%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS217+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 : n004.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 12:59:56 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 196 ( 80 ~; 63 |; 46 &)
% ( 4 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 128 ( 98 !; 30 ?)
% 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(f19,axiom,
! [Ax,C] :
( ( ? [I2] :
( model(I2,not(C))
& model(I2,Ax) )
& ? [I1] :
( model(I1,C)
& model(I1,Ax) ) )
<=> status(Ax,C,noc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [S1,S2] :
( ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) )
<=> nota(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(f27,axiom,
? [F] :
! [I] : model(I,F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
? [Ax,C] :
( ? [I4] : ~ model(I4,C)
& ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,Ax)
=> model(I2,C) )
& ? [I1] : model(I1,Ax) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
nota(noc,thm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ nota(noc,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(f166,plain,
! [Ax,C] :
( ( ~ status(Ax,C,noc)
| ( ? [I2] :
( model(I2,not(C))
& model(I2,Ax) )
& ? [I1] :
( model(I1,C)
& model(I1,Ax) ) ) )
& ( status(Ax,C,noc)
| ! [I2] :
( ~ model(I2,not(C))
| ~ model(I2,Ax) )
| ! [I1] :
( ~ model(I1,C)
| ~ model(I1,Ax) ) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f167,plain,
( ! [Ax,C] :
( ~ status(Ax,C,noc)
| ( ? [I2] :
( model(I2,not(C))
& model(I2,Ax) )
& ? [I1] :
( model(I1,C)
& model(I1,Ax) ) ) )
& ! [Ax,C] :
( status(Ax,C,noc)
| ! [I2] :
( ~ model(I2,not(C))
| ~ model(I2,Ax) )
| ! [I1] :
( ~ model(I1,C)
| ~ model(I1,Ax) ) ) ),
inference(miniscoping,[status(thm)],[f166]) ).
fof(f168,plain,
( ! [Ax,C] :
( ~ status(Ax,C,noc)
| ( model(sK41_skl(C,Ax),not(C))
& model(sK41_skl(C,Ax),Ax)
& model(sK40_skl(C,Ax),C)
& model(sK40_skl(C,Ax),Ax) ) )
& ! [Ax,C] :
( status(Ax,C,noc)
| ! [I2] :
( ~ model(I2,not(C))
| ~ model(I2,Ax) )
| ! [I1] :
( ~ model(I1,C)
| ~ model(I1,Ax) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40_skl,sK41_skl]),skolemize(I1,sK40_skl(C,Ax)),skolemize(I2,sK41_skl(C,Ax))],[f167]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( status(X1,X2,noc)
| ~ model(X3,not(X2))
| ~ model(X3,X1)
| ~ model(X0,X2)
| ~ model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f187,plain,
! [S1,S2] :
( ( ~ nota(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f188,plain,
( ! [S1,S2] :
( ~ nota(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ! [S1,S2] :
( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(miniscoping,[status(thm)],[f187]) ).
fof(f189,plain,
( ! [S1,S2] :
( ~ nota(S1,S2)
| ( ~ status(sK46_skl(S2,S1),sK47_skl(S2,S1),S2)
& status(sK46_skl(S2,S1),sK47_skl(S2,S1),S1) ) )
& ! [S1,S2] :
( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46_skl,sK47_skl]),skolemize(Ax,sK46_skl(S2,S1)),skolemize(C,sK47_skl(S2,S1))],[f188]) ).
fof(f190,plain,
! [X0,X1,X2,X3] :
( nota(X2,X3)
| status(X0,X1,X3)
| ~ status(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
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(f209,plain,
! [X0,X1] :
( model(X0,not(X1))
| model(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f215,plain,
! [I] : model(I,sK52_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(F,sK52_skl)],[f27]) ).
fof(f216,plain,
! [X0] : model(X0,sK52_skl),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f227,plain,
? [Ax,C] :
( ? [I4] : ~ model(I4,C)
& ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f228,plain,
? [C] :
( ? [I4] : ~ model(I4,C)
& ? [Ax] :
( ? [I3] :
( model(I3,C)
& ~ model(I3,Ax) )
& ! [I2] :
( model(I2,C)
| ~ model(I2,Ax) )
& ? [I1] : model(I1,Ax) ) ),
inference(miniscoping,[status(thm)],[f227]) ).
fof(f229,plain,
( ~ model(sK66_skl,sK62_skl)
& model(sK65_skl,sK62_skl)
& ~ model(sK65_skl,sK63_skl)
& ! [I2] :
( model(I2,sK62_skl)
| ~ model(I2,sK63_skl) )
& model(sK64_skl,sK63_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62_skl,sK63_skl,sK64_skl,sK65_skl,sK66_skl]),skolemize(C,sK62_skl),skolemize(Ax,sK63_skl),skolemize(I1,sK64_skl),skolemize(I3,sK65_skl),skolemize(I4,sK66_skl)],[f228]) ).
fof(f233,plain,
model(sK65_skl,sK62_skl),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f234,plain,
~ model(sK66_skl,sK62_skl),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f240,plain,
~ nota(noc,thm),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f253,plain,
! [X0] :
( ~ status(X0,sK62_skl,thm)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f234,f68]) ).
fof(f257,plain,
! [X0,X1] :
( status(X0,X1,thm)
| ~ status(X0,X1,noc) ),
inference(resolution,[status(thm)],[f190,f240]) ).
fof(f260,plain,
! [X0] :
( ~ model(sK66_skl,X0)
| ~ status(X0,sK62_skl,noc) ),
inference(resolution,[status(thm)],[f257,f253]) ).
fof(f264,plain,
! [X0,X1,X2] :
( ~ model(X2,not(sK62_skl))
| ~ model(X2,X0)
| ~ model(X1,sK62_skl)
| ~ model(X1,X0)
| ~ model(sK66_skl,X0) ),
inference(resolution,[status(thm)],[f260,f169]) ).
fof(f268,plain,
! [X0,X1] :
( ~ model(X1,not(sK62_skl))
| ~ model(X1,sK52_skl)
| ~ model(X0,sK62_skl)
| ~ model(X0,sK52_skl) ),
inference(resolution,[status(thm)],[f264,f216]) ).
fof(f270,plain,
! [X0,X1] :
( ~ model(X1,not(sK62_skl))
| ~ model(X1,sK52_skl)
| ~ model(X0,sK62_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f268,f216]) ).
fof(f271,plain,
! [X0,X1] :
( ~ model(X1,not(sK62_skl))
| ~ model(X0,sK62_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f216]) ).
fof(f275,plain,
! [X0] : ~ model(X0,not(sK62_skl)),
inference(resolution,[status(thm)],[f271,f233]) ).
fof(f289,plain,
! [X0] : model(X0,sK62_skl),
inference(resolution,[status(thm)],[f275,f209]) ).
fof(f295,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f234,f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS217+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:57:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.44 % Refutation found
% 0.10/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.075441 seconds
% 0.10/0.45 % CPU time: 0.336047 seconds
% 0.10/0.45 % Total memory used: 23.696 MB
% 0.10/0.45 % Net memory used: 23.231 MB
%------------------------------------------------------------------------------