%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS127+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:59:45 PM UTC 2026
% Result : Unsatisfiable 0.02s 15.25s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 134 ( 12 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 151 ( 56 ~; 52 |; 36 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 76 ( 58 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] :
( cc(X)
=> cdxcomp(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
cUnsatisfiable(i2003_11_14_17_22_27794),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f64,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
( ! [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
( ! [X] :
( ( sK2_skl(X) != sK3_skl(X)
& rr(X,sK3_skl(X))
& rr(X,sK2_skl(X)) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& cd(sK1_skl(X))
& rr(X,sK1_skl(X))
& cc(sK0_skl(X))
& rr(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X)),skolemize(Y0,sK2_skl(X)),skolemize(Y1,sK3_skl(X))],[f65]) ).
fof(f67,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0] :
( cc(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
! [X0] :
( rr(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f70,plain,
! [X0] :
( cd(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f71,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rr(X0,X2)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f75,plain,
! [X] :
( cdxcomp(X)
| ~ cc(X) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f76,plain,
! [X0] :
( cdxcomp(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
! [X] :
( cd(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f78,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cd(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cd(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
( ! [X] :
( ra_Px1(X,sK4_skl(X))
| cd(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y,sK4_skl(X))],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cdxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f84,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cdxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ! [X] :
( ra_Px1(X,sK5_skl(X))
| ~ cdxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(Y0,sK5_skl(X))],[f84]) ).
fof(f86,plain,
! [X0] :
( ra_Px1(X0,sK5_skl(X0))
| ~ cdxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
cUnsatisfiable(i2003_11_14_17_22_27794),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f90,plain,
rr(i2003_11_14_17_22_27794,sK0_skl(i2003_11_14_17_22_27794)),
inference(resolution,[status(thm)],[f67,f88]) ).
fof(f91,plain,
cc(sK0_skl(i2003_11_14_17_22_27794)),
inference(resolution,[status(thm)],[f68,f88]) ).
fof(f92,plain,
cdxcomp(sK0_skl(i2003_11_14_17_22_27794)),
inference(resolution,[status(thm)],[f91,f76]) ).
fof(f93,plain,
cd(sK1_skl(i2003_11_14_17_22_27794)),
inference(resolution,[status(thm)],[f70,f88]) ).
fof(f94,plain,
rr(i2003_11_14_17_22_27794,sK1_skl(i2003_11_14_17_22_27794)),
inference(resolution,[status(thm)],[f69,f88]) ).
fof(f97,plain,
ra_Px1(sK0_skl(i2003_11_14_17_22_27794),sK5_skl(sK0_skl(i2003_11_14_17_22_27794))),
inference(resolution,[status(thm)],[f86,f92]) ).
fof(f98,plain,
! [X0] :
( sK1_skl(i2003_11_14_17_22_27794) = X0
| ~ rr(i2003_11_14_17_22_27794,X0)
| ~ cUnsatisfiable(i2003_11_14_17_22_27794) ),
inference(resolution,[status(thm)],[f71,f94]) ).
fof(f100,plain,
! [X0] :
( sK1_skl(i2003_11_14_17_22_27794) = X0
| ~ rr(i2003_11_14_17_22_27794,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f88]) ).
fof(f103,plain,
sK1_skl(i2003_11_14_17_22_27794) = sK0_skl(i2003_11_14_17_22_27794),
inference(resolution,[status(thm)],[f100,f90]) ).
fof(f110,plain,
ra_Px1(sK1_skl(i2003_11_14_17_22_27794),sK5_skl(sK0_skl(i2003_11_14_17_22_27794))),
inference(forward_demodulation,[status(thm)],[f103,f97]) ).
fof(f111,plain,
ra_Px1(sK1_skl(i2003_11_14_17_22_27794),sK5_skl(sK1_skl(i2003_11_14_17_22_27794))),
inference(forward_demodulation,[status(thm)],[f103,f110]) ).
fof(f113,plain,
~ cd(sK1_skl(i2003_11_14_17_22_27794)),
inference(resolution,[status(thm)],[f111,f81]) ).
fof(f114,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f113,f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KRS127+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.02/15.23 % CPULimit : 300
% 0.02/15.23 % WCLimit : 300
% 0.02/15.23 % DateTime : Sun Sep 20 22:54:38 UTC 2026
% 0.02/15.23 % CPUTime :
% 0.02/15.23 % Drodi V4.1.1
% 0.02/15.25 % Refutation found
% 0.02/15.25 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/15.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/15.25 % Elapsed time: 0.023571 seconds
% 0.02/15.25 % CPU time: 0.038377 seconds
% 0.02/15.25 % Total memory used: 2.326 MB
% 0.02/15.25 % Net memory used: 2.245 MB
%------------------------------------------------------------------------------