%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:59:42 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 149 ( 12 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 160 ( 63 ~; 58 |; 31 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 96 ( 81 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp1xcomp(Y)
& rf2(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf3(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,Z] :
( ( rf1(X,Z)
& rf1(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Y,Z] :
( ( rf2(X,Z)
& rf2(X,Y) )
=> Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
cUnsatisfiable(i2003_11_14_17_20_57644),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] :
( rf3(X,Y)
=> rf1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X,Y] :
( rf3(X,Y)
=> rf2(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf2(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf3(X,Y) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( cp1xcomp(Y)
& rf2(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf3(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f84,plain,
( ! [X] :
( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf2(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf3(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ? [Y] :
( cp1xcomp(Y)
& rf2(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf3(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
( ! [X] :
( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf2(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf3(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( cp1xcomp(sK2_skl(X))
& rf2(X,sK2_skl(X))
& cp1(sK1_skl(X))
& rf1(X,sK1_skl(X))
& cp2(sK0_skl(X))
& rf3(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X)),skolemize(Y,sK2_skl(X))],[f84]) ).
fof(f86,plain,
! [X0] :
( rf3(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0] :
( rf1(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f89,plain,
! [X0] :
( cp1(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
! [X0] :
( rf2(X0,sK2_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f91,plain,
! [X0] :
( cp1xcomp(sK2_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f93,plain,
! [X] :
( cp1(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f94,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cp1(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(NNF_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cp1(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(miniscoping,[status(thm)],[f94]) ).
fof(f96,plain,
( ! [X] :
( ra_Px1(X,sK3_skl(X))
| cp1(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cp1(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f99,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cp1xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f100,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cp1xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ! [X] :
( ra_Px1(X,sK4_skl(X))
| ~ cp1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(Y0,sK4_skl(X))],[f100]) ).
fof(f102,plain,
! [X0] :
( ra_Px1(X0,sK4_skl(X0))
| ~ cp1xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f104,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf1(X,Z)
| ~ rf1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f105,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf1(X,Z)
| ~ rf1(X,Y) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf1(X0,X2)
| ~ rf1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
! [X,Y,Z] :
( Y = Z
| ~ rf2(X,Z)
| ~ rf2(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f108,plain,
! [Y,Z] :
( Y = Z
| ! [X] :
( ~ rf2(X,Z)
| ~ rf2(X,Y) ) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rf2(X0,X2)
| ~ rf2(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f113,plain,
cUnsatisfiable(i2003_11_14_17_20_57644),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f114,plain,
! [X,Y] :
( rf1(X,Y)
| ~ rf3(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f115,plain,
! [X0,X1] :
( rf1(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X,Y] :
( rf2(X,Y)
| ~ rf3(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f117,plain,
! [X0,X1] :
( rf2(X0,X1)
| ~ rf3(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,plain,
rf3(i2003_11_14_17_20_57644,sK0_skl(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[f86,f113]) ).
fof(f121,plain,
rf1(i2003_11_14_17_20_57644,sK1_skl(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[f88,f113]) ).
fof(f122,plain,
cp1(sK1_skl(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[f89,f113]) ).
fof(f123,plain,
rf2(i2003_11_14_17_20_57644,sK2_skl(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[f90,f113]) ).
fof(f124,plain,
cp1xcomp(sK2_skl(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[f91,f113]) ).
fof(f126,plain,
ra_Px1(sK2_skl(i2003_11_14_17_20_57644),sK4_skl(sK2_skl(i2003_11_14_17_20_57644))),
inference(resolution,[status(thm)],[f102,f124]) ).
fof(f129,plain,
rf2(i2003_11_14_17_20_57644,sK0_skl(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[f119,f117]) ).
fof(f130,plain,
rf1(i2003_11_14_17_20_57644,sK0_skl(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[f119,f115]) ).
fof(f132,plain,
! [X0] :
( X0 = sK1_skl(i2003_11_14_17_20_57644)
| ~ rf1(i2003_11_14_17_20_57644,X0) ),
inference(resolution,[status(thm)],[f121,f106]) ).
fof(f134,plain,
! [X0] :
( X0 = sK2_skl(i2003_11_14_17_20_57644)
| ~ rf2(i2003_11_14_17_20_57644,X0) ),
inference(resolution,[status(thm)],[f123,f109]) ).
fof(f137,plain,
~ cp1(sK2_skl(i2003_11_14_17_20_57644)),
inference(resolution,[status(thm)],[f126,f97]) ).
fof(f145,plain,
sK0_skl(i2003_11_14_17_20_57644) = sK1_skl(i2003_11_14_17_20_57644),
inference(resolution,[status(thm)],[f132,f130]) ).
fof(f147,plain,
sK0_skl(i2003_11_14_17_20_57644) = sK2_skl(i2003_11_14_17_20_57644),
inference(resolution,[status(thm)],[f134,f129]) ).
fof(f151,plain,
cp1(sK0_skl(i2003_11_14_17_20_57644)),
inference(backward_demodulation,[status(thm)],[f145,f122]) ).
fof(f154,plain,
~ cp1(sK0_skl(i2003_11_14_17_20_57644)),
inference(backward_demodulation,[status(thm)],[f147,f137]) ).
fof(f158,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f154,f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:48:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.40 % Elapsed time: 0.030356 seconds
% 0.10/0.40 % CPU time: 0.080333 seconds
% 0.10/0.40 % Total memory used: 2.692 MB
% 0.10/0.40 % Net memory used: 2.608 MB
%------------------------------------------------------------------------------