%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET578+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 : n015.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 02:10:07 PM UTC 2026
% Result : Theorem 0.16s 15.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 126 ( 6 unt; 18 def)
% Number of atoms : 353 ( 26 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 382 ( 155 ~; 159 |; 38 &)
% ( 27 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 19 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 126 ( 113 !; 13 ?)
% 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(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
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] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
& member(E,C) ) )
=> B = intersection(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
& member(E,C) ) )
=> 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(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f20,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f21,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)],[f20]) ).
fof(f22,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)],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
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] :
( B != intersection(C,D)
& ! [E] :
( member(E,B)
<=> ( member(E,D)
& member(E,C) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
? [B,C,D] :
( B != intersection(C,D)
& ! [E] :
( ( ~ member(E,D)
| ~ member(E,C)
| member(E,B) )
& ( ( member(E,D)
& member(E,C) )
| ~ member(E,B) ) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
? [B,C,D] :
( B != intersection(C,D)
& ! [E] :
( ~ member(E,D)
| ~ member(E,C)
| member(E,B) )
& ! [E] :
( ( member(E,D)
& member(E,C) )
| ~ member(E,B) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( sK2_skl != intersection(sK3_skl,sK4_skl)
& ! [E] :
( ~ member(E,sK4_skl)
| ~ member(E,sK3_skl)
| member(E,sK2_skl) )
& ! [E] :
( ( member(E,sK4_skl)
& member(E,sK3_skl) )
| ~ member(E,sK2_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)],[f37]) ).
fof(f39,plain,
! [X0] :
( member(X0,sK3_skl)
| ~ member(X0,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( member(X0,sK4_skl)
| ~ member(X0,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [X0] :
( ~ member(X0,sK4_skl)
| ~ member(X0,sK3_skl)
| member(X0,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
sK2_skl != intersection(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f16]) ).
fof(f49,plain,
( ~ subset(intersection(sK3_skl,sK4_skl),sK2_skl)
| ~ subset(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f18,f42]) ).
fof(f51,definition,
( sQ0_spl
<=> subset(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ0_spl
| ~ subset(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ1_spl
<=> subset(intersection(sK3_skl,sK4_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ1_spl
| ~ subset(intersection(sK3_skl,sK4_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f51,f54]) ).
fof(f61,plain,
( sQ0_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f26,f53]) ).
fof(f62,plain,
( sQ0_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK4_skl)
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f61,f13]) ).
fof(f66,definition,
( sQ2_spl
<=> member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ2_spl
| member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f68,plain,
( sQ2_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,definition,
( sQ3_spl
<=> member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( sQ3_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f62,f66,f69,f51]) ).
fof(f73,plain,
( sQ1_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f56,f26]) ).
fof(f74,plain,
( sQ1_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK4_skl)
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f73,f41]) ).
fof(f76,plain,
! [X0] :
( sQ1_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(X0,sK2_skl)) ),
inference(resolution,[status(thm)],[f73,f12]) ).
fof(f78,definition,
( sQ4_spl
<=> member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f81,definition,
( sQ5_spl
<=> member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f74,f78,f81,f54]) ).
fof(f92,plain,
! [X0] :
( sQ2_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),X0)
| ~ subset(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f68,f24]) ).
fof(f122,plain,
( sQ3_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f71,f40]) ).
fof(f139,definition,
( sQ7_spl
<=> member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( sQ7_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f153,definition,
! [X0] :
( sQ9_spl
<=> ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f154,plain,
! [X0] :
( ~ sQ9_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),X0) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f160,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f67,f154]) ).
fof(f161,plain,
( ~ sQ2_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f184,definition,
( sQ13_spl
<=> member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ7_spl
| subset(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f141,f25]) ).
fof(f194,plain,
( sQ7_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK4_skl)
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f141,f41]) ).
fof(f198,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f193,f51,f139]) ).
fof(f199,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f194,f66,f69,f139]) ).
fof(f206,plain,
( sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f122,f139,f69]) ).
fof(f240,plain,
! [X0] :
( sQ1_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl)
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),X0) ),
inference(resolution,[status(thm)],[f76,f13]) ).
fof(f243,plain,
! [X0,X1] :
( sQ1_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(intersection(X0,sK2_skl),X1)) ),
inference(resolution,[status(thm)],[f76,f11]) ).
fof(f246,definition,
! [X0] :
( sQ19_spl
<=> ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),X0) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f247,plain,
! [X0] :
( ~ sQ19_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),X0) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( sQ1_spl
| ~ sQ13_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f240,f246,f184,f54]) ).
