.01/0.62 fof(f76,lemma,(
% 1.01/0.62 (! [A] : unordered_pair(A,A) = singleton(A) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f77,axiom,(
% 1.01/0.62 (! [A] :( empty(A)=> A = empty_set ) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f85,lemma,(
% 1.01/0.62 (! [A,B,C] :( singleton(A) = unordered_pair(B,C)=> B = C ) )),
% 1.01/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.01/0.62 fof(f86,plain,(
% 1.01/0.62 ![A,B]: (~in(A,B)|~in(B,A))),
% 1.01/0.62 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 1.01/0.62 fof(f87,plain,(
% 1.01/0.62 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f86])).
% 1.01/0.62 fof(f90,plain,(
% 1.01/0.62 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f3])).
% 1.01/0.62 fof(f98,plain,(
% 1.01/0.62 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 1.01/0.62 inference(NNF_transformation,[status(thm)],[f7])).
% 1.01/0.62 fof(f99,plain,(
% 1.01/0.62 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 1.01/0.62 inference(miniscoping,[status(thm)],[f98])).
% 1.01/0.62 fof(f100,plain,(
% 1.01/0.62 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sK0_skl(B,A),B)|~sK0_skl(B,A)=A)&(in(sK0_skl(B,A),B)|sK0_skl(B,A)=A))))),
% 1.01/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f99])).
% 1.01/0.62 fof(f101,plain,(
% 1.01/0.62 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f100])).
% 1.01/0.62 fof(f105,plain,(
% 1.01/0.62 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 1.01/0.62 inference(NNF_transformation,[status(thm)],[f8])).
% 1.01/0.62 fof(f106,plain,(
% 1.01/0.62 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 1.01/0.62 inference(miniscoping,[status(thm)],[f105])).
% 1.01/0.62 fof(f107,plain,(
% 1.01/0.62 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK1_skl(A),A)))),
% 1.01/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f106])).
% 1.01/0.62 fof(f109,plain,(
% 1.01/0.62 ![X0]: (X0=empty_set|in(sK1_skl(X0),X0))),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f107])).
% 1.01/0.62 fof(f117,plain,(
% 1.01/0.62 ![A,B,C]: ((~C=unordered_pair(A,B)|(![D]: ((~in(D,C)|(D=A|D=B))&(in(D,C)|(~D=A&~D=B)))))&(C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 1.01/0.62 inference(NNF_transformation,[status(thm)],[f10])).
% 1.01/0.62 fof(f118,plain,(
% 1.01/0.62 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 1.01/0.62 inference(miniscoping,[status(thm)],[f117])).
% 1.01/0.62 fof(f119,plain,(
% 1.01/0.62 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|((~in(sK3_skl(C,B,A),C)|(~sK3_skl(C,B,A)=A&~sK3_skl(C,B,A)=B))&(in(sK3_skl(C,B,A),C)|(sK3_skl(C,B,A)=A|sK3_skl(C,B,A)=B)))))),
% 1.01/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f118])).
% 1.01/0.62 fof(f120,plain,(
% 1.01/0.62 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|~in(X3,X0)|X3=X1|X3=X2)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f119])).
% 1.01/0.62 fof(f121,plain,(
% 1.01/0.62 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X1)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f119])).
% 1.01/0.62 fof(f122,plain,(
% 1.01/0.62 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f119])).
% 1.01/0.62 fof(f126,plain,(
% 1.01/0.62 ![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)))))))),
% 1.01/0.62 inference(NNF_transformation,[status(thm)],[f11])).
% 1.01/0.62 fof(f127,plain,(
% 1.01/0.62 (![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)))))))),
% 1.01/0.62 inference(miniscoping,[status(thm)],[f126])).
% 1.01/0.62 fof(f128,plain,(
% 1.01/0.62 (![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(sK4_skl(C,B,A),C)|(~in(sK4_skl(C,B,A),A)&~in(sK4_skl(C,B,A),B)))&(in(sK4_skl(C,B,A),C)|(in(sK4_skl(C,B,A),A)|in(sK4_skl(C,B,A),B))))))),
% 1.01/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f127])).
