%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS234+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 : n007.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 12:59:57 PM UTC 2026
% Result : Theorem 0.18s 0.55s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 5 unt; 2 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 138 ( 54 ~; 53 |; 21 &)
% ( 7 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 108 ( 98 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Ax,C] :
( ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) )
<=> status(Ax,C,uns) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> ~ status(Ax,C,S2) )
<=> nevera(S1,S2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [I,F] :
( model(I,F)
<~> model(I,not(F)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
nevera(uns,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ nevera(uns,thm),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f62,plain,
! [Ax,C] :
( ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) )
<=> status(Ax,C,thm) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f63,plain,
! [Ax,C] :
( ( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ( status(Ax,C,thm)
| ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [Ax,C] :
( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,thm)
| ? [I1] :
( ~ model(I1,C)
& model(I1,Ax) ) ) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
( ! [Ax,C] :
( ~ status(Ax,C,thm)
| ! [I1] :
( model(I1,C)
| ~ model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,thm)
| ( ~ model(sK9_skl(C,Ax),C)
& model(sK9_skl(C,Ax),Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(I1,sK9_skl(C,Ax))],[f64]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ status(X1,X2,thm)
| model(X0,X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f160,plain,
! [Ax,C] :
( ( ~ status(Ax,C,uns)
| ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) ) )
& ( status(Ax,C,uns)
| ? [I2] : ~ model(I2,not(C))
| ? [I1] : ~ model(I1,Ax) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f161,plain,
( ! [Ax,C] :
( ~ status(Ax,C,uns)
| ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,uns)
| ? [I2] : ~ model(I2,not(C))
| ? [I1] : ~ model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f162,plain,
( ! [Ax,C] :
( ~ status(Ax,C,uns)
| ( ! [I2] : model(I2,not(C))
& ! [I1] : model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,uns)
| ~ model(sK39_skl(C,Ax),not(C))
| ~ model(sK38_skl(C,Ax),Ax) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl]),skolemize(I1,sK38_skl(C,Ax)),skolemize(I2,sK39_skl(C,Ax))],[f161]) ).
fof(f164,plain,
! [X0,X1,X2] :
( ~ status(X1,X2,uns)
| model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ~ status(X2,X1,uns)
| model(X0,not(X1)) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f193,plain,
! [S1,S2] :
( ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) )
<=> nevera(S1,S2) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f194,plain,
! [S1,S2] :
( ( ~ nevera(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( nevera(S1,S2)
| ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) ) ) ),
inference(NNF_transformation,[status(thm)],[f193]) ).
fof(f195,plain,
( ! [S1,S2] :
( ~ nevera(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ! [S1,S2] :
( nevera(S1,S2)
| ? [Ax,C] :
( status(Ax,C,S2)
& status(Ax,C,S1) ) ) ),
inference(miniscoping,[status(thm)],[f194]) ).
fof(f196,plain,
( ! [S1,S2] :
( ~ nevera(S1,S2)
| ! [Ax,C] :
( ~ status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ! [S1,S2] :
( nevera(S1,S2)
| ( status(sK48_skl(S2,S1),sK49_skl(S2,S1),S2)
& status(sK48_skl(S2,S1),sK49_skl(S2,S1),S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48_skl,sK49_skl]),skolemize(Ax,sK48_skl(S2,S1)),skolemize(C,sK49_skl(S2,S1))],[f195]) ).
fof(f197,plain,
! [X0,X1] :
( nevera(X1,X0)
| status(sK48_skl(X0,X1),sK49_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [X0,X1] :
( nevera(X1,X0)
| status(sK48_skl(X0,X1),sK49_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f207,plain,
! [I,F] :
( ( ~ model(I,not(F))
| ~ model(I,F) )
& ( model(I,not(F))
| model(I,F) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f208,plain,
( ! [I,F] :
( ~ model(I,not(F))
| ~ model(I,F) )
& ! [I,F] :
( model(I,not(F))
| model(I,F) ) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f210,plain,
! [X0,X1] :
( ~ model(X0,not(X1))
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f240,plain,
~ nevera(uns,thm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f275,plain,
! [X0,X1,X2] :
( ~ status(X2,X1,uns)
| ~ model(X0,X1) ),
inference(resolution,[status(thm)],[f210,f165]) ).
fof(f421,plain,
! [X0,X1] :
( model(X1,sK48_skl(X0,uns))
| nevera(uns,X0) ),
inference(resolution,[status(thm)],[f197,f164]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ~ status(sK48_skl(X0,uns),X2,thm)
| model(X1,X2)
| nevera(uns,X0) ),
inference(resolution,[status(thm)],[f421,f68]) ).
fof(f440,plain,
! [X0] :
( nevera(uns,thm)
| model(X0,sK49_skl(thm,uns))
| nevera(uns,thm) ),
inference(resolution,[status(thm)],[f436,f198]) ).
fof(f441,definition,
( sQ4_spl
<=> nevera(uns,thm) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ4_spl
| nevera(uns,thm) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
! [X0] :
( sQ5_spl
<=> model(X0,sK49_skl(thm,uns)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f445,plain,
! [X0] :
( ~ sQ5_spl
| model(X0,sK49_skl(thm,uns)) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f440,f441,f444]) ).
fof(f448,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f240]) ).
fof(f449,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f448]) ).
fof(f451,plain,
! [X0] :
( ~ sQ5_spl
| ~ status(X0,sK49_skl(thm,uns),uns) ),
inference(resolution,[status(thm)],[f445,f275]) ).
fof(f452,plain,
( ~ sQ5_spl
| nevera(uns,thm) ),
inference(resolution,[status(thm)],[f451,f197]) ).
fof(f453,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f452,f441,f444]) ).
fof(f454,plain,
$false,
inference(sat_refutation,[status(thm)],[f447,f449,f453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS234+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 22:55:35 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.55 % Refutation found
% 0.18/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.58 % Elapsed time: 0.123388 seconds
% 0.18/0.58 % CPU time: 0.566656 seconds
% 0.18/0.58 % Total memory used: 20.815 MB
% 0.18/0.58 % Net memory used: 20.100 MB
%------------------------------------------------------------------------------