%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 15.91s 2.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU168+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:54:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 15.91/2.47 % Refutation found
% 15.91/2.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 15.91/2.47 % SZS output start CNFRefutation for theBenchmark
% 15.91/2.47 fof(f2,axiom,(
% 15.91/2.47 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 15.91/2.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.91/2.47 fof(f3,axiom,(
% 15.91/2.47 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 15.91/2.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.91/2.47 fof(f6,axiom,(
% 15.91/2.47 (! [A,B] : subset(A,A) )),
% 15.91/2.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.91/2.47 fof(f7,conjecture,(
% 15.91/2.47 (! [A] :(? [B] :( in(A,B)& (! [C,D] :( ( in(C,B)& subset(D,C) )=> in(D,B) ))& (! [C] :( in(C,B)=> in(powerset(C),B) ))& (! [C] :~ ( subset(C,B)& ~ are_equipotent(C,B)& ~ in(C,B) ) )) ))),
% 15.91/2.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.91/2.47 fof(f8,negated_conjecture,(
% 15.91/2.47 ~((! [A] :(? [B] :( in(A,B)& (! [C,D] :( ( in(C,B)& subset(D,C) )=> in(D,B) ))& (! [C] :( in(C,B)=> in(powerset(C),B) ))& (! [C] :~ ( subset(C,B)& ~ are_equipotent(C,B)& ~ in(C,B) ) )) )))),
% 15.91/2.47 inference(negated_conjecture,[status(cth)],[f7])).
% 15.91/2.47 fof(f9,axiom,(
% 15.91/2.47 (! [A] :(? [B] :( in(A,B)& (! [C,D] :( ( in(C,B)& subset(D,C) )=> in(D,B) ))& (! [C] :~ ( in(C,B)& (! [D] :~ ( in(D,B)& (! [E] :( subset(E,C)=> in(E,D) ) )) )))& (! [C] :~ ( subset(C,B)& ~ are_equipotent(C,B)& ~ in(C,B) ) )) ))),
% 15.91/2.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.91/2.47 fof(f12,plain,(
% 15.91/2.47 ![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))))))),
% 15.91/2.47 inference(NNF_transformation,[status(thm)],[f2])).
% 15.91/2.47 fof(f13,plain,(
% 15.91/2.47 (![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))))))),
% 15.91/2.47 inference(miniscoping,[status(thm)],[f12])).
% 15.91/2.47 fof(f14,plain,(
% 15.91/2.47 (![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_skl(B,A),B)|~subset(sK0_skl(B,A),A))&(in(sK0_skl(B,A),B)|subset(sK0_skl(B,A),A)))))),
% 15.91/2.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f13])).
% 15.91/2.47 fof(f15,plain,(
% 15.91/2.47 ![X0,X1,X2]: (~X0=powerset(X1)|~in(X2,X0)|subset(X2,X1))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f14])).
% 15.91/2.47 fof(f16,plain,(
% 15.91/2.47 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f14])).
% 15.91/2.47 fof(f19,plain,(
% 15.91/2.47 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 15.91/2.47 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 15.91/2.47 fof(f20,plain,(
% 15.91/2.47 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 15.91/2.47 inference(NNF_transformation,[status(thm)],[f19])).
% 15.91/2.47 fof(f21,plain,(
% 15.91/2.47 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 15.91/2.47 inference(miniscoping,[status(thm)],[f20])).
% 15.91/2.47 fof(f22,plain,(
% 15.91/2.47 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK1_skl(B,A),A)&~in(sK1_skl(B,A),B))))),
% 15.91/2.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f21])).
% 15.91/2.47 fof(f23,plain,(
% 15.91/2.47 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f22])).
% 15.91/2.47 fof(f24,plain,(
% 15.91/2.47 ![X0,X1]: (subset(X0,X1)|in(sK1_skl(X1,X0),X0))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f22])).
% 15.91/2.47 fof(f25,plain,(
% 15.91/2.47 ![X0,X1]: (subset(X0,X1)|~in(sK1_skl(X1,X0),X1))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f22])).
% 15.91/2.47 fof(f30,plain,(
% 15.91/2.47 ![A]: subset(A,A)),
% 15.91/2.47 inference(miniscoping,[status(thm)],[f6])).
% 15.91/2.47 fof(f31,plain,(
% 15.91/2.47 ![X0]: (subset(X0,X0))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f30])).
% 15.91/2.47 fof(f32,plain,(
% 15.91/2.47 (?[A]: ![B]: (((~in(A,B)|(?[C,D]: ((in(C,B)&subset(D,C))&~in(D,B))))|(?[C]: (in(C,B)&~in(powerset(C),B))))|(?[C]: ((subset(C,B)&~are_equipotent(C,B))&~in(C,B)))))),
% 15.91/2.47 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 15.91/2.47 fof(f33,definition,(
% 15.91/2.47 ![B,C,D]: (sP0_prd(D,C,B)<=>((in(C,B)&subset(D,C))&~in(D,B)))),
% 15.91/2.47 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 15.91/2.47 fof(f34,definition,(
% 15.91/2.47 ![B,C]: (sP1_prd(C,B)<=>(in(C,B)&~in(powerset(C),B)))),
% 15.91/2.47 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 15.91/2.47 fof(f35,plain,(
% 15.91/2.47 ?[A]: ![B]: (((~in(A,B)|(?[C,D]: sP0_prd(D,C,B)))|(?[C]: sP1_prd(C,B)))|(?[C]: ((subset(C,B)&~are_equipotent(C,B))&~in(C,B))))),
% 15.91/2.47 inference(formula_renaming,[status(thm)],[f32,f34,f33])).
% 15.91/2.47 fof(f36,plain,(
% 15.91/2.47 ![B]: (((~in(sK4_skl,B)|sP0_prd(sK6_skl(B),sK5_skl(B),B))|sP1_prd(sK7_skl(B),B))|((subset(sK8_skl(B),B)&~are_equipotent(sK8_skl(B),B))&~in(sK8_skl(B),B)))),
% 15.91/2.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK4_skl),skolemize(C,sK5_skl(B)),skolemize(D,sK6_skl(B)),skolemize(C,sK7_skl(B)),skolemize(C,sK8_skl(B))],[f35])).
% 15.91/2.47 fof(f37,plain,(
% 15.91/2.47 ![X0]: (~in(sK4_skl,X0)|sP0_prd(sK6_skl(X0),sK5_skl(X0),X0)|sP1_prd(sK7_skl(X0),X0)|subset(sK8_skl(X0),X0))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f36])).
% 15.91/2.47 fof(f38,plain,(
% 15.91/2.47 ![X0]: (~in(sK4_skl,X0)|sP0_prd(sK6_skl(X0),sK5_skl(X0),X0)|sP1_prd(sK7_skl(X0),X0)|~are_equipotent(sK8_skl(X0),X0))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f36])).
% 15.91/2.47 fof(f39,plain,(
% 15.91/2.47 ![X0]: (~in(sK4_skl,X0)|sP0_prd(sK6_skl(X0),sK5_skl(X0),X0)|sP1_prd(sK7_skl(X0),X0)|~in(sK8_skl(X0),X0))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f36])).
% 15.91/2.47 fof(f40,plain,(
% 15.91/2.47 ![A]: (?[B]: (((in(A,B)&(![C,D]: ((~in(C,B)|~subset(D,C))|in(D,B))))&(![C]: (~in(C,B)|(?[D]: (in(D,B)&(![E]: (~subset(E,C)|in(E,D))))))))&(![C]: ((~subset(C,B)|are_equipotent(C,B))|in(C,B)))))),
% 15.91/2.47 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 15.91/2.47 fof(f41,plain,(
% 15.91/2.47 ![A]: ?[B]: (((in(A,B)&(![D]: ((![C]: (~in(C,B)|~subset(D,C)))|in(D,B))))&(![C]: (~in(C,B)|(?[D]: (in(D,B)&(![E]: (~subset(E,C)|in(E,D))))))))&(![C]: ((~subset(C,B)|are_equipotent(C,B))|in(C,B))))),
% 15.91/2.47 inference(miniscoping,[status(thm)],[f40])).