% 1.01/0.62 fof(f134,plain,(
% 1.01/0.62 ![X0,X1,X2]: (X0=set_union2(X1,X2)|in(sK4_skl(X0,X2,X1),X0)|in(sK4_skl(X0,X2,X1),X1)|in(sK4_skl(X0,X2,X1),X2))),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f128])).
% 1.01/0.62 fof(f169,plain,(
% 1.01/0.62 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(unordered_pair(X0,X1),singleton(X0)))),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f16])).
% 1.01/0.62 fof(f193,plain,(
% 1.01/0.62 ![X0]: (~singleton(X0)=empty_set)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f35])).
% 1.01/0.62 fof(f218,plain,(
% 1.01/0.62 empty(sK11_skl)),
% 1.01/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(A,sK11_skl)],[f44])).
% 1.01/0.62 fof(f219,plain,(
% 1.01/0.62 empty(sK11_skl)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f218])).
% 1.01/0.62 fof(f238,plain,(
% 1.01/0.62 powerset(empty_set)=singleton(empty_set)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f54])).
% 1.01/0.62 fof(f254,plain,(
% 1.01/0.62 (?[A,B,C,D]: (ordered_pair(A,B)=ordered_pair(C,D)&(~A=C|~B=D)))),
% 1.01/0.62 inference(pre_NNF_transformation,[status(thm)],[f62])).
% 1.01/0.62 fof(f255,plain,(
% 1.01/0.62 (ordered_pair(sK14_skl,sK15_skl)=ordered_pair(sK16_skl,sK17_skl)&(~sK14_skl=sK16_skl|~sK15_skl=sK17_skl))),
% 1.01/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(A,sK14_skl),skolemize(B,sK15_skl),skolemize(C,sK16_skl),skolemize(D,sK17_skl)],[f254])).
% 1.01/0.62 fof(f256,plain,(
% 1.01/0.62 ordered_pair(sK14_skl,sK15_skl)=ordered_pair(sK16_skl,sK17_skl)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f255])).
% 1.01/0.62 fof(f257,plain,(
% 1.01/0.62 ~sK14_skl=sK16_skl|~sK15_skl=sK17_skl),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f255])).
% 1.01/0.62 fof(f288,plain,(
% 1.01/0.62 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f76])).
% 1.01/0.62 fof(f289,plain,(
% 1.01/0.62 ![A]: (~empty(A)|A=empty_set)),
% 1.01/0.62 inference(pre_NNF_transformation,[status(thm)],[f77])).
% 1.01/0.62 fof(f290,plain,(
% 1.01/0.62 ![X0]: (~empty(X0)|X0=empty_set)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f289])).
% 1.01/0.62 fof(f309,plain,(
% 1.01/0.62 ![A,B,C]: (~singleton(A)=unordered_pair(B,C)|B=C)),
% 1.01/0.62 inference(pre_NNF_transformation,[status(thm)],[f85])).
% 1.01/0.62 fof(f310,plain,(
% 1.01/0.62 ![B,C]: ((![A]: ~singleton(A)=unordered_pair(B,C))|B=C)),
% 1.01/0.62 inference(miniscoping,[status(thm)],[f309])).
% 1.01/0.62 fof(f311,plain,(
% 1.01/0.62 ![X0,X1,X2]: (~singleton(X0)=unordered_pair(X1,X2)|X1=X2)),
% 1.01/0.62 inference(cnf_transformation,[status(thm)],[f310])).
% 1.01/0.62 fof(f312,definition,(
% 1.01/0.62 sQ0_spl <=> (sK14_skl=sK16_skl)),
% 1.01/0.62 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 1.01/0.62 fof(f313,plain,(
% 1.01/0.62 sK14_skl=sK16_skl|~sQ0_spl),
% 1.01/0.62 inference(component_clause,[status(thm)],[f312])).
% 1.01/0.62 fof(f314,plain,(
% 1.01/0.62 ~sK14_skl=sK16_skl|sQ0_spl),
% 1.01/0.62 inference(component_clause,[status(thm)],[f312])).
