%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET011+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:08:49 PM UTC 2026
% Result : Theorem 0.13s 0.54s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 129 ( 9 unt; 18 def)
% Number of atoms : 366 ( 33 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 392 ( 155 ~; 181 |; 30 &)
% ( 25 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 19 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 143 ( 137 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [B,C] : difference(B,difference(B,C)) = intersection(B,C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [B,C] : difference(B,difference(B,C)) = intersection(B,C),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
( ! [B,C,D] :
( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ! [B,C,D] :
( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
( ! [B,C,D] :
( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ! [B,C,D] :
( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f26,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
( ! [B,C] :
( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [B,C] :
( ( ~ member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f34,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f35,plain,
( ! [B,C] :
( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
( ! [B,C] :
( ( ( member(sK1_skl(C,B),C)
| member(sK1_skl(C,B),B) )
& ( ~ member(sK1_skl(C,B),C)
| ~ member(sK1_skl(C,B),B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f35]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| ~ member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
? [B,C] : difference(B,difference(B,C)) != intersection(B,C),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
difference(sK2_skl,difference(sK2_skl,sK3_skl)) != intersection(sK2_skl,sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f41]) ).
fof(f43,plain,
difference(sK2_skl,difference(sK2_skl,sK3_skl)) != intersection(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f57,definition,
( sQ1_spl
<=> subset(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ1_spl
| ~ subset(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ~ member(X3,X2)
| ~ member(X3,X0)
| ~ subset(X0,difference(X1,X2)) ),
inference(resolution,[status(thm)],[f30,f18]) ).
fof(f66,plain,
( ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),intersection(sK2_skl,sK3_skl))
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(resolution,[status(thm)],[f39,f43]) ).
fof(f67,plain,
( ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl)))
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f39,f43]) ).
fof(f68,definition,
( sQ2_spl
<=> member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( ~ sQ2_spl
| member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f70,plain,
( sQ2_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,definition,
( sQ3_spl
<=> member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),intersection(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),intersection(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f73,plain,
( sQ3_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),intersection(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f66,f68,f71]) ).
fof(f75,definition,
( sQ4_spl
<=> member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f77,plain,
( sQ4_spl
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ5_spl
<=> member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ5_spl
| member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f80,plain,
( sQ5_spl
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f67,f75,f78]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ member(sK1_skl(X2,difference(X0,X1)),X1)
| member(sK1_skl(X2,difference(X0,X1)),X2)
| difference(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f40,f18]) ).
fof(f87,plain,
( sQ4_spl
| member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl)))
| intersection(sK2_skl,sK3_skl) = difference(sK2_skl,difference(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f77,f40]) ).
fof(f88,plain,
( sQ4_spl
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK3_skl)
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f77,f14]) ).
fof(f93,definition,
( sQ6_spl
<=> intersection(sK2_skl,sK3_skl) = difference(sK2_skl,difference(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| intersection(sK2_skl,sK3_skl) = difference(sK2_skl,difference(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ4_spl
| sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f87,f93,f78,f75]) ).
fof(f97,definition,
( sQ7_spl
<=> member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( sQ7_spl
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK2_skl) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ8_spl
<=> member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f88,f97,f100,f75]) ).
fof(f104,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f43]) ).
fof(f105,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( sQ2_spl
| member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),intersection(sK2_skl,sK3_skl))
| difference(sK2_skl,difference(sK2_skl,sK3_skl)) = intersection(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f70,f40]) ).
fof(f107,plain,
( sQ2_spl
| member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,sK3_skl))
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK2_skl) ),
inference(resolution,[status(thm)],[f70,f19]) ).
fof(f112,plain,
( sQ2_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f106,f93,f71,f68]) ).
fof(f113,definition,
( sQ9_spl
<=> member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( sQ9_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK2_skl) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,definition,
( sQ10_spl
<=> member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( ~ sQ10_spl
| member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f118,plain,
( sQ10_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( sQ2_spl
| sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f107,f113,f116,f68]) ).
fof(f132,plain,
( sQ1_spl
| ~ member(sK0_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(resolution,[status(thm)],[f59,f32]) ).
fof(f165,plain,
( sQ3_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,sK3_skl))
| difference(sK2_skl,difference(sK2_skl,sK3_skl)) = intersection(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f73,f84]) ).
fof(f166,plain,
( sQ3_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK3_skl)
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK2_skl) ),
inference(resolution,[status(thm)],[f73,f14]) ).
fof(f171,plain,
( sQ3_spl
| ~ sQ10_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f165,f93,f116,f71]) ).
fof(f172,definition,
( sQ15_spl
<=> member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ3_spl
| ~ sQ15_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f166,f113,f172,f71]) ).
fof(f177,plain,
! [X0] :
( sQ9_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),difference(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f115,f17]) ).
fof(f179,plain,
! [X0] :
( sQ9_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),intersection(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f115,f12]) ).
fof(f180,plain,
( ~ sQ3_spl
| sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f72,f179]) ).
fof(f181,plain,
( ~ sQ3_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f180]) ).
fof(f182,plain,
( sQ5_spl
| member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,sK3_skl))
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f80,f19]) ).
fof(f183,plain,
! [X0] :
( sQ5_spl
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),X0)
| ~ subset(X0,difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(resolution,[status(thm)],[f80,f30]) ).
fof(f187,definition,
( sQ16_spl
<=> member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( sQ5_spl
| sQ16_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f182,f97,f187,f78]) ).
fof(f199,plain,
( ~ sQ5_spl
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f79,f18]) ).
fof(f208,plain,
( sQ1_spl
| member(sK0_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,sK3_skl))
| ~ member(sK0_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f132,f19]) ).
fof(f213,definition,
( sQ17_spl
<=> member(sK0_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f216,definition,
( sQ18_spl
<=> member(sK0_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( sQ1_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f208,f213,f216,f57]) ).
