%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET010+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:08:48 PM UTC 2026
% Result : Theorem 270.73s 34.60s
% Output : CNFRefutation 237.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of formulae : 117 ( 17 unt; 14 def)
% Number of atoms : 317 ( 26 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 333 ( 133 ~; 140 |; 35 &)
% ( 22 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 162 ( 155 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C,D] :
( ( subset(D,C)
& subset(B,C) )
=> subset(union(B,D),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [B,C,D] : difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
( ! [B,C,D] :
( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ! [B,C,D] :
( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,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)],[f2]) ).
fof(f21,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)],[f20]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,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)],[f3]) ).
fof(f26,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)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,plain,
! [B,C,D] :
( subset(union(B,D),C)
| ~ subset(D,C)
| ~ subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [B,C,D] :
( subset(difference(D,C),difference(D,B))
| ~ subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f34,plain,
! [B,C] :
( ! [D] : subset(difference(D,C),difference(D,B))
| ~ subset(B,C) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( subset(difference(X2,X1),difference(X2,X0))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f37,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)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f42,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f44,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)],[f43]) ).
fof(f45,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)],[f44]) ).
fof(f46,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))],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,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)],[f12]) ).
fof(f52,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)],[f51]) ).
fof(f53,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))],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| ~ member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f58,plain,
? [B,C,D] : difference(B,intersection(C,D)) != union(difference(B,C),difference(B,D)),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f59,plain,
difference(sK2_skl,intersection(sK3_skl,sK4_skl)) != union(difference(sK2_skl,sK3_skl),difference(sK2_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)],[f58]) ).
fof(f60,plain,
difference(sK2_skl,intersection(sK3_skl,sK4_skl)) != union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f38]) ).
fof(f75,plain,
! [X0,X1] : subset(intersection(X0,X1),X1),
inference(paramodulation,[status(thm)],[f42,f32]) ).
fof(f82,plain,
! [X0,X1,X2] :
( subset(difference(X1,X2),X0)
| ~ member(sK0_skl(X0,difference(X1,X2)),X2) ),
inference(resolution,[status(thm)],[f28,f48]) ).
fof(f661,plain,
( ~ subset(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl)))
| ~ subset(difference(sK2_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f40,f60]) ).
fof(f663,definition,
( sQ0_spl
<=> subset(difference(sK2_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( sQ0_spl
| ~ subset(difference(sK2_skl,intersection(sK3_skl,sK4_skl)),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f663]) ).
fof(f666,definition,
( sQ1_spl
<=> subset(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f668,plain,
( sQ1_spl
| ~ subset(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f669,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f661,f663,f666]) ).
fof(f686,plain,
( ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)))
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f56,f60]) ).
fof(f688,definition,
( sQ2_spl
<=> member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( ~ sQ2_spl
| member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f688]) ).
fof(f690,plain,
( sQ2_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f688]) ).
fof(f691,definition,
( sQ3_spl
<=> member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f692,plain,
( ~ sQ3_spl
| member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f691]) ).
fof(f693,plain,
( sQ3_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f691]) ).
fof(f694,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f686,f688,f691]) ).
fof(f702,plain,
( sQ0_spl
| ~ member(sK0_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f665,f82]) ).
fof(f1301,definition,
( sQ6_spl
<=> union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)) = difference(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1302,plain,
( ~ sQ6_spl
| union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)) = difference(sK2_skl,intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f1301]) ).
fof(f1305,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1302,f60]) ).
fof(f1306,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f1305]) ).
fof(f1307,plain,
( sQ2_spl
| member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)))
| difference(sK2_skl,intersection(sK3_skl,sK4_skl)) = union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f690,f57]) ).
fof(f1309,plain,
! [X0] :
( sQ2_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),X0)
| ~ subset(X0,difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f690,f47]) ).
fof(f1318,plain,
( sQ2_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1307,f1301,f691,f688]) ).
fof(f1319,definition,
( sQ7_spl
<=> member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1321,plain,
( sQ7_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK2_skl) ),
inference(component_clause,[status(thm)],[f1319]) ).
fof(f1472,plain,
( ~ sQ2_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f689,f28]) ).
fof(f1481,plain,
( sQ3_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),difference(sK2_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f693,f19]) ).
fof(f1482,plain,
( sQ3_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),difference(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f693,f18]) ).