% 1.01/0.62 fof(f315,definition,(
% 1.01/0.62 sQ1_spl <=> (sK15_skl=sK17_skl)),
% 1.01/0.62 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 1.01/0.62 fof(f317,plain,(
% 1.01/0.62 ~sK15_skl=sK17_skl|sQ1_spl),
% 1.01/0.62 inference(component_clause,[status(thm)],[f315])).
% 1.01/0.62 fof(f318,plain,(
% 1.01/0.62 ~sQ0_spl|~sQ1_spl),
% 1.01/0.62 inference(split_clause,[status(thm)],[f257,f312,f315])).
% 1.01/0.62 fof(f321,plain,(
% 1.01/0.62 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 1.01/0.63 inference(destructive_equality_resolution,[status(thm)],[f101])).
% 1.01/0.63 fof(f326,plain,(
% 1.01/0.63 ![X0,X1,X2]: (~in(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 1.01/0.63 inference(destructive_equality_resolution,[status(thm)],[f120])).
% 1.01/0.63 fof(f327,plain,(
% 1.01/0.63 ![X0,X1]: (in(X0,unordered_pair(X0,X1)))),
% 1.01/0.63 inference(destructive_equality_resolution,[status(thm)],[f121])).
% 1.01/0.63 fof(f328,plain,(
% 1.01/0.63 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 1.01/0.63 inference(destructive_equality_resolution,[status(thm)],[f122])).
% 1.01/0.63 fof(f601,plain,(
% 1.01/0.63 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(singleton(X0),unordered_pair(X0,X1)))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f169,f90])).
% 1.01/0.63 fof(f633,plain,(
% 1.01/0.63 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(unordered_pair(X1,X0),singleton(X0)))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f90,f169])).
% 1.01/0.63 fof(f789,plain,(
% 1.01/0.63 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(singleton(X0),unordered_pair(X1,X0)))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f90,f601])).
% 1.01/0.63 fof(f972,plain,(
% 1.01/0.63 sK11_skl=empty_set),
% 1.01/0.63 inference(resolution,[status(thm)],[f290,f219])).
% 1.01/0.63 fof(f978,plain,(
% 1.01/0.63 ![X0]: (~singleton(X0)=sK11_skl)),
% 1.01/0.63 inference(backward_demodulation,[status(thm)],[f972,f193])).
% 1.01/0.63 fof(f986,plain,(
% 1.01/0.63 ![X0,X1]: (in(singleton(X0),ordered_pair(X0,X1)))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f789,f327])).
% 1.01/0.63 fof(f1000,plain,(
% 1.01/0.63 ![X0,X1]: (in(unordered_pair(X0,X1),ordered_pair(X1,X0)))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f633,f327])).
% 1.01/0.63 fof(f1001,plain,(
% 1.01/0.63 ![X0,X1]: (in(unordered_pair(X0,X1),ordered_pair(X0,X1)))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f169,f327])).
% 1.01/0.63 fof(f1004,plain,(
% 1.01/0.63 ![X0,X1]: (~in(unordered_pair(X0,X1),X1))),
% 1.01/0.63 inference(resolution,[status(thm)],[f328,f87])).
% 1.01/0.63 fof(f1059,plain,(
% 1.01/0.63 in(singleton(sK14_skl),ordered_pair(sK16_skl,sK17_skl))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f256,f986])).
% 1.01/0.63 fof(f1081,plain,(
% 1.01/0.63 in(unordered_pair(sK15_skl,sK14_skl),ordered_pair(sK16_skl,sK17_skl))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f256,f1000])).
% 1.01/0.63 fof(f1265,plain,(
% 1.01/0.63 ![X0]: (ordered_pair(X0,X0)=unordered_pair(singleton(X0),singleton(X0)))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f288,f789])).
% 1.01/0.63 fof(f1278,plain,(
% 1.01/0.63 ![X0]: (ordered_pair(X0,X0)=singleton(singleton(X0)))),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f288,f1265])).
% 1.01/0.63 fof(f1748,plain,(
% 1.01/0.63 ![X0]: (X0=sK11_skl|in(sK1_skl(X0),X0))),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f972,f109])).