fof(f258,plain,
( sQ2_spl
| ~ member(sK0_skl(intersection(sK3_skl,sK4_skl),sK2_skl),sK2_skl)
| ~ subset(sK3_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f92,f39]) ).
fof(f262,definition,
( sQ20_spl
<=> subset(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ20_spl
| ~ subset(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f271,definition,
( sQ22_spl
<=> subset(sK3_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ22_spl
| ~ subset(sK3_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f258,f271,f139,f66]) ).
fof(f275,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f273,f43]) ).
fof(f276,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f275]) ).
fof(f297,plain,
( ~ sQ19_spl
| subset(intersection(sK3_skl,sK4_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f247,f25]) ).
fof(f305,plain,
( ~ sQ19_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f297,f56]) ).
fof(f306,plain,
( ~ sQ19_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f305]) ).
fof(f342,plain,
( sQ20_spl
| ~ member(sK0_skl(sK3_skl,sK2_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f264,f26]) ).
fof(f353,plain,
! [X0,X1] :
( sQ1_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),X1)
| ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(X0,sK2_skl)) ),
inference(resolution,[status(thm)],[f243,f13]) ).
fof(f361,definition,
! [X0] :
( sQ23_spl
<=> ~ member(sK0_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(X0,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ1_spl
| sQ19_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f353,f361,f246,f54]) ).
fof(f375,plain,
( ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl)
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f383,definition,
( sQ26_spl
<=> member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( ~ sQ26_spl
| member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f385,plain,
( sQ26_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,definition,
( sQ27_spl
<=> member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( sQ27_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl) ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f389,plain,
( ~ sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f375,f383,f386]) ).
fof(f390,plain,
( sQ26_spl
| member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl)
| intersection(sK3_skl,sK4_skl) = sK2_skl ),
inference(resolution,[status(thm)],[f385,f34]) ).
fof(f391,plain,
( sQ26_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK4_skl)
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f385,f13]) ).
fof(f395,definition,
( sQ28_spl
<=> intersection(sK3_skl,sK4_skl) = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ28_spl
| intersection(sK3_skl,sK4_skl) = sK2_skl ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( sQ26_spl
| sQ27_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f390,f395,f386,f383]) ).
fof(f399,definition,
( sQ29_spl
<=> member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ29_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK3_skl) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,definition,
( sQ30_spl
<=> member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( sQ30_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( sQ26_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f391,f399,f402,f383]) ).
fof(f406,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f42]) ).
fof(f407,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f425,plain,
( sQ20_spl
| ~ member(sK0_skl(sK3_skl,sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f342,f39]) ).
fof(f450,plain,
( sQ27_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK4_skl)
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f388,f41]) ).
fof(f454,plain,
( sQ27_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f450,f399,f402,f386]) ).
fof(f455,plain,
( sQ20_spl
| subset(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f425,f25]) ).
fof(f460,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f264]) ).
fof(f461,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f460]) ).
fof(f507,plain,
( sQ29_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f401,f39]) ).
fof(f510,plain,
! [X0] :
( sQ29_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(sK3_skl,X0)) ),
inference(resolution,[status(thm)],[f401,f11]) ).
fof(f511,plain,
( sQ29_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f507,f386,f399]) ).
fof(f517,plain,
( sQ30_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f404,f40]) ).
fof(f519,plain,
! [X0] :
( sQ30_spl
| ~ member(sK1_skl(sK2_skl,intersection(sK3_skl,sK4_skl)),intersection(X0,sK4_skl)) ),
inference(resolution,[status(thm)],[f404,f12]) ).
fof(f521,plain,
( ~ sQ26_spl
| sQ30_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f384,f519]) ).
fof(f522,plain,
( ~ sQ26_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( sQ30_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f517,f386,f402]) ).
fof(f524,plain,
( ~ sQ26_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f384,f510]) ).
fof(f525,plain,
( ~ sQ26_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f526,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f72,f84,f161,f198,f199,f206,f249,f274,f276,f306,f364,f389,f398,f405,f407,f454,f461,f511,f522,f523,f525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.39 % Computer : n015.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Mon Sep 21 05:30:22 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.16/15.40 % Drodi V4.1.1
% 0.16/15.45 % Refutation found
% 0.16/15.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/15.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/15.49 % Elapsed time: 0.079022 seconds
% 0.16/15.49 % CPU time: 0.289446 seconds
% 0.16/15.49 % Total memory used: 104.939 MB
% 0.16/15.49 % Net memory used: 104.218 MB
%------------------------------------------------------------------------------