%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET086+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:09:16 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 2 unt; 3 def)
% Number of atoms : 58 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 65 ( 29 ~; 21 |; 12 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 20 ( 12 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,conjecture,
! [X] :
? [U] :
( ( U = X
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
| ( X = singleton(U)
& member(U,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [X] :
? [U] :
( ( U = X
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
| ( X = singleton(U)
& member(U,universal_class) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f191,plain,
? [X] :
! [U] :
( ( U != X
| ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
& ( X != singleton(U)
| ~ member(U,universal_class) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f192,plain,
? [X] :
( ( ! [U] : U != X
| ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
& ! [U] :
( X != singleton(U)
| ~ member(U,universal_class) ) ),
inference(miniscoping,[status(thm)],[f191]) ).
fof(f193,plain,
( ( ! [U] : U != sK7_skl
| ( sK7_skl = singleton(sK8_skl)
& member(sK8_skl,universal_class) ) )
& ! [U] :
( sK7_skl != singleton(U)
| ~ member(U,universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(X,sK7_skl),skolemize(Y,sK8_skl)],[f192]) ).
fof(f194,plain,
! [X0] :
( sK7_skl != singleton(X0)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f195,plain,
! [X0] :
( X0 != sK7_skl
| member(sK8_skl,universal_class) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f196,plain,
! [X0] :
( X0 != sK7_skl
| sK7_skl = singleton(sK8_skl) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f197,definition,
( sQ0_spl
<=> member(sK8_skl,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ0_spl
| member(sK8_skl,universal_class) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,definition,
! [X0] :
( sQ1_spl
<=> X0 != sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f201,plain,
! [X0] :
( ~ sQ1_spl
| X0 != sK7_skl ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f195,f197,f200]) ).
fof(f204,definition,
( sQ2_spl
<=> sK7_skl = singleton(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ2_spl
| sK7_skl = singleton(sK8_skl) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f196,f204,f200]) ).
fof(f214,plain,
( ~ sQ1_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f201]) ).
fof(f215,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f214]) ).
fof(f216,plain,
( ~ sQ2_spl
| ~ member(sK8_skl,universal_class) ),
inference(resolution,[status(thm)],[f194,f205]) ).
fof(f218,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f198]) ).
fof(f219,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f220,plain,
$false,
inference(sat_refutation,[status(thm)],[f203,f207,f215,f219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET086+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:50:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.054988 seconds
% 0.14/0.42 % CPU time: 0.072848 seconds
% 0.14/0.42 % Total memory used: 9.812 MB
% 0.14/0.42 % Net memory used: 9.802 MB
%------------------------------------------------------------------------------