% 1.01/0.63 fof(f1749,plain,(
% 1.01/0.63 ![X0]: (singleton(X0)=sK11_skl|sK1_skl(singleton(X0))=X0)),
% 1.01/0.63 inference(resolution,[status(thm)],[f1748,f321])).
% 1.01/0.63 fof(f1752,plain,(
% 1.01/0.63 ![X0]: (X0=sK11_skl|~in(X0,sK1_skl(X0)))),
% 1.01/0.63 inference(resolution,[status(thm)],[f1748,f87])).
% 1.01/0.63 fof(f1753,plain,(
% 1.01/0.63 ![X0]: (sK1_skl(singleton(X0))=X0)),
% 1.01/0.63 inference(forward_subsumption_resolution,[status(thm)],[f1749,f978])).
% 1.01/0.63 fof(f1864,plain,(
% 1.01/0.63 powerset(sK11_skl)=singleton(empty_set)),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f972,f238])).
% 1.01/0.63 fof(f1865,plain,(
% 1.01/0.63 powerset(sK11_skl)=singleton(sK11_skl)),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f972,f1864])).
% 1.01/0.63 fof(f1866,plain,(
% 1.01/0.63 sK1_skl(powerset(sK11_skl))=sK11_skl),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f1865,f1753])).
% 1.01/0.63 fof(f1872,plain,(
% 1.01/0.63 ordered_pair(sK11_skl,sK11_skl)=singleton(powerset(sK11_skl))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f1865,f1278])).
% 1.01/0.63 fof(f1878,plain,(
% 1.01/0.63 ![X0]: (in(powerset(sK11_skl),ordered_pair(sK11_skl,X0)))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f1865,f986])).
% 1.01/0.63 fof(f1880,plain,(
% 1.01/0.63 ~powerset(sK11_skl)=sK11_skl),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f1865,f978])).
% 1.01/0.63 fof(f1906,plain,(
% 1.01/0.63 powerset(sK11_skl)=sK11_skl|in(sK11_skl,powerset(sK11_skl))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f1866,f1748])).
% 1.01/0.63 fof(f1907,definition,(
% 1.01/0.63 sQ2_spl <=> (powerset(sK11_skl)=sK11_skl)),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f1908,plain,(
% 1.01/0.63 powerset(sK11_skl)=sK11_skl|~sQ2_spl),
% 1.01/0.63 inference(component_clause,[status(thm)],[f1907])).
% 1.01/0.63 fof(f1910,definition,(
% 1.01/0.63 sQ3_spl <=> (in(sK11_skl,powerset(sK11_skl)))),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f1913,plain,(
% 1.01/0.63 sQ2_spl|sQ3_spl),
% 1.01/0.63 inference(split_clause,[status(thm)],[f1906,f1907,f1910])).
% 1.01/0.63 fof(f1914,plain,(
% 1.01/0.63 $false|~sQ2_spl),
% 1.01/0.63 inference(forward_subsumption_resolution,[status(thm)],[f1908,f1880])).
% 1.01/0.63 fof(f1915,plain,(
% 1.01/0.63 ~sQ2_spl),
% 1.01/0.63 inference(contradiction_clause,[status(thm)],[f1914])).
% 1.01/0.63 fof(f1978,plain,(
% 1.01/0.63 ![X0,X1,X2]: (~in(X0,ordered_pair(X1,X2))|X0=unordered_pair(X1,X2)|X0=singleton(X1))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f169,f326])).
% 1.01/0.63 fof(f2053,plain,(
% 1.01/0.63 ![X0]: (~in(X0,ordered_pair(sK11_skl,sK11_skl))|X0=powerset(sK11_skl))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f1872,f321])).
% 1.01/0.63 fof(f2250,plain,(
% 1.01/0.63 ![X0]: (powerset(sK11_skl)=unordered_pair(sK11_skl,X0)|powerset(sK11_skl)=singleton(sK11_skl))),
% 1.01/0.63 inference(resolution,[status(thm)],[f1978,f1878])).
