%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU114+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:19:15 PM UTC 2026
% Result : Theorem 0.84s 0.63s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 188 ( 23 unt; 26 def)
% Number of atoms : 535 ( 31 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 593 ( 246 ~; 238 |; 67 &)
% ( 34 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 27 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 222 ( 215 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] : subset(finite_subsets(A),powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f46,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f52,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f53,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f58,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f64,plain,
! [A,B] :
( ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) )
| ~ preboolean(B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f65,plain,
! [A,B] :
( ( ( ? [C] :
( ( ( finite(C)
& subset(C,A) )
| in(C,B) )
& ( ~ finite(C)
| ~ subset(C,A)
| ~ in(C,B) ) )
| B = finite_subsets(A) )
& ( ! [C] :
( ( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [B] :
( ( ! [A] :
( ? [C] :
( ( ( finite(C)
& subset(C,A) )
| in(C,B) )
& ( ~ finite(C)
| ~ subset(C,A)
| ~ in(C,B) ) )
| B = finite_subsets(A) )
& ! [A] :
( ( ! [C] :
( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ! [C] :
( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
! [B] :
( ( ! [A] :
( ( ( ( finite(sK1_skl(A,B))
& subset(sK1_skl(A,B),A) )
| in(sK1_skl(A,B),B) )
& ( ~ finite(sK1_skl(A,B))
| ~ subset(sK1_skl(A,B),A)
| ~ in(sK1_skl(A,B),B) ) )
| B = finite_subsets(A) )
& ! [A] :
( ( ! [C] :
( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ! [C] :
( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(A,B))],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( ~ finite(sK1_skl(X1,X0))
| ~ subset(sK1_skl(X1,X0),X1)
| ~ in(sK1_skl(X1,X0),X0)
| X0 = finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f72,plain,
! [X0,X1] :
( subset(sK1_skl(X1,X0),X1)
| in(sK1_skl(X1,X0),X0)
| X0 = finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f73,plain,
! [X0,X1] :
( finite(sK1_skl(X1,X0))
| in(sK1_skl(X1,X0),X0)
| X0 = finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f74,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f77,plain,
( ! [A] : preboolean(powerset(A))
& ! [A] : diff_closed(powerset(A))
& ! [A] : cup_closed(powerset(A))
& ! [A] : ~ empty(powerset(A)) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f81,plain,
! [X0] : preboolean(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f84,plain,
( ! [A] : preboolean(finite_subsets(A))
& ! [A] : diff_closed(finite_subsets(A))
& ! [A] : cup_closed(finite_subsets(A))
& ! [A] : ~ empty(finite_subsets(A)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f85,plain,
! [X0] : ~ empty(finite_subsets(X0)),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f104,plain,
! [A] :
( finite(sK7_skl(A))
& natural(sK7_skl(A))
& ordinal(sK7_skl(A))
& epsilon_connected(sK7_skl(A))
& epsilon_transitive(sK7_skl(A))
& one_to_one(sK7_skl(A))
& function(sK7_skl(A))
& relation(sK7_skl(A))
& empty(sK7_skl(A))
& element(sK7_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(B,sK7_skl(A))],[f20]) ).
fof(f105,plain,
! [X0] : element(sK7_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f114,plain,
! [X0] : finite(sK7_skl(X0)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f115,plain,
! [A] :
( empty(sK8_skl(A))
& element(sK8_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(B,sK8_skl(A))],[f21]) ).
fof(f116,plain,
! [X0] : element(sK8_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] : empty(sK8_skl(X0)),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f135,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f136,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f138,plain,
? [A] :
( finite_subsets(A) != powerset(A)
& finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f139,plain,
( finite_subsets(sK12_skl) != powerset(sK12_skl)
& finite(sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f138]) ).
fof(f140,plain,
finite(sK12_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
finite_subsets(sK12_skl) != powerset(sK12_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f142,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f143,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f145,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f151,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f152,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f156,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f157,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f156]) ).
