%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS124+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 : n003.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 12:59:44 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.54s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 5 unt; 2 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 159 ( 65 ~; 57 |; 27 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 65 ( 53 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rr(X,Y)
=> ca_Ax3(Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( cc(X)
=> cdxcomp(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( cd(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( cdxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] :
( ca_Ax3(X)
<=> ( cc(X)
& cd(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
cUnsatisfiable(i2003_11_14_17_22_10903),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( ca_Ax3(Y)
| ~ rr(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Ax3(Y)
& rr(X,Y) )
| ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ! [Y] :
( ca_Ax3(Y)
| ~ rr(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Ax3(Y)
& rr(X,Y) )
| ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y] :
( ca_Ax3(Y)
| ~ rr(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [X] :
( ( ~ ca_Ax3(sK1_skl(X))
& rr(X,sK1_skl(X)) )
| ! [Y] :
( ~ cowlThing(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y] :
( ca_Ax3(Y)
| ~ rr(X,Y) )
& cowlThing(sK0_skl(X))
& rr(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X))],[f24]) ).
fof(f26,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( ca_Ax3(X1)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f31,plain,
! [X] :
( cdxcomp(X)
| ~ cc(X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [X0] :
( cdxcomp(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f37,plain,
! [X] :
( cd(X)
<=> ! [Y] : ~ ra_Px1(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f38,plain,
! [X] :
( ( ? [Y] : ra_Px1(X,Y)
| cd(X) )
& ( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [X] :
( ? [Y] : ra_Px1(X,Y)
| cd(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [X] :
( ra_Px1(X,sK2_skl(X))
| cd(X) )
& ! [X] :
( ! [Y] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ ra_Px1(X0,X1)
| ~ cd(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ( ? [Y0] : ra_Px1(X,Y0)
| ~ cdxcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f44,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ! [X] :
( ? [Y0] : ra_Px1(X,Y0)
| ~ cdxcomp(X) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px1(X,Y0)
| cdxcomp(X) