%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET594+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 : 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 02:10:10 PM UTC 2026
% Result : Theorem 1.10s 0.60s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 12 unt; 6 def)
% Number of atoms : 175 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 178 ( 72 ~; 70 |; 22 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 113 ( 108 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f12,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)],[f11]) ).
fof(f13,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)],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,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)],[f2]) ).
fof(f19,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)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,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)],[f3]) ).
fof(f24,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)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f28,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f29,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)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f43,plain,
? [B,C,D] :
( ~ subset(B,union(C,D))
& union(intersection(B,C),intersection(B,D)) = B ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
( ~ subset(sK2_skl,union(sK3_skl,sK4_skl))
& union(intersection(sK2_skl,sK3_skl),intersection(sK2_skl,sK4_skl)) = 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)],[f43]) ).
fof(f45,plain,
union(intersection(sK2_skl,sK3_skl),intersection(sK2_skl,sK4_skl)) = sK2_skl,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
~ subset(sK2_skl,union(sK3_skl,sK4_skl)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( member(X0,union(X2,X3))
| ~ member(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[f26,f21]) ).
fof(f87,plain,
! [X0] :
( member(X0,intersection(sK2_skl,sK4_skl))
| member(X0,intersection(sK2_skl,sK3_skl))
| ~ member(X0,sK2_skl) ),
inference(paramodulation,[status(thm)],[f45,f20]) ).
fof(f94,plain,
member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK2_skl),
inference(resolution,[status(thm)],[f16,f46]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(X1,X0),intersection(X1,X2))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f17,f25]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(X1,X0),X2)
| ~ subset(X2,X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f17,f15]) ).
fof(f103,plain,
! [X0] : member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),union(X0,sK2_skl)),
inference(resolution,[status(thm)],[f94,f22]) ).
fof(f109,plain,
! [X0] : ~ member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),intersection(union(sK3_skl,sK4_skl),X0)),
inference(resolution,[status(thm)],[f98,f46]) ).
fof(f121,definition,
( sQ0_spl
<=> subset(sK2_skl,union(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ0_spl
| subset(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f202,plain,
! [X0] :
( member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK2_skl)
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),X0) ),
inference(resolution,[status(thm)],[f103,f20]) ).
fof(f214,definition,
! [X0] :
( sQ2_spl
<=> member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0] :
( ~ sQ2_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),X0) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
( sQ3_spl
<=> member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ3_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f202,f214,f217]) ).
fof(f221,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f109,f215]) ).
fof(f223,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f46]) ).
fof(f224,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f223]) ).
fof(f225,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f255,plain,
( ~ sQ3_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),intersection(sK2_skl,sK4_skl))
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),intersection(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f87,f218]) ).
fof(f260,definition,
( sQ4_spl
<=> member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),intersection(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( ~ sQ4_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),intersection(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,definition,
( sQ5_spl
<=> member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),intersection(sK2_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ5_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),intersection(sK2_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( ~ sQ3_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f255,f260,f263,f217]) ).
fof(f400,plain,
! [X0] :
( ~ sQ4_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),union(sK3_skl,X0)) ),
inference(resolution,[status(thm)],[f261,f63]) ).
fof(f420,plain,
! [X0] :
( ~ sQ5_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),union(sK4_skl,X0)) ),
inference(resolution,[status(thm)],[f264,f63]) ).
fof(f438,plain,
( ~ sQ4_spl
| subset(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f400,f17]) ).
fof(f452,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f438,f121,f260]) ).
fof(f457,plain,
! [X0] :
( ~ sQ5_spl
| ~ subset(union(sK4_skl,X0),union(sK3_skl,sK4_skl))
| subset(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f420,f99]) ).
fof(f467,definition,
! [X0] :
( sQ11_spl
<=> ~ subset(union(sK4_skl,X0),union(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f468,plain,
! [X0] :
( ~ sQ11_spl
| ~ subset(union(sK4_skl,X0),union(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( ~ sQ5_spl
| sQ11_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f457,f121,f467,f263]) ).
fof(f478,plain,
! [X0] :
( ~ sQ11_spl
| ~ subset(union(X0,sK4_skl),union(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f33,f468]) ).
fof(f483,plain,
( ~ sQ11_spl
| $false ),
inference(resolution,[status(thm)],[f478,f47]) ).
fof(f486,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f487,plain,
$false,
inference(sat_refutation,[status(thm)],[f220,f224,f225,f266,f452,f470,f486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:31:06 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 1.10/0.60 % Refutation found
% 1.10/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.10/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.10/0.63 % Elapsed time: 0.270627 seconds
% 1.10/0.63 % CPU time: 1.827979 seconds
% 1.10/0.63 % Total memory used: 126.743 MB
% 1.10/0.63 % Net memory used: 123.465 MB
%------------------------------------------------------------------------------