% 15.91/2.47 fof(f42,plain,(
% 15.91/2.47 ![A]: (((in(A,sK9_skl(A))&(![D]: ((![C]: (~in(C,sK9_skl(A))|~subset(D,C)))|in(D,sK9_skl(A)))))&(![C]: (~in(C,sK9_skl(A))|(in(sK10_skl(C,A),sK9_skl(A))&(![E]: (~subset(E,C)|in(E,sK10_skl(C,A))))))))&(![C]: ((~subset(C,sK9_skl(A))|are_equipotent(C,sK9_skl(A)))|in(C,sK9_skl(A)))))),
% 15.91/2.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(B,sK9_skl(A)),skolemize(D,sK10_skl(C,A))],[f41])).
% 15.91/2.47 fof(f43,plain,(
% 15.91/2.47 ![X0]: (in(X0,sK9_skl(X0)))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f42])).
% 15.91/2.47 fof(f44,plain,(
% 15.91/2.47 ![X0,X1,X2]: (~in(X0,sK9_skl(X1))|~subset(X2,X0)|in(X2,sK9_skl(X1)))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f42])).
% 15.91/2.47 fof(f45,plain,(
% 15.91/2.47 ![X0,X1]: (~in(X0,sK9_skl(X1))|in(sK10_skl(X0,X1),sK9_skl(X1)))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f42])).
% 15.91/2.47 fof(f46,plain,(
% 15.91/2.47 ![X0,X1,X2]: (~in(X0,sK9_skl(X1))|~subset(X2,X0)|in(X2,sK10_skl(X0,X1)))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f42])).
% 15.91/2.47 fof(f47,plain,(
% 15.91/2.47 ![X0,X1]: (~subset(X0,sK9_skl(X1))|are_equipotent(X0,sK9_skl(X1))|in(X0,sK9_skl(X1)))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f42])).
% 15.91/2.47 fof(f48,plain,(
% 15.91/2.47 ![B,C,D]: ((~sP0_prd(D,C,B)|((in(C,B)&subset(D,C))&~in(D,B)))&(sP0_prd(D,C,B)|((~in(C,B)|~subset(D,C))|in(D,B))))),
% 15.91/2.47 inference(NNF_transformation,[status(thm)],[f33])).
% 15.91/2.47 fof(f49,plain,(
% 15.91/2.47 (![B,C,D]: (~sP0_prd(D,C,B)|((in(C,B)&subset(D,C))&~in(D,B))))&(![B,C,D]: (sP0_prd(D,C,B)|((~in(C,B)|~subset(D,C))|in(D,B))))),
% 15.91/2.47 inference(miniscoping,[status(thm)],[f48])).
% 15.91/2.47 fof(f50,plain,(
% 15.91/2.47 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|in(X1,X2))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f49])).
% 15.91/2.47 fof(f51,plain,(
% 15.91/2.47 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|subset(X0,X1))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f49])).
% 15.91/2.47 fof(f52,plain,(
% 15.91/2.47 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|~in(X0,X2))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f49])).
% 15.91/2.47 fof(f54,plain,(
% 15.91/2.47 ![B,C]: ((~sP1_prd(C,B)|(in(C,B)&~in(powerset(C),B)))&(sP1_prd(C,B)|(~in(C,B)|in(powerset(C),B))))),
% 15.91/2.47 inference(NNF_transformation,[status(thm)],[f34])).
% 15.91/2.47 fof(f55,plain,(
% 15.91/2.47 (![B,C]: (~sP1_prd(C,B)|(in(C,B)&~in(powerset(C),B))))&(![B,C]: (sP1_prd(C,B)|(~in(C,B)|in(powerset(C),B))))),
% 15.91/2.47 inference(miniscoping,[status(thm)],[f54])).