fof(f158,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f162,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f164,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f168,plain,
( ~ subset(powerset(sK12_skl),finite_subsets(sK12_skl))
| ~ subset(finite_subsets(sK12_skl),powerset(sK12_skl)) ),
inference(resolution,[status(thm)],[f56,f141]) ).
fof(f170,definition,
( sQ0_spl
<=> subset(finite_subsets(sK12_skl),powerset(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ0_spl
| ~ subset(finite_subsets(sK12_skl),powerset(sK12_skl)) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,definition,
( sQ1_spl
<=> subset(powerset(sK12_skl),finite_subsets(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ1_spl
| ~ subset(powerset(sK12_skl),finite_subsets(sK12_skl)) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f168,f170,f173]) ).
fof(f178,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f137]) ).
fof(f179,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f187,plain,
( sQ1_spl
| ~ in(sK0_skl(finite_subsets(sK12_skl),powerset(sK12_skl)),finite_subsets(sK12_skl)) ),
inference(resolution,[status(thm)],[f63,f175]) ).
fof(f188,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f74]) ).
fof(f189,plain,
( sQ1_spl
| ~ in(powerset(sK12_skl),finite_subsets(finite_subsets(sK12_skl))) ),
inference(resolution,[status(thm)],[f188,f175]) ).
fof(f198,plain,
! [X0] :
( sQ1_spl
| ~ in(powerset(sK12_skl),X0)
| ~ subset(X0,finite_subsets(finite_subsets(sK12_skl))) ),
inference(resolution,[status(thm)],[f189,f61]) ).
fof(f204,plain,
! [X0] :
( sQ1_spl
| ~ in(sK0_skl(finite_subsets(sK12_skl),powerset(sK12_skl)),X0)
| ~ subset(X0,finite_subsets(sK12_skl)) ),
inference(resolution,[status(thm)],[f187,f61]) ).
fof(f214,plain,
! [X0] :
( sQ1_spl
| ~ in(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl))))
| ~ in(powerset(sK12_skl),X0) ),
inference(resolution,[status(thm)],[f198,f188]) ).
fof(f215,plain,
! [X0] :
( sQ1_spl
| ~ in(sK0_skl(finite_subsets(finite_subsets(sK12_skl)),X0),finite_subsets(finite_subsets(sK12_skl)))
| ~ in(powerset(sK12_skl),X0) ),
inference(resolution,[status(thm)],[f198,f63]) ).
fof(f223,plain,
! [X0,X1] :
( sQ1_spl
| ~ in(sK0_skl(finite_subsets(sK12_skl),powerset(sK12_skl)),X1)
| ~ subset(X1,X0)
| ~ subset(X0,finite_subsets(sK12_skl)) ),
inference(resolution,[status(thm)],[f204,f61]) ).
fof(f260,plain,
! [X0] :
( sQ1_spl
| subset(powerset(sK12_skl),finite_subsets(sK12_skl))
| ~ subset(powerset(sK12_skl),X0)
| ~ subset(X0,finite_subsets(sK12_skl)) ),
inference(resolution,[status(thm)],[f223,f62]) ).
fof(f275,definition,
! [X0] :
( sQ12_spl
<=> ( ~ subset(powerset(sK12_skl),X0)
| ~ subset(X0,finite_subsets(sK12_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f276,plain,
! [X0] :
( ~ sQ12_spl
| ~ subset(powerset(sK12_skl),X0)
| ~ subset(X0,finite_subsets(sK12_skl)) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f260,f275,f173]) ).
fof(f287,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f158,f62]) ).
fof(f289,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ subset(X1,X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f158,f61]) ).
fof(f295,plain,
! [X0,X1] :
( sQ1_spl
| ~ in(sK0_skl(finite_subsets(sK12_skl),powerset(sK12_skl)),X0)
| ~ subset(X1,finite_subsets(sK12_skl))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f287,f223]) ).