% 1.01/0.63 fof(f2255,plain,(
% 1.01/0.63 unordered_pair(sK15_skl,sK14_skl)=unordered_pair(sK16_skl,sK17_skl)|unordered_pair(sK15_skl,sK14_skl)=singleton(sK16_skl)),
% 1.01/0.63 inference(resolution,[status(thm)],[f1978,f1081])).
% 1.01/0.63 fof(f2259,plain,(
% 1.01/0.63 singleton(sK14_skl)=unordered_pair(sK16_skl,sK17_skl)|singleton(sK14_skl)=singleton(sK16_skl)),
% 1.01/0.63 inference(resolution,[status(thm)],[f1978,f1059])).
% 1.01/0.63 fof(f2266,plain,(
% 1.01/0.63 ![X0]: (~in(X0,ordered_pair(sK16_skl,sK17_skl))|X0=unordered_pair(sK14_skl,sK15_skl)|X0=singleton(sK14_skl))),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f256,f1978])).
% 1.01/0.63 fof(f2268,definition,(
% 1.01/0.63 ![X0]: (sQ8_spl <=> (powerset(sK11_skl)=unordered_pair(sK11_skl,X0)))),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f2269,plain,(
% 1.01/0.63 ![X0]: (powerset(sK11_skl)=unordered_pair(sK11_skl,X0)|~sQ8_spl)),
% 1.01/0.63 inference(component_clause,[status(thm)],[f2268])).
% 1.01/0.63 fof(f2271,definition,(
% 1.01/0.63 sQ9_spl <=> (powerset(sK11_skl)=singleton(sK11_skl))),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f2274,plain,(
% 1.01/0.63 sQ8_spl|sQ9_spl),
% 1.01/0.63 inference(split_clause,[status(thm)],[f2250,f2268,f2271])).
% 1.01/0.63 fof(f2282,definition,(
% 1.01/0.63 sQ12_spl <=> (unordered_pair(sK15_skl,sK14_skl)=unordered_pair(sK16_skl,sK17_skl))),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f2283,plain,(
% 1.01/0.63 unordered_pair(sK15_skl,sK14_skl)=unordered_pair(sK16_skl,sK17_skl)|~sQ12_spl),
% 1.01/0.63 inference(component_clause,[status(thm)],[f2282])).
% 1.01/0.63 fof(f2285,definition,(
% 1.01/0.63 sQ13_spl <=> (unordered_pair(sK15_skl,sK14_skl)=singleton(sK16_skl))),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f2286,plain,(
% 1.01/0.63 unordered_pair(sK15_skl,sK14_skl)=singleton(sK16_skl)|~sQ13_spl),
% 1.01/0.63 inference(component_clause,[status(thm)],[f2285])).
% 1.01/0.63 fof(f2288,plain,(
% 1.01/0.63 sQ12_spl|sQ13_spl),
% 1.01/0.63 inference(split_clause,[status(thm)],[f2255,f2282,f2285])).
% 1.01/0.63 fof(f2296,definition,(
% 1.01/0.63 sQ16_spl <=> (singleton(sK14_skl)=unordered_pair(sK16_skl,sK17_skl))),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f2297,plain,(
% 1.01/0.63 singleton(sK14_skl)=unordered_pair(sK16_skl,sK17_skl)|~sQ16_spl),
% 1.01/0.63 inference(component_clause,[status(thm)],[f2296])).
% 1.01/0.63 fof(f2298,plain,(
% 1.01/0.63 ~singleton(sK14_skl)=unordered_pair(sK16_skl,sK17_skl)|sQ16_spl),
% 1.01/0.63 inference(component_clause,[status(thm)],[f2296])).
% 1.01/0.63 fof(f2299,definition,(
% 1.01/0.63 sQ17_spl <=> (singleton(sK14_skl)=singleton(sK16_skl))),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f2300,plain,(
% 1.01/0.63 singleton(sK14_skl)=singleton(sK16_skl)|~sQ17_spl),
% 1.01/0.63 inference(component_clause,[status(thm)],[f2299])).
% 1.01/0.63 fof(f2302,plain,(
% 1.01/0.63 sQ16_spl|sQ17_spl),
% 1.01/0.63 inference(split_clause,[status(thm)],[f2259,f2296,f2299])).