% 15.91/2.47 fof(f56,plain,(
% 15.91/2.47 ![X0,X1]: (~sP1_prd(X0,X1)|in(X0,X1))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f55])).
% 15.91/2.47 fof(f57,plain,(
% 15.91/2.47 ![X0,X1]: (~sP1_prd(X0,X1)|~in(powerset(X0),X1))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f55])).
% 15.91/2.47 fof(f58,plain,(
% 15.91/2.47 ![X0,X1]: (sP1_prd(X0,X1)|~in(X0,X1)|in(powerset(X0),X1))),
% 15.91/2.47 inference(cnf_transformation,[status(thm)],[f55])).
% 15.91/2.47 fof(f59,plain,(
% 15.91/2.47 ![X0,X1]: (~in(X0,powerset(X1))|subset(X0,X1))),
% 15.91/2.47 inference(destructive_equality_resolution,[status(thm)],[f15])).
% 15.91/2.47 fof(f60,plain,(
% 15.91/2.47 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 15.91/2.47 inference(destructive_equality_resolution,[status(thm)],[f16])).
% 15.91/2.47 fof(f61,plain,(
% 15.91/2.47 ![X0]: (in(X0,powerset(X0)))),
% 15.91/2.47 inference(resolution,[status(thm)],[f60,f31])).
% 15.91/2.47 fof(f78,plain,(
% 15.91/2.47 ![X0,X1]: (~subset(powerset(X0),X1)|in(X0,X1))),
% 15.91/2.47 inference(resolution,[status(thm)],[f23,f61])).
% 15.91/2.47 fof(f89,plain,(
% 15.91/2.47 sP0_prd(sK6_skl(sK9_skl(sK4_skl)),sK5_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|sP1_prd(sK7_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|subset(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))),
% 15.91/2.47 inference(resolution,[status(thm)],[f43,f37])).
% 15.91/2.47 fof(f95,definition,(
% 15.91/2.47 sQ3_spl <=> (sP0_prd(sK6_skl(sK9_skl(sK4_skl)),sK5_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl)))),
% 15.91/2.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 15.91/2.47 fof(f96,plain,(
% 15.91/2.47 sP0_prd(sK6_skl(sK9_skl(sK4_skl)),sK5_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ3_spl),
% 15.91/2.47 inference(component_clause,[status(thm)],[f95])).
% 15.91/2.47 fof(f98,definition,(
% 15.91/2.47 sQ4_spl <=> (sP1_prd(sK7_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl)))),
% 15.91/2.47 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 15.91/2.47 fof(f99,plain,(
% 15.91/2.47 sP1_prd(sK7_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ4_spl),
% 15.91/2.47 inference(component_clause,[status(thm)],[f98])).
% 15.91/2.47 fof(f101,definition,(
% 15.91/2.47 sQ5_spl <=> (subset(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl)))),
% 15.91/2.47 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 15.91/2.47 fof(f102,plain,(
% 15.91/2.47 subset(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ5_spl),
% 15.91/2.47 inference(component_clause,[status(thm)],[f101])).
% 15.91/2.47 fof(f104,plain,(
% 15.91/2.47 sQ3_spl|sQ4_spl|sQ5_spl),
% 15.91/2.47 inference(split_clause,[status(thm)],[f89,f95,f98,f101])).
% 15.91/2.47 fof(f108,plain,(
% 15.91/2.47 ![X0,X1]: (subset(powerset(X0),X1)|subset(sK1_skl(X1,powerset(X0)),X0))),
% 15.91/2.47 inference(resolution,[status(thm)],[f24,f59])).
% 15.91/2.47 fof(f115,plain,(
% 15.91/2.47 in(sK8_skl(sK9_skl(sK4_skl)),powerset(sK9_skl(sK4_skl)))|~sQ5_spl),
% 15.91/2.47 inference(resolution,[status(thm)],[f102,f60])).