fof(f222,plain,
! [X0] :
( sQ7_spl
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f99,f17]) ).
fof(f224,plain,
! [X0] :
( sQ7_spl
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f99,f12]) ).
fof(f225,plain,
( ~ sQ4_spl
| sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f76,f224]) ).
fof(f226,plain,
( ~ sQ4_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f227,plain,
( ~ sQ5_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f222]) ).
fof(f228,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f276,definition,
( sQ20_spl
<=> subset(difference(sK2_skl,difference(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ20_spl
| ~ subset(difference(sK2_skl,difference(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f280,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f44]) ).
fof(f281,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f282,plain,
( ~ sQ2_spl
| sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f69,f177]) ).
fof(f283,plain,
( ~ sQ2_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f282]) ).
fof(f292,plain,
( ~ sQ5_spl
| member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK3_skl)
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f199,f19]) ).
fof(f297,plain,
( ~ sQ5_spl
| sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f292,f97,f100,f78]) ).
fof(f345,plain,
( ~ sQ10_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f117,f18]) ).
fof(f386,plain,
! [X0,X1,X2] :
( member(sK1_skl(X2,X0),X2)
| X0 = X2
| ~ subset(X0,difference(X1,X0)) ),
inference(resolution,[status(thm)],[f65,f40]) ).
fof(f387,plain,
! [X0,X1,X2,X3] :
( member(sK1_skl(X3,X0),X3)
| X0 = X3
| ~ member(sK1_skl(X3,X0),X2)
| ~ subset(X0,difference(X1,X2)) ),
inference(resolution,[status(thm)],[f65,f40]) ).
fof(f407,plain,
! [X0,X1,X2,X3] :
( member(sK1_skl(X3,X2),X3)
| X2 = X3
| ~ member(sK1_skl(X3,X2),X0)
| ~ subset(X0,difference(X1,X2)) ),
inference(resolution,[status(thm)],[f65,f40]) ).
fof(f437,plain,
! [X0] :
( sQ5_spl
| intersection(sK2_skl,sK3_skl) = difference(sK2_skl,difference(sK2_skl,sK3_skl))
| ~ subset(intersection(sK2_skl,sK3_skl),difference(X0,intersection(sK2_skl,sK3_skl))) ),
inference(resolution,[status(thm)],[f386,f80]) ).
fof(f447,definition,
! [X0] :
( sQ23_spl
<=> ~ subset(intersection(sK2_skl,sK3_skl),difference(X0,intersection(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( sQ5_spl
| sQ6_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f437,f447,f93,f78]) ).
fof(f460,plain,
! [X0,X1] :
( sQ5_spl
| intersection(sK2_skl,sK3_skl) = difference(sK2_skl,difference(sK2_skl,sK3_skl))
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),X1)
| ~ subset(intersection(sK2_skl,sK3_skl),difference(X0,X1)) ),
inference(resolution,[status(thm)],[f387,f80]) ).
fof(f470,definition,
! [X0,X1] :
( sQ24_spl
<=> ( ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),X1)
| ~ subset(intersection(sK2_skl,sK3_skl),difference(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( sQ5_spl
| sQ6_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f460,f470,f93,f78]) ).
fof(f474,plain,
! [X0,X1] :
( sQ5_spl
| intersection(sK2_skl,sK3_skl) = difference(sK2_skl,difference(sK2_skl,sK3_skl))
| ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),X0)
| ~ subset(X0,difference(X1,intersection(sK2_skl,sK3_skl))) ),
inference(resolution,[status(thm)],[f407,f80]) ).
fof(f484,definition,
! [X0,X1] :
( sQ25_spl
<=> ( ~ member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),X0)
| ~ subset(X0,difference(X1,intersection(sK2_skl,sK3_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( sQ5_spl
| sQ6_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f474,f484,f93,f78]) ).
fof(f577,plain,
( sQ5_spl
| member(sK1_skl(difference(sK2_skl,difference(sK2_skl,sK3_skl)),intersection(sK2_skl,sK3_skl)),difference(sK2_skl,difference(sK2_skl,sK3_skl)))
| intersection(sK2_skl,sK3_skl) = difference(sK2_skl,difference(sK2_skl,sK3_skl))
| ~ subset(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))) ),
inference(resolution,[status(thm)],[f183,f40]) ).
fof(f587,plain,
( sQ5_spl
| sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f577,f57,f93,f78]) ).
fof(f738,plain,
! [X0] :
( ~ sQ10_spl
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),intersection(X0,sK3_skl)) ),
inference(resolution,[status(thm)],[f345,f13]) ).
fof(f740,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f72,f738]) ).
fof(f741,plain,
( ~ sQ3_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f844,plain,
( sQ10_spl
| member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK3_skl)
| ~ member(sK1_skl(intersection(sK2_skl,sK3_skl),difference(sK2_skl,difference(sK2_skl,sK3_skl))),sK2_skl) ),
inference(resolution,[status(thm)],[f118,f19]) ).
fof(f849,plain,
( sQ10_spl
| sQ15_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f844,f113,f172,f116]) ).
fof(f850,plain,
$false,
inference(sat_refutation,[status(thm)],[f74,f81,f96,f103,f105,f112,f119,f171,f175,f181,f190,f219,f226,f228,f281,f283,f297,f450,f473,f487,f587,f741,f849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET011+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 04:42:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.54 % Refutation found
% 0.13/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.52/0.55 % Elapsed time: 0.177941 seconds
% 0.52/0.55 % CPU time: 1.078647 seconds
% 0.52/0.55 % Total memory used: 116.825 MB
% 0.52/0.55 % Net memory used: 114.618 MB
%------------------------------------------------------------------------------