fof(f301,definition,
! [X0] :
( sQ16_spl
<=> ( ~ in(sK0_skl(finite_subsets(sK12_skl),powerset(sK12_skl)),X0)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f304,definition,
! [X1] :
( sQ17_spl
<=> ~ subset(X1,finite_subsets(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f305,plain,
! [X0] :
( ~ sQ17_spl
| ~ subset(X0,finite_subsets(sK12_skl)) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,plain,
( sQ1_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f295,f301,f304,f173]) ).
fof(f308,plain,
( ~ finite(sK1_skl(sK12_skl,powerset(sK12_skl)))
| ~ subset(sK1_skl(sK12_skl,powerset(sK12_skl)),sK12_skl)
| ~ in(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl))
| ~ preboolean(powerset(sK12_skl)) ),
inference(resolution,[status(thm)],[f71,f141]) ).
fof(f309,definition,
( sQ18_spl
<=> preboolean(powerset(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ18_spl
| ~ preboolean(powerset(sK12_skl)) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,definition,
( sQ19_spl
<=> in(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( sQ19_spl
| ~ in(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl)) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,definition,
( sQ20_spl
<=> subset(sK1_skl(sK12_skl,powerset(sK12_skl)),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( sQ20_spl
| ~ subset(sK1_skl(sK12_skl,powerset(sK12_skl)),sK12_skl) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,definition,
( sQ21_spl
<=> finite(sK1_skl(sK12_skl,powerset(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ21_spl
| ~ finite(sK1_skl(sK12_skl,powerset(sK12_skl))) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f308,f309,f312,f315,f318]) ).
fof(f322,plain,
! [X0] :
( sQ1_spl
| ~ in(powerset(sK12_skl),sK1_skl(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl)))))
| subset(sK1_skl(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl)))),X0)
| finite_subsets(finite_subsets(finite_subsets(sK12_skl))) = finite_subsets(X0)
| ~ preboolean(finite_subsets(finite_subsets(finite_subsets(sK12_skl)))) ),
inference(resolution,[status(thm)],[f72,f214]) ).
fof(f329,definition,
( sQ22_spl
<=> preboolean(finite_subsets(finite_subsets(finite_subsets(sK12_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ22_spl
| ~ preboolean(finite_subsets(finite_subsets(finite_subsets(sK12_skl)))) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
! [X0] :
( sQ23_spl
<=> ( ~ in(powerset(sK12_skl),sK1_skl(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl)))))
| subset(sK1_skl(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl)))),X0)
| finite_subsets(finite_subsets(finite_subsets(sK12_skl))) = finite_subsets(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ1_spl
| sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f322,f329,f332,f173]) ).
fof(f336,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f331,f74]) ).
fof(f337,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f338,plain,
! [X0] :
( sQ1_spl
| ~ in(powerset(sK12_skl),sK1_skl(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl)))))
| finite(sK1_skl(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl)))))
| finite_subsets(finite_subsets(finite_subsets(sK12_skl))) = finite_subsets(X0)
| ~ preboolean(finite_subsets(finite_subsets(finite_subsets(sK12_skl)))) ),
inference(resolution,[status(thm)],[f73,f214]) ).
fof(f342,definition,
! [X0] :
( sQ24_spl
<=> ( ~ in(powerset(sK12_skl),sK1_skl(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl)))))
| finite(sK1_skl(X0,finite_subsets(finite_subsets(finite_subsets(sK12_skl)))))
| finite_subsets(finite_subsets(finite_subsets(sK12_skl))) = finite_subsets(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( sQ1_spl
| sQ24_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f338,f329,f342,f173]) ).
fof(f358,plain,
! [X0] :
( ~ sQ12_spl
| ~ empty(X0)
| ~ subset(powerset(sK12_skl),X0) ),
inference(resolution,[status(thm)],[f276,f287]) ).
fof(f362,plain,
! [X0] :
( ~ sQ12_spl
| ~ empty(powerset(sK12_skl))
| ~ subset(X0,finite_subsets(sK12_skl)) ),
inference(resolution,[status(thm)],[f276,f287]) ).
fof(f366,definition,
( sQ26_spl
<=> empty(powerset(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( ~ sQ12_spl
| ~ sQ26_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f362,f304,f366,f275]) ).