% 15.91/2.47 fof(f172,plain,(
% 15.91/2.47 sP1_prd(sK8_skl(sK9_skl(sK4_skl)),powerset(sK9_skl(sK4_skl)))|in(powerset(sK8_skl(sK9_skl(sK4_skl))),powerset(sK9_skl(sK4_skl)))|~sQ5_spl),
% 15.91/2.47 inference(resolution,[status(thm)],[f115,f58])).
% 15.91/2.47 fof(f174,definition,(
% 15.91/2.47 sQ10_spl <=> (sP1_prd(sK8_skl(sK9_skl(sK4_skl)),powerset(sK9_skl(sK4_skl))))),
% 15.91/2.47 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 15.91/2.47 fof(f175,plain,(
% 15.91/2.47 sP1_prd(sK8_skl(sK9_skl(sK4_skl)),powerset(sK9_skl(sK4_skl)))|~sQ10_spl),
% 15.91/2.47 inference(component_clause,[status(thm)],[f174])).
% 15.91/2.47 fof(f177,definition,(
% 15.91/2.47 sQ11_spl <=> (in(powerset(sK8_skl(sK9_skl(sK4_skl))),powerset(sK9_skl(sK4_skl))))),
% 15.91/2.47 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 15.91/2.47 fof(f178,plain,(
% 15.91/2.47 in(powerset(sK8_skl(sK9_skl(sK4_skl))),powerset(sK9_skl(sK4_skl)))|~sQ11_spl),
% 15.91/2.47 inference(component_clause,[status(thm)],[f177])).
% 15.91/2.47 fof(f180,plain,(
% 15.91/2.47 sQ10_spl|sQ11_spl|~sQ5_spl),
% 15.91/2.47 inference(split_clause,[status(thm)],[f172,f174,f177,f101])).
% 15.91/2.47 fof(f182,plain,(
% 15.91/2.47 in(sK8_skl(sK9_skl(sK4_skl)),powerset(sK9_skl(sK4_skl)))|~sQ10_spl),
% 15.91/2.47 inference(resolution,[status(thm)],[f175,f56])).
% 15.91/2.47 fof(f191,plain,(
% 15.91/2.47 subset(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ10_spl),
% 15.91/2.47 inference(resolution,[status(thm)],[f182,f59])).
% 15.91/2.47 fof(f199,plain,(
% 15.91/2.47 are_equipotent(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|in(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ10_spl),
% 15.91/2.47 inference(resolution,[status(thm)],[f47,f191])).
% 15.91/2.47 fof(f202,definition,(
% 15.91/2.47 sQ12_spl <=> (are_equipotent(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl)))),
% 15.91/2.47 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 15.91/2.47 fof(f203,plain,(
% 15.91/2.48 are_equipotent(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ12_spl),
% 15.91/2.48 inference(component_clause,[status(thm)],[f202])).
% 15.91/2.48 fof(f205,definition,(
% 15.91/2.48 sQ13_spl <=> (in(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl)))),
% 15.91/2.48 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 15.91/2.48 fof(f206,plain,(
% 15.91/2.48 in(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ13_spl),
% 15.91/2.48 inference(component_clause,[status(thm)],[f205])).
% 15.91/2.48 fof(f208,plain,(
% 15.91/2.48 sQ12_spl|sQ13_spl|~sQ10_spl),
% 15.91/2.48 inference(split_clause,[status(thm)],[f199,f202,f205,f174])).
% 15.91/2.48 fof(f209,plain,(
% 15.91/2.48 subset(sK6_skl(sK9_skl(sK4_skl)),sK5_skl(sK9_skl(sK4_skl)))|~sQ3_spl),
% 15.91/2.48 inference(resolution,[status(thm)],[f96,f51])).
% 15.91/2.48 fof(f210,plain,(
% 15.91/2.48 in(sK5_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ3_spl),
% 15.91/2.48 inference(resolution,[status(thm)],[f96,f50])).
% 15.91/2.48 fof(f215,plain,(
% 15.91/2.48 ~in(sK4_skl,sK9_skl(sK4_skl))|sP0_prd(sK6_skl(sK9_skl(sK4_skl)),sK5_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|sP1_prd(sK7_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ13_spl),
% 15.91/2.48 inference(resolution,[status(thm)],[f206,f39])).