% 1.01/0.63 fof(f2425,plain,(
% 1.01/0.63 in(sK17_skl,singleton(sK14_skl))|~sQ16_spl),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f2297,f328])).
% 1.01/0.63 fof(f2426,plain,(
% 1.01/0.63 in(sK16_skl,singleton(sK14_skl))|~sQ16_spl),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f2297,f327])).
% 1.01/0.63 fof(f2461,plain,(
% 1.01/0.63 sK17_skl=sK14_skl|~sQ16_spl),
% 1.01/0.63 inference(resolution,[status(thm)],[f2425,f321])).
% 1.01/0.63 fof(f2490,plain,(
% 1.01/0.63 ~sK17_skl=sK16_skl|~sQ16_spl|sQ0_spl),
% 1.01/0.63 inference(backward_demodulation,[status(thm)],[f2461,f314])).
% 1.01/0.63 fof(f2560,plain,(
% 1.01/0.63 in(sK16_skl,singleton(sK17_skl))|~sQ16_spl),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f2461,f2426])).
% 1.01/0.63 fof(f2561,plain,(
% 1.01/0.63 sK16_skl=sK17_skl|~sQ16_spl),
% 1.01/0.63 inference(resolution,[status(thm)],[f2560,f321])).
% 1.01/0.63 fof(f2564,plain,(
% 1.01/0.63 $false|sQ0_spl|~sQ16_spl),
% 1.01/0.63 inference(forward_subsumption_resolution,[status(thm)],[f2561,f2490])).
% 1.01/0.63 fof(f2565,plain,(
% 1.01/0.63 sQ0_spl|~sQ16_spl),
% 1.01/0.63 inference(contradiction_clause,[status(thm)],[f2564])).
% 1.01/0.63 fof(f2573,plain,(
% 1.01/0.63 ![X0]: (~in(powerset(sK11_skl),X0)|~sQ8_spl)),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f2269,f1004])).
% 1.01/0.63 fof(f2659,plain,(
% 1.01/0.63 $false|~sQ8_spl),
% 1.01/0.63 inference(backward_subsumption_resolution,[status(thm)],[f1878,f2573])).
% 1.01/0.63 fof(f2664,plain,(
% 1.01/0.63 ~sQ8_spl),
% 1.01/0.63 inference(contradiction_clause,[status(thm)],[f2659])).
% 1.01/0.63 fof(f2671,plain,(
% 1.01/0.63 unordered_pair(sK15_skl,sK16_skl)=unordered_pair(sK16_skl,sK17_skl)|~sQ0_spl|~sQ12_spl),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f313,f2283])).
% 1.01/0.63 fof(f2688,plain,(
% 1.01/0.63 in(sK15_skl,unordered_pair(sK16_skl,sK17_skl))|~sQ0_spl|~sQ12_spl),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f2671,f327])).
% 1.01/0.63 fof(f2943,plain,(
% 1.01/0.63 sK15_skl=sK16_skl|sK15_skl=sK17_skl|~sQ0_spl|~sQ12_spl),
% 1.01/0.63 inference(resolution,[status(thm)],[f2688,f326])).
% 1.01/0.63 fof(f2950,definition,(
% 1.01/0.63 sQ24_spl <=> (sK15_skl=sK16_skl)),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f2951,plain,(
% 1.01/0.63 sK15_skl=sK16_skl|~sQ24_spl),
% 1.01/0.63 inference(component_clause,[status(thm)],[f2950])).
% 1.01/0.63 fof(f2953,plain,(
% 1.01/0.63 sQ24_spl|sQ1_spl|~sQ0_spl|~sQ12_spl),
% 1.01/0.63 inference(split_clause,[status(thm)],[f2943,f2950,f315,f312,f2282])).
% 1.01/0.63 fof(f2959,plain,(
% 1.01/0.63 sK1_skl(singleton(sK16_skl))=sK14_skl|~sQ17_spl),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f2300,f1753])).
% 1.01/0.63 fof(f2983,plain,(
% 1.01/0.63 sK16_skl=sK14_skl|~sQ17_spl),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f1753,f2959])).