fof(f1522,plain,
( sQ0_spl
| ~ member(sK0_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl)
| ~ member(sK0_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f702,f24]) ).
fof(f1532,definition,
( sQ21_spl
<=> member(sK0_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1535,definition,
( sQ22_spl
<=> member(sK0_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1538,plain,
( sQ0_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1522,f1532,f1535,f663]) ).
fof(f1539,plain,
( sQ1_spl
| ~ subset(difference(sK2_skl,sK4_skl),difference(sK2_skl,intersection(sK3_skl,sK4_skl)))
| ~ subset(difference(sK2_skl,sK3_skl),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f668,f31]) ).
fof(f1541,definition,
( sQ23_spl
<=> subset(difference(sK2_skl,sK3_skl),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1543,plain,
( sQ23_spl
| ~ subset(difference(sK2_skl,sK3_skl),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f1541]) ).
fof(f1544,definition,
( sQ24_spl
<=> subset(difference(sK2_skl,sK4_skl),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1546,plain,
( sQ24_spl
| ~ subset(difference(sK2_skl,sK4_skl),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f1544]) ).
fof(f1547,plain,
( sQ1_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1539,f1541,f1544,f666]) ).
fof(f1611,definition,
( sQ31_spl
<=> subset(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1613,plain,
( sQ31_spl
| ~ subset(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f1611]) ).
fof(f1615,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1613,f61]) ).
fof(f1616,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1615]) ).
fof(f1649,plain,
! [X0] :
( sQ7_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),difference(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f1321,f27]) ).
fof(f1834,definition,
( sQ33_spl
<=> member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1837,definition,
( sQ34_spl
<=> member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f3418,plain,
( ~ sQ3_spl
| sQ2_spl
| ~ subset(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f1309,f692]) ).
fof(f3491,definition,
( sQ57_spl
<=> subset(difference(sK2_skl,intersection(sK3_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f3493,plain,
( sQ57_spl
| ~ subset(difference(sK2_skl,intersection(sK3_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f3491]) ).
fof(f3495,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3493,f61]) ).
fof(f3496,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f3495]) ).
fof(f3497,plain,
( ~ sQ2_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f1649]) ).
fof(f3498,plain,
( ~ sQ2_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f3497]) ).
fof(f3553,plain,
( sQ24_spl
| ~ subset(intersection(sK3_skl,sK4_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f1546,f35]) ).
fof(f3557,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3553,f75]) ).
fof(f3558,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f3557]) ).
fof(f3883,plain,
( ~ sQ2_spl
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl)
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl) ),
inference(resolution,[status(thm)],[f1472,f24]) ).
fof(f3893,plain,
( ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f3883,f1834,f1837,f688]) ).
fof(f3926,plain,
( sQ23_spl
| ~ subset(intersection(sK3_skl,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f1543,f35]) ).
fof(f3930,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3926,f32]) ).
fof(f3931,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f3930]) ).
fof(f9180,plain,
( sQ3_spl
| member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK3_skl)
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK2_skl) ),
inference(resolution,[status(thm)],[f1482,f29]) ).
fof(f9192,plain,
( sQ3_spl
| sQ33_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f9180,f1319,f1834,f691]) ).
fof(f9194,plain,
( sQ3_spl
| member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK4_skl)
| ~ member(sK1_skl(union(difference(sK2_skl,sK3_skl),difference(sK2_skl,sK4_skl)),difference(sK2_skl,intersection(sK3_skl,sK4_skl))),sK2_skl) ),
inference(resolution,[status(thm)],[f1481,f29]) ).
fof(f9206,plain,
( sQ3_spl
| sQ34_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f9194,f1319,f1837,f691]) ).
fof(f9207,plain,
( ~ sQ3_spl
| sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f3418,f666,f688,f691]) ).
fof(f9210,plain,
$false,
inference(sat_refutation,[status(thm)],[f669,f694,f1306,f1318,f1538,f1547,f1616,f3496,f3498,f3558,f3893,f3931,f9192,f9206,f9207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:46:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 270.73/34.60 % Refutation found
% 270.73/34.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 270.73/34.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 34.28/34.74 % Elapsed time: 34.356024 seconds
% 34.28/34.74 % CPU time: 272.216861 seconds
% 34.28/34.74 % Total memory used: 975.740 MB
% 34.28/34.74 % Net memory used: 901.029 MB
%------------------------------------------------------------------------------