% 15.91/2.48 fof(f221,definition,(
% 15.91/2.48 sQ14_spl <=> (in(sK4_skl,sK9_skl(sK4_skl)))),
% 15.91/2.48 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 15.91/2.48 fof(f223,plain,(
% 15.91/2.48 ~in(sK4_skl,sK9_skl(sK4_skl))|sQ14_spl),
% 15.91/2.48 inference(component_clause,[status(thm)],[f221])).
% 15.91/2.48 fof(f224,plain,(
% 15.91/2.48 ~sQ14_spl|sQ3_spl|sQ4_spl|~sQ13_spl),
% 15.91/2.48 inference(split_clause,[status(thm)],[f215,f221,f95,f98,f205])).
% 15.91/2.48 fof(f232,plain,(
% 15.91/2.48 $false|sQ14_spl),
% 15.91/2.48 inference(forward_subsumption_resolution,[status(thm)],[f223,f43])).
% 15.91/2.48 fof(f233,plain,(
% 15.91/2.48 sQ14_spl),
% 15.91/2.48 inference(contradiction_clause,[status(thm)],[f232])).
% 15.91/2.48 fof(f234,plain,(
% 15.91/2.48 ~in(sK4_skl,sK9_skl(sK4_skl))|sP0_prd(sK6_skl(sK9_skl(sK4_skl)),sK5_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|sP1_prd(sK7_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ12_spl),
% 15.91/2.48 inference(resolution,[status(thm)],[f203,f38])).
% 15.91/2.48 fof(f235,plain,(
% 15.91/2.48 ~sQ14_spl|sQ3_spl|sQ4_spl|~sQ12_spl),
% 15.91/2.48 inference(split_clause,[status(thm)],[f234,f221,f95,f98,f202])).
% 15.91/2.48 fof(f236,plain,(
% 15.91/2.48 ![X0]: (~subset(X0,sK5_skl(sK9_skl(sK4_skl)))|in(X0,sK9_skl(sK4_skl))|~sQ3_spl)),
% 15.91/2.48 inference(resolution,[status(thm)],[f210,f44])).
% 15.91/2.48 fof(f284,plain,(
% 15.91/2.48 ![X0,X1,X2]: (~in(X0,sK9_skl(X1))|~subset(X2,sK10_skl(X0,X1))|in(X2,sK9_skl(X1)))),
% 15.91/2.48 inference(resolution,[status(thm)],[f45,f44])).
% 15.91/2.48 fof(f293,plain,(
% 15.91/2.48 ![X0,X1,X2]: (subset(powerset(X0),X1)|~in(X0,sK9_skl(X2))|in(sK1_skl(X1,powerset(X0)),sK10_skl(X0,X2)))),
% 15.91/2.48 inference(resolution,[status(thm)],[f108,f46])).
% 15.91/2.48 fof(f839,plain,(
% 15.91/2.48 subset(powerset(sK8_skl(sK9_skl(sK4_skl))),sK9_skl(sK4_skl))|~sQ11_spl),
% 15.91/2.48 inference(resolution,[status(thm)],[f178,f59])).
% 15.91/2.48 fof(f932,plain,(
% 15.91/2.48 in(sK8_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ11_spl),
% 15.91/2.48 inference(resolution,[status(thm)],[f839,f78])).
% 15.91/2.48 fof(f978,plain,(
% 15.91/2.48 ![X0,X1]: (subset(powerset(X0),sK10_skl(X0,X1))|~in(X0,sK9_skl(X1))|subset(powerset(X0),sK10_skl(X0,X1)))),
% 15.91/2.48 inference(resolution,[status(thm)],[f293,f25])).
% 15.91/2.48 fof(f984,plain,(
% 15.91/2.48 ![X0,X1]: (subset(powerset(X0),sK10_skl(X0,X1))|~in(X0,sK9_skl(X1)))),
% 15.91/2.48 inference(duplicate_literals_removal,[status(thm)],[f978])).
