%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET143+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 : n014.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 02:09:28 PM UTC 2026
% Result : Theorem 19.21s 2.93s
% Output : CNFRefutation 19.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 108 ( 16 unt; 14 def)
% Number of atoms : 267 ( 30 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 268 ( 109 ~; 122 |; 19 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 78 !; 5 ?)
% 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] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,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(f10,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)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,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)],[f6]) ).
fof(f29,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)],[f28]) ).
fof(f30,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))],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| ~ member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f35,plain,
? [B,C,D] : intersection(intersection(B,C),D) != intersection(B,intersection(C,D)),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
intersection(intersection(sK2_skl,sK3_skl),sK4_skl) != intersection(sK2_skl,intersection(sK3_skl,sK4_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f35]) ).
fof(f37,plain,
intersection(intersection(sK2_skl,sK3_skl),sK4_skl) != intersection(sK2_skl,intersection(sK3_skl,sK4_skl)),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f16]) ).
fof(f44,plain,
intersection(sK4_skl,intersection(sK2_skl,sK3_skl)) != intersection(sK2_skl,intersection(sK3_skl,sK4_skl)),
inference(paramodulation,[status(thm)],[f19,f37]) ).
fof(f71,plain,
( ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,sK3_skl),sK4_skl))
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f33,f37]) ).
fof(f93,definition,
( sQ10_spl
<=> member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ10_spl
| member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f95,plain,
( sQ10_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
( sQ11_spl
<=> member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,sK3_skl),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ11_spl
| member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,sK3_skl),sK4_skl)) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f98,plain,
( sQ11_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,sK3_skl),sK4_skl)) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f93,f96]) ).
fof(f104,plain,
( sQ10_spl
| member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,sK3_skl),sK4_skl))
| intersection(sK2_skl,intersection(sK3_skl,sK4_skl)) = intersection(intersection(sK2_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f95,f34]) ).
fof(f105,plain,
( sQ10_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK3_skl,sK4_skl))
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK2_skl) ),
inference(resolution,[status(thm)],[f95,f13]) ).
fof(f111,definition,
( sQ12_spl
<=> intersection(sK2_skl,intersection(sK3_skl,sK4_skl)) = intersection(intersection(sK2_skl,sK3_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ12_spl
| intersection(sK2_skl,intersection(sK3_skl,sK4_skl)) = intersection(intersection(sK2_skl,sK3_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ10_spl
| sQ11_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f104,f111,f96,f93]) ).
fof(f115,definition,
( sQ13_spl
<=> member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( sQ13_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK2_skl) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
( sQ14_spl
<=> member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ14_spl
| member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f120,plain,
( sQ14_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ10_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f105,f115,f118,f93]) ).
fof(f122,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f37]) ).
fof(f123,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f122]) ).
fof(f164,plain,
! [X0] :
( sQ13_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f117,f11]) ).
fof(f182,plain,
( sQ13_spl
| member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,sK3_skl),sK4_skl))
| intersection(sK2_skl,intersection(sK3_skl,sK4_skl)) = intersection(intersection(sK2_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f164,f34]) ).
fof(f186,plain,
! [X0,X1] :
( sQ13_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,X0),X1)) ),
inference(resolution,[status(thm)],[f164,f11]) ).
fof(f191,plain,
( sQ13_spl
| sQ11_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f182,f111,f96,f115]) ).
fof(f193,plain,
( ~ sQ11_spl
| sQ13_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f97,f186]) ).
fof(f194,plain,
( ~ sQ11_spl
| sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f214,plain,
( ~ sQ11_spl
| member(sK1_skl(intersection(sK4_skl,intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,sK3_skl),sK4_skl)) ),
inference(paramodulation,[status(thm)],[f19,f97]) ).
fof(f216,plain,
( ~ sQ11_spl
| member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK4_skl,intersection(sK2_skl,sK3_skl))) ),
inference(paramodulation,[status(thm)],[f19,f97]) ).
fof(f236,definition,
( sQ21_spl
<=> intersection(sK4_skl,intersection(sK2_skl,sK3_skl)) = intersection(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( ~ sQ21_spl
| intersection(sK4_skl,intersection(sK2_skl,sK3_skl)) = intersection(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f247,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f44]) ).
fof(f248,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f269,definition,
( sQ26_spl
<=> member(sK1_skl(intersection(sK4_skl,intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ26_spl
| ~ member(sK1_skl(intersection(sK4_skl,intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f276,plain,
( sQ14_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl)
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f120,f13]) ).
fof(f278,plain,
! [X0] :
( sQ14_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(X0,intersection(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f120,f12]) ).
fof(f282,definition,
( sQ28_spl
<=> member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ28_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,definition,
( sQ29_spl
<=> member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ29_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( sQ14_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f276,f282,f285,f118]) ).
fof(f294,plain,
! [X0] :
( sQ26_spl
| ~ member(sK1_skl(intersection(sK4_skl,intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(X0,sK4_skl)) ),
inference(resolution,[status(thm)],[f271,f12]) ).