% 1.01/0.63 fof(f2984,plain,(
% 1.01/0.63 $false|sQ0_spl|~sQ17_spl),
% 1.01/0.63 inference(forward_subsumption_resolution,[status(thm)],[f2983,f314])).
% 1.01/0.63 fof(f2985,plain,(
% 1.01/0.63 sQ0_spl|~sQ17_spl),
% 1.01/0.63 inference(contradiction_clause,[status(thm)],[f2984])).
% 1.01/0.63 fof(f3067,plain,(
% 1.01/0.63 ~sK16_skl=sK17_skl|~sQ24_spl|sQ1_spl),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f2951,f317])).
% 1.01/0.63 fof(f3068,plain,(
% 1.01/0.63 sK17_skl=sK16_skl|~sQ16_spl|~sQ0_spl),
% 1.01/0.63 inference(backward_demodulation,[status(thm)],[f2461,f313])).
% 1.01/0.63 fof(f3069,plain,(
% 1.01/0.63 $false|~sQ24_spl|sQ1_spl|~sQ16_spl|~sQ0_spl),
% 1.01/0.63 inference(forward_subsumption_resolution,[status(thm)],[f3068,f3067])).
% 1.01/0.63 fof(f3070,plain,(
% 1.01/0.63 ~sQ24_spl|sQ1_spl|~sQ16_spl|~sQ0_spl),
% 1.01/0.63 inference(contradiction_clause,[status(thm)],[f3069])).
% 1.01/0.63 fof(f3075,plain,(
% 1.01/0.63 ~singleton(sK16_skl)=unordered_pair(sK16_skl,sK17_skl)|~sQ0_spl|sQ16_spl),
% 1.01/0.63 inference(forward_demodulation,[status(thm)],[f313,f2298])).
% 1.01/0.63 fof(f3197,plain,(
% 1.01/0.63 powerset(sK11_skl)=sK11_skl|~in(powerset(sK11_skl),sK11_skl)),
% 1.01/0.63 inference(paramodulation,[status(thm)],[f1866,f1752])).
% 1.01/0.63 fof(f3200,definition,(
% 1.01/0.63 sQ25_spl <=> (in(powerset(sK11_skl),sK11_skl))),
% 1.01/0.63 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 1.01/0.63 fof(f3203,plain,(
% 1.01/0.63 sQ2_spl|~sQ25_spl),
% 1.01/0.63 inference(split_clause,[status(thm)],[f3197,f1907,f3200])).
% 1.01/0.64 fof(f3281,plain,(
% 1.01/0.64 ordered_pair(sK11_skl,sK11_skl)=set_union2(ordered_pair(sK11_skl,sK11_skl),ordered_pair(sK11_skl,sK11_skl))|sK4_skl(ordered_pair(sK11_skl,sK11_skl),ordered_pair(sK11_skl,sK11_skl),ordered_pair(sK11_skl,sK11_skl))=powerset(sK11_skl)),
% 1.01/0.64 inference(resolution,[status(thm)],[f134,f2053])).
% 1.01/0.64 fof(f3343,definition,(
% 1.01/0.64 sQ26_spl <=> (ordered_pair(sK11_skl,sK11_skl)=set_union2(ordered_pair(sK11_skl,sK11_skl),ordered_pair(sK11_skl,sK11_skl)))),
% 1.01/0.64 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 1.01/0.64 fof(f3346,definition,(
% 1.01/0.64 sQ27_spl <=> (sK4_skl(ordered_pair(sK11_skl,sK11_skl),ordered_pair(sK11_skl,sK11_skl),ordered_pair(sK11_skl,sK11_skl))=powerset(sK11_skl))),
% 1.01/0.64 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 1.01/0.64 fof(f3349,plain,(
% 1.01/0.64 sQ26_spl|sQ27_spl),
% 1.01/0.64 inference(split_clause,[status(thm)],[f3281,f3343,f3346])).