% 15.91/2.48 fof(f1122,plain,(
% 15.91/2.48 ~in(sK4_skl,sK9_skl(sK4_skl))|sP0_prd(sK6_skl(sK9_skl(sK4_skl)),sK5_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|sP1_prd(sK7_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ11_spl),
% 15.91/2.48 inference(resolution,[status(thm)],[f932,f39])).
% 15.91/2.48 fof(f1130,plain,(
% 15.91/2.48 ~sQ14_spl|sQ3_spl|sQ4_spl|~sQ11_spl),
% 15.91/2.48 inference(split_clause,[status(thm)],[f1122,f221,f95,f98,f177])).
% 15.91/2.48 fof(f1381,plain,(
% 15.91/2.48 ![X0,X1]: (~in(X0,sK9_skl(X1))|~in(X0,sK9_skl(X1))|in(powerset(X0),sK9_skl(X1)))),
% 15.91/2.48 inference(resolution,[status(thm)],[f984,f284])).
% 15.91/2.48 fof(f1389,plain,(
% 15.91/2.48 ![X0,X1]: (~in(X0,sK9_skl(X1))|in(powerset(X0),sK9_skl(X1)))),
% 15.91/2.48 inference(duplicate_literals_removal,[status(thm)],[f1381])).
% 15.91/2.48 fof(f1393,plain,(
% 15.91/2.48 ![X0,X1]: (~in(X0,sK9_skl(X1))|~sP1_prd(X0,sK9_skl(X1)))),
% 15.91/2.48 inference(resolution,[status(thm)],[f1389,f57])).
% 15.91/2.48 fof(f1406,plain,(
% 15.91/2.48 ![X0,X1]: (~sP1_prd(X0,sK9_skl(X1)))),
% 15.91/2.48 inference(forward_subsumption_resolution,[status(thm)],[f1393,f56])).
% 15.91/2.48 fof(f1439,plain,(
% 15.91/2.48 $false|~sQ4_spl),
% 15.91/2.48 inference(forward_subsumption_resolution,[status(thm)],[f99,f1406])).
% 15.91/2.50 fof(f1440,plain,(
% 15.91/2.50 ~sQ4_spl),
% 15.91/2.50 inference(contradiction_clause,[status(thm)],[f1439])).
% 15.91/2.50 fof(f3090,plain,(
% 15.91/2.50 in(sK6_skl(sK9_skl(sK4_skl)),sK9_skl(sK4_skl))|~sQ3_spl),
% 15.91/2.50 inference(resolution,[status(thm)],[f236,f209])).
% 15.91/2.50 fof(f3136,plain,(
% 15.91/2.50 ![X0]: (~sP0_prd(sK6_skl(sK9_skl(sK4_skl)),X0,sK9_skl(sK4_skl))|~sQ3_spl)),
% 15.91/2.50 inference(resolution,[status(thm)],[f3090,f52])).
% 15.91/2.50 fof(f3172,plain,(
% 15.91/2.50 $false|~sQ3_spl),
% 15.91/2.50 inference(backward_subsumption_resolution,[status(thm)],[f96,f3136])).
% 15.91/2.50 fof(f3173,plain,(
% 15.91/2.50 ~sQ3_spl),
% 15.91/2.50 inference(contradiction_clause,[status(thm)],[f3172])).
% 15.91/2.50 fof(f3174,plain,(
% 15.91/2.50 $false),
% 15.91/2.50 inference(sat_refutation,[status(thm)],[f104,f180,f208,f224,f233,f235,f1130,f1440,f3173])).
% 15.91/2.50 % SZS output end CNFRefutation for theBenchmark.p
% 2.13/2.52 % Elapsed time: 2.146790 seconds
% 2.13/2.52 % CPU time: 16.647316 seconds
% 2.13/2.52 % Total memory used: 177.468 MB
% 2.13/2.52 % Net memory used: 145.295 MB
%------------------------------------------------------------------------------