fof(f374,plain,
( ~ sQ17_spl
| $false ),
inference(resolution,[status(thm)],[f305,f162]) ).
fof(f375,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f380,definition,
! [X0] :
( sQ27_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f381,plain,
! [X0] :
( ~ sQ27_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f384,plain,
( ~ sQ27_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f381]) ).
fof(f388,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f411,definition,
( sQ28_spl
<=> finite(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( sQ28_spl
| ~ finite(sK12_skl) ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f414,definition,
( sQ29_spl
<=> powerset(sK12_skl) = finite_subsets(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( ~ sQ29_spl
| powerset(sK12_skl) = finite_subsets(sK12_skl) ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f418,definition,
! [X0] :
( sQ30_spl
<=> ~ finite(X0) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f419,plain,
! [X0] :
( ~ sQ30_spl
| ~ finite(X0) ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f425,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f311,f81]) ).
fof(f426,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f427,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f141]) ).
fof(f428,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f427]) ).
fof(f429,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f413,f140]) ).
fof(f430,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f441,plain,
( sQ20_spl
| in(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl))
| powerset(sK12_skl) = finite_subsets(sK12_skl)
| ~ preboolean(powerset(sK12_skl)) ),
inference(resolution,[status(thm)],[f317,f72]) ).
fof(f445,plain,
( sQ20_spl
| sQ19_spl
| sQ29_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f441,f309,f414,f312,f315]) ).
fof(f449,plain,
( ~ sQ30_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f114,f419]) ).
fof(f455,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f490,plain,
! [X0] :
( sQ21_spl
| ~ element(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(X0))
| ~ finite(X0) ),
inference(resolution,[status(thm)],[f46,f320]) ).
fof(f585,plain,
! [X0] :
( sQ1_spl
| ~ in(powerset(sK12_skl),X0)
| empty(finite_subsets(finite_subsets(sK12_skl)))
| ~ element(sK0_skl(finite_subsets(finite_subsets(sK12_skl)),X0),finite_subsets(finite_subsets(sK12_skl))) ),
inference(resolution,[status(thm)],[f143,f215]) ).
fof(f587,plain,
( sQ1_spl
| empty(finite_subsets(finite_subsets(sK12_skl)))
| ~ element(powerset(sK12_skl),finite_subsets(finite_subsets(sK12_skl))) ),
inference(resolution,[status(thm)],[f143,f189]) ).
fof(f596,definition,
! [X0] :
( sQ33_spl
<=> ( ~ in(powerset(sK12_skl),X0)
| ~ element(sK0_skl(finite_subsets(finite_subsets(sK12_skl)),X0),finite_subsets(finite_subsets(sK12_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f599,definition,
( sQ34_spl
<=> empty(finite_subsets(finite_subsets(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( ~ sQ34_spl
| empty(finite_subsets(finite_subsets(sK12_skl))) ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f602,plain,
( sQ1_spl
| sQ34_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f585,f596,f599,f173]) ).
fof(f604,definition,
( sQ35_spl
<=> element(powerset(sK12_skl),finite_subsets(finite_subsets(sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( sQ1_spl
| sQ34_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f587,f604,f599,f173]) ).
fof(f616,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f85]) ).
fof(f617,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f650,plain,
( sQ19_spl
| empty(powerset(sK12_skl))
| ~ element(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl)) ),
inference(resolution,[status(thm)],[f314,f143]) ).
fof(f653,definition,
( sQ39_spl
<=> element(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( ~ sQ39_spl
| element(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl)) ),
inference(component_clause,[status(thm)],[f653]) ).
fof(f655,plain,
( sQ39_spl
| ~ element(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl)) ),
inference(component_clause,[status(thm)],[f653]) ).
fof(f656,plain,
( sQ19_spl
| sQ26_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f650,f653,f366,f312]) ).
fof(f717,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ empty(X1)
| ~ element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f153,f62]) ).
