%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS233+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.16s 0.58s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 6 unt; 3 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 170 ( 74 ~; 64 |; 21 &)
% ( 8 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 100 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Ax,C] :
( ! [I1] :
( model(I1,Ax)
=> model(I1,C) )
<=> status(Ax,C,thm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Ax,C] :
( ? [I1] :
( model(I1,not(C))
& model(I1,Ax) )
<=> status(Ax,C,csa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> ~ status(Ax,C,S2) )
<=> nevera(S1,S2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [I,F] :
( model(I,F)
<~> model(I,not(F)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
nevera(csa,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ nevera(csa,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(f154,plain,
! [Ax,C] :
( ( ~ status(Ax,C,csa)
| ? [I1] :
( model(I1,not(C))
& model(I1,Ax) ) )
& ( status(Ax,C,csa)
| ! [I1] :
( ~ model(I1,not(C))
| ~ model(I1,Ax) ) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f155,plain,
( ! [Ax,C] :
( ~ status(Ax,C,csa)
| ? [I1] :
( model(I1,not(C))
& model(I1,Ax) ) )
& ! [Ax,C] :
( status(Ax,C,csa)
| ! [I1] :
( ~ model(I1,not(C))
| ~ model(I1,Ax) ) ) ),
inference(miniscoping,[status(thm)],[f154]) ).
fof(f156,plain,
( ! [Ax,C] :
( ~ status(Ax,C,csa)
| ( model(sK37_skl(C,Ax),not(C))
& model(sK37_skl(C,Ax),Ax) ) )
& ! [Ax,C] :
( status(Ax,C,csa)
| ! [I1] :
( ~ model(I1,not(C))
| ~ model(I1,Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37_skl]),skolemize(I1,sK37_skl(C,Ax))],[f155]) ).
fof(f158,plain,
! [X0,X1] :
( ~ status(X1,X0,csa)
| model(sK37_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f159,plain,
! [X0,X1] :
( ~ status(X1,X0,csa)
| model(sK37_skl(X0,X1),not(X0)) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
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(f199,plain,
! [X0,X1,X2,X3] :
( ~ nevera(X2,X3)
| ~ status(X0,X1,X3)
| ~ status(X0,X1,X2) ),
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(csa,thm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f411,plain,
! [X0,X1] :
( ~ status(X1,X0,csa)
| ~ model(sK37_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f210,f159]) ).
fof(f427,definition,
! [X0,X1] :
( sQ19_spl
<=> ( ~ status(X0,X1,csa)
| ~ status(X0,X1,thm) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f428,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ status(X0,X1,csa)
| ~ status(X0,X1,thm) ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f430,definition,
( sQ20_spl
<=> nevera(thm,csa) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( ~ sQ20_spl
| nevera(thm,csa) ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f434,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ status(X0,X1,csa)
| ~ status(X0,X1,thm) ),
inference(resolution,[status(thm)],[f431,f199]) ).
fof(f436,plain,
! [X0] :
( ~ sQ19_spl
| nevera(csa,X0)
| ~ status(sK48_skl(X0,csa),sK49_skl(X0,csa),thm) ),
inference(resolution,[status(thm)],[f428,f197]) ).
fof(f443,plain,
( ~ sQ19_spl
| nevera(csa,thm)
| nevera(csa,thm) ),
inference(resolution,[status(thm)],[f436,f198]) ).
fof(f445,definition,
( sQ21_spl
<=> nevera(csa,thm) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ21_spl
| nevera(csa,thm) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( ~ sQ19_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f443,f445,f427]) ).
fof(f449,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f240]) ).
fof(f450,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f451,plain,
( ~ sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f434,f427,f430]) ).
fof(f546,plain,
! [X0,X1,X2] :
( ~ status(X1,X0,csa)
| ~ status(X2,X0,thm)
| ~ model(sK37_skl(X0,X1),X2) ),
inference(resolution,[status(thm)],[f68,f411]) ).
fof(f548,plain,
! [X0,X1] :
( ~ status(X0,X1,csa)
| ~ status(X0,X1,csa)
| ~ status(X0,X1,thm) ),
inference(resolution,[status(thm)],[f546,f158]) ).
fof(f550,plain,
! [X0,X1] :
( ~ status(X0,X1,csa)
| ~ status(X0,X1,thm) ),
inference(duplicate_literals_removal,[status(thm)],[f548]) ).
fof(f551,plain,
! [X0] :
( nevera(X0,csa)
| ~ status(sK48_skl(csa,X0),sK49_skl(csa,X0),thm) ),
inference(resolution,[status(thm)],[f550,f198]) ).
fof(f556,plain,
( nevera(thm,csa)
| nevera(thm,csa) ),
inference(resolution,[status(thm)],[f551,f197]) ).
fof(f558,plain,
sQ20_spl,
inference(split_clause,[status(thm)],[f556,f430]) ).
fof(f559,plain,
$false,
inference(sat_refutation,[status(thm)],[f448,f450,f451,f558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS233+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n014.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 20 22:57:20 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.58 % Refutation found
% 0.16/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.62 % Elapsed time: 0.177250 seconds
% 0.16/0.62 % CPU time: 1.145002 seconds
% 0.16/0.62 % Total memory used: 31.283 MB
% 0.16/0.62 % Net memory used: 29.283 MB
%------------------------------------------------------------------------------