fof(f296,plain,
( ~ sQ11_spl
| sQ26_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f214,f294]) ).
fof(f297,plain,
( ~ sQ11_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f299,plain,
! [X0] :
( sQ28_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(X0,sK3_skl)) ),
inference(resolution,[status(thm)],[f284,f12]) ).
fof(f300,plain,
! [X0] :
( sQ28_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK3_skl,X0)) ),
inference(resolution,[status(thm)],[f284,f11]) ).
fof(f304,plain,
! [X0] :
( sQ29_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(X0,sK4_skl)) ),
inference(resolution,[status(thm)],[f287,f12]) ).
fof(f306,plain,
( sQ29_spl
| ~ member(sK1_skl(intersection(sK4_skl,intersection(sK2_skl,sK3_skl)),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl) ),
inference(paramodulation,[status(thm)],[f19,f287]) ).
fof(f310,plain,
( sQ29_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f306,f269,f285]) ).
fof(f370,definition,
( sQ31_spl
<=> subset(intersection(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( sQ31_spl
| ~ subset(intersection(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f374,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f38]) ).
fof(f375,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f411,plain,
( sQ11_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl)
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f98,f13]) ).
fof(f419,definition,
( sQ34_spl
<=> member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( sQ34_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( sQ11_spl
| ~ sQ29_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f411,f419,f285,f96]) ).
fof(f449,definition,
( sQ37_spl
<=> subset(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(intersection(sK2_skl,sK3_skl),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( sQ37_spl
| ~ subset(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(intersection(sK2_skl,sK3_skl),sK4_skl)) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f453,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f38]) ).
fof(f454,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f453]) ).
fof(f636,definition,
( sQ43_spl
<=> subset(intersection(sK4_skl,intersection(sK2_skl,sK3_skl)),intersection(sK4_skl,intersection(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( sQ43_spl
| ~ subset(intersection(sK4_skl,intersection(sK2_skl,sK3_skl)),intersection(sK4_skl,intersection(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f640,plain,
( sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f638,f38]) ).
fof(f641,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f640]) ).
fof(f1180,definition,
! [X0] :
( sQ59_spl
<=> ( ~ subset(intersection(sK2_skl,intersection(sK3_skl,sK4_skl)),X0)
| ~ subset(X0,intersection(sK2_skl,intersection(sK3_skl,sK4_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1181,plain,
! [X0] :
( ~ sQ59_spl
| ~ subset(intersection(sK2_skl,intersection(sK3_skl,sK4_skl)),X0)
| ~ subset(X0,intersection(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f1180]) ).
fof(f3883,plain,
( sQ14_spl
| member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(intersection(sK2_skl,sK3_skl),sK4_skl))
| intersection(sK2_skl,intersection(sK3_skl,sK4_skl)) = intersection(intersection(sK2_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f278,f34]) ).
fof(f3892,plain,
( sQ14_spl
| sQ11_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f3883,f111,f96,f118]) ).
fof(f5029,plain,
( ~ sQ59_spl
| $false ),
inference(resolution,[status(thm)],[f1181,f38]) ).
fof(f5033,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f5029]) ).
fof(f5063,plain,
! [X0,X1] :
( sQ28_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(X0,intersection(sK3_skl,X1))) ),
inference(resolution,[status(thm)],[f300,f12]) ).
fof(f5072,plain,
! [X0,X1] :
( sQ28_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(X0,intersection(X1,sK3_skl))) ),
inference(resolution,[status(thm)],[f299,f12]) ).
fof(f5079,plain,
( ~ sQ11_spl
| sQ28_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f216,f5072]) ).
fof(f5081,plain,
( ~ sQ11_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f5079]) ).
fof(f5082,plain,
( ~ sQ10_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f5063]) ).
fof(f5083,plain,
( ~ sQ10_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f5082]) ).
fof(f5084,plain,
( ~ sQ14_spl
| sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f119,f304]) ).
fof(f5085,plain,
( ~ sQ14_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f5084]) ).
fof(f5173,plain,
( sQ34_spl
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl)
| ~ member(sK1_skl(intersection(intersection(sK2_skl,sK3_skl),sK4_skl),intersection(sK2_skl,intersection(sK3_skl,sK4_skl))),sK2_skl) ),
inference(resolution,[status(thm)],[f421,f13]) ).
fof(f5179,plain,
( sQ34_spl
| ~ sQ28_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f5173,f115,f282,f419]) ).
fof(f5180,plain,
$false,
inference(sat_refutation,[status(thm)],[f99,f114,f121,f123,f191,f194,f248,f288,f297,f310,f375,f422,f454,f641,f3892,f5033,f5081,f5083,f5085,f5179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET143+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:55:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 19.21/2.93 % Refutation found
% 19.21/2.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.21/2.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.25/2.98 % Elapsed time: 2.602080 seconds
% 15.25/2.98 % CPU time: 20.231571 seconds
% 15.25/2.98 % Total memory used: 192.821 MB
% 15.25/2.98 % Net memory used: 181.788 MB
%------------------------------------------------------------------------------