%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET014+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:08:51 PM UTC 2026
% Result : Theorem 0.13s 0.50s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 2 unt; 6 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 180 ( 67 ~; 83 |; 17 &)
% ( 11 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 70 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,X,Y] :
( ( subset(Y,A)
& subset(X,A) )
<=> subset(union(X,Y),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,X,Y] :
( ( subset(Y,A)
& subset(X,A) )
<=> subset(union(X,Y),A) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ! [X,A,B] :
( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f68,plain,
? [A,X,Y] :
( ( subset(Y,A)
& subset(X,A) )
<~> subset(union(X,Y),A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A,X,Y] :
( ( ~ subset(union(X,Y),A)
| ~ subset(Y,A)
| ~ subset(X,A) )
& ( subset(union(X,Y),A)
| ( subset(Y,A)
& subset(X,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ( ~ subset(union(sK4_skl,sK5_skl),sK3_skl)
| ~ subset(sK5_skl,sK3_skl)
| ~ subset(sK4_skl,sK3_skl) )
& ( subset(union(sK4_skl,sK5_skl),sK3_skl)
| ( subset(sK5_skl,sK3_skl)
& subset(sK4_skl,sK3_skl) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f69]) ).
fof(f71,plain,
( subset(union(sK4_skl,sK5_skl),sK3_skl)
| subset(sK4_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
( subset(union(sK4_skl,sK5_skl),sK3_skl)
| subset(sK5_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
( ~ subset(union(sK4_skl,sK5_skl),sK3_skl)
| ~ subset(sK5_skl,sK3_skl)
| ~ subset(sK4_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f74,definition,
( sQ0_spl
<=> subset(sK4_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ0_spl
| subset(sK4_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ1_spl
<=> subset(union(sK4_skl,sK5_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ1_spl
| subset(union(sK4_skl,sK5_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f74,f77]) ).
fof(f81,definition,
( sQ2_spl
<=> subset(sK5_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ2_spl
| subset(sK5_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f72,f81,f77]) ).
fof(f85,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f74,f81,f77]) ).
fof(f94,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,union(X0,X1)),X1)
| member(sK0_skl(X2,union(X0,X1)),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f37]) ).
fof(f127,plain,
! [X0] :
( subset(union(X0,X0),X0)
| subset(union(X0,X0),X0) ),
inference(resolution,[status(thm)],[f20,f94]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(X1,X0),X2)
| ~ subset(X2,X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f135,plain,
! [X0] : subset(union(X0,X0),X0),
inference(duplicate_literals_removal,[status(thm)],[f127]) ).
fof(f165,plain,
! [X0] :
( ~ sQ1_spl
| ~ member(sK0_skl(sK3_skl,X0),union(sK4_skl,sK5_skl))
| subset(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f134,f78]) ).
fof(f166,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),union(X1,X1))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f134,f135]) ).
fof(f266,plain,
! [X0] :
( ~ sQ1_spl
| ~ member(sK0_skl(sK3_skl,X0),sK5_skl)
| subset(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f165,f39]) ).
fof(f267,plain,
! [X0] :
( ~ sQ1_spl
| ~ member(sK0_skl(sK3_skl,X0),sK4_skl)
| subset(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f165,f38]) ).
fof(f277,plain,
! [X0] :
( ~ sQ0_spl
| ~ member(sK0_skl(sK3_skl,X0),sK4_skl)
| subset(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f75,f134]) ).
fof(f297,plain,
( ~ sQ1_spl
| subset(sK5_skl,sK3_skl)
| subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f266,f19]) ).
fof(f299,definition,
( sQ5_spl
<=> subset(union(sK5_skl,sK5_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f297,f81,f77]) ).
fof(f307,plain,
! [X0] :
( ~ sQ2_spl
| ~ member(sK0_skl(sK3_skl,X0),sK5_skl)
| subset(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f82,f134]) ).
fof(f308,plain,
( ~ sQ2_spl
| subset(union(sK5_skl,sK5_skl),sK3_skl)
| subset(union(sK5_skl,sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f307,f94]) ).
fof(f309,plain,
! [X0] :
( ~ sQ2_spl
| member(sK0_skl(sK3_skl,union(X0,sK5_skl)),X0)
| subset(union(X0,sK5_skl),sK3_skl)
| subset(union(X0,sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f307,f94]) ).
fof(f314,plain,
( ~ sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f308,f299,f81]) ).
fof(f315,plain,
! [X0] :
( ~ sQ2_spl
| member(sK0_skl(sK3_skl,union(X0,sK5_skl)),X0)
| subset(union(X0,sK5_skl),sK3_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f309]) ).
fof(f381,plain,
( ~ sQ1_spl
| subset(sK4_skl,sK3_skl)
| subset(sK4_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f267,f19]) ).
fof(f387,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f381,f74,f77]) ).
fof(f541,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| subset(union(sK4_skl,sK5_skl),sK3_skl)
| subset(union(sK4_skl,sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f315,f277]) ).
fof(f543,plain,
( ~ sQ2_spl
| subset(union(union(sK3_skl,sK3_skl),sK5_skl),sK3_skl)
| subset(union(union(sK3_skl,sK3_skl),sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f315,f166]) ).
fof(f544,plain,
( ~ sQ2_spl
| subset(union(sK3_skl,sK5_skl),sK3_skl)
| subset(union(sK3_skl,sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f315,f20]) ).
fof(f558,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f541,f77,f81,f74]) ).
fof(f560,definition,
( sQ6_spl
<=> subset(union(union(sK3_skl,sK3_skl),sK5_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( ~ sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f543,f560,f81]) ).
fof(f564,definition,
( sQ7_spl
<=> subset(union(sK3_skl,sK5_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f544,f564,f81]) ).
fof(f568,plain,
$false,
inference(sat_refutation,[status(thm)],[f80,f84,f85,f306,f314,f387,f558,f563,f567]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014+4 : 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 : n005.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 04:42:02 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.50 % Refutation found
% 0.13/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.86/0.53 % Elapsed time: 0.164846 seconds
% 0.86/0.53 % CPU time: 1.021555 seconds
% 0.86/0.53 % Total memory used: 98.342 MB
% 0.86/0.53 % Net memory used: 95.438 MB
%------------------------------------------------------------------------------