% 1.01/0.64 fof(f3367,plain,(
% 1.01/0.64 ![X0]: (~in(X0,ordered_pair(sK16_skl,sK17_skl))|X0=unordered_pair(sK16_skl,sK15_skl)|X0=singleton(sK14_skl)|~sQ0_spl)),
% 1.01/0.64 inference(forward_demodulation,[status(thm)],[f313,f2266])).
% 1.01/0.64 fof(f3368,plain,(
% 1.01/0.64 ![X0]: (~in(X0,ordered_pair(sK16_skl,sK17_skl))|X0=unordered_pair(sK16_skl,sK16_skl)|X0=singleton(sK14_skl)|~sQ24_spl|~sQ0_spl)),
% 1.01/0.64 inference(forward_demodulation,[status(thm)],[f2951,f3367])).
% 1.01/0.64 fof(f3369,plain,(
% 1.01/0.64 ![X0]: (~in(X0,ordered_pair(sK16_skl,sK17_skl))|X0=singleton(sK16_skl)|X0=singleton(sK14_skl)|~sQ24_spl|~sQ0_spl)),
% 1.01/0.64 inference(forward_demodulation,[status(thm)],[f288,f3368])).
% 1.01/0.64 fof(f3370,plain,(
% 1.01/0.64 ![X0]: (~in(X0,ordered_pair(sK16_skl,sK17_skl))|X0=singleton(sK16_skl)|X0=singleton(sK16_skl)|~sQ24_spl|~sQ0_spl)),
% 1.01/0.64 inference(forward_demodulation,[status(thm)],[f313,f3369])).
% 1.01/0.64 fof(f3371,plain,(
% 1.01/0.64 ![X0]: (~in(X0,ordered_pair(sK16_skl,sK17_skl))|X0=singleton(sK16_skl)|~sQ24_spl|~sQ0_spl)),
% 1.01/0.64 inference(duplicate_literals_removal,[status(thm)],[f3370])).
% 1.01/0.64 fof(f3382,plain,(
% 1.01/0.64 unordered_pair(sK16_skl,sK17_skl)=singleton(sK16_skl)|~sQ24_spl|~sQ0_spl),
% 1.01/0.64 inference(resolution,[status(thm)],[f3371,f1001])).
% 1.01/0.64 fof(f3401,plain,(
% 1.01/0.64 $false|sQ16_spl|~sQ24_spl|~sQ0_spl),
% 1.01/0.64 inference(forward_subsumption_resolution,[status(thm)],[f3382,f3075])).
% 1.01/0.64 fof(f3402,plain,(
% 1.01/0.64 sQ16_spl|~sQ24_spl|~sQ0_spl),
% 1.01/0.64 inference(contradiction_clause,[status(thm)],[f3401])).
% 1.01/0.64 fof(f3404,plain,(
% 1.01/0.64 unordered_pair(sK15_skl,sK16_skl)=singleton(sK16_skl)|~sQ0_spl|~sQ13_spl),
% 1.01/0.64 inference(forward_demodulation,[status(thm)],[f313,f2286])).
% 1.01/0.64 fof(f3760,plain,(
% 1.01/0.64 sK15_skl=sK16_skl|~sQ0_spl|~sQ13_spl),
% 1.01/0.64 inference(resolution,[status(thm)],[f3404,f311])).
% 1.01/0.64 fof(f3797,plain,(
% 1.01/0.64 sQ24_spl|~sQ0_spl|~sQ13_spl),
% 1.01/0.64 inference(split_clause,[status(thm)],[f3760,f2950,f312,f2285])).
% 1.01/0.64 fof(f3831,plain,(
% 1.01/0.64 $false),
% 1.01/0.64 inference(sat_refutation,[status(thm)],[f318,f1913,f1915,f2274,f2288,f2302,f2565,f2664,f2953,f2985,f3070,f3203,f3349,f3402,f3797])).
% 1.01/0.64 % SZS output end CNFRefutation for theBenchmark.p
% 1.01/0.66 % Elapsed time: 0.276162 seconds
% 1.01/0.66 % CPU time: 1.811680 seconds
% 1.01/0.66 % Total memory used: 162.013 MB
% 1.01/0.66 % Net memory used: 160.527 MB
%------------------------------------------------------------------------------