fof(f722,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,sK8_skl(X1)) ),
inference(resolution,[status(thm)],[f153,f116]) ).
fof(f723,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,sK7_skl(X1)) ),
inference(resolution,[status(thm)],[f153,f105]) ).
fof(f848,plain,
( sQ39_spl
| ~ subset(sK1_skl(sK12_skl,powerset(sK12_skl)),sK12_skl) ),
inference(resolution,[status(thm)],[f655,f147]) ).
fof(f850,plain,
( sQ39_spl
| ~ in(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl)) ),
inference(resolution,[status(thm)],[f655,f136]) ).
fof(f851,plain,
( sQ39_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f850,f312,f653]) ).
fof(f993,plain,
! [X0,X1] :
( subset(sK8_skl(X0),X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f722,f62]) ).
fof(f998,plain,
! [X0,X1] :
( subset(sK7_skl(X0),X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f723,f62]) ).
fof(f1116,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ in(X1,sK7_skl(X2))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f289,f998]) ).
fof(f1117,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ in(X1,sK8_skl(X2))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f289,f993]) ).
fof(f1122,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ in(X1,X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f289,f287]) ).
fof(f1133,definition,
! [X1,X2] :
( sQ42_spl
<=> ( ~ empty(X2)
| ~ in(X1,sK7_skl(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1136,plain,
( sQ42_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f1116,f380,f1133]) ).
fof(f1137,definition,
! [X1,X2] :
( sQ43_spl
<=> ( ~ empty(X2)
| ~ in(X1,sK8_skl(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1140,plain,
( sQ43_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f1117,f380,f1137]) ).
fof(f1141,definition,
! [X1,X2] :
( sQ44_spl
<=> ( ~ empty(X2)
| ~ in(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1144,plain,
( sQ44_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f1122,f380,f1141]) ).
fof(f1829,plain,
( sQ21_spl
| ~ sQ39_spl
| ~ finite(sK12_skl) ),
inference(resolution,[status(thm)],[f654,f490]) ).
fof(f1832,plain,
( sQ21_spl
| ~ sQ39_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1829,f411,f653,f318]) ).
fof(f1840,plain,
( sQ39_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f848,f315,f653]) ).
fof(f1865,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ empty(X1)
| ~ empty(X0)
| ~ element(powerset(sK12_skl),powerset(X0)) ),
inference(resolution,[status(thm)],[f717,f358]) ).
fof(f1868,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X0)
| ~ empty(X2)
| ~ empty(X1)
| ~ element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f717,f289]) ).
fof(f1871,definition,
! [X0] :
( sQ68_spl
<=> ( ~ empty(X0)
| ~ element(powerset(sK12_skl),powerset(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1874,plain,
( ~ sQ12_spl
| sQ27_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f1865,f1871,f380,f275]) ).
fof(f1875,definition,
! [X0,X1,X3] :
( sQ69_spl
<=> ( ~ in(X3,X0)
| ~ empty(X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1878,plain,
( sQ27_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1868,f1875,f380]) ).
fof(f1961,plain,
( sQ20_spl
| ~ element(sK1_skl(sK12_skl,powerset(sK12_skl)),powerset(sK12_skl)) ),
inference(resolution,[status(thm)],[f317,f146]) ).
fof(f1969,plain,
( sQ20_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1961,f653,f315]) ).
fof(f1970,plain,
$false,
inference(sat_refutation,[status(thm)],[f176,f179,f278,f307,f321,f335,f337,f345,f369,f375,f388,f426,f428,f430,f445,f455,f602,f607,f617,f656,f851,f1136,f1140,f1144,f1832,f1840,f1874,f1878,f1969]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU114+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n017.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:46:26 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.84/0.63 % Refutation found
% 0.84/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.84/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.84/0.67 % Elapsed time: 0.223751 seconds
% 0.84/0.67 % CPU time: 1.431320 seconds
% 0.84/0.67 % Total memory used: 100.944 MB
% 0.84/0.67 % Net memory used: 98.984 MB
%------------------------------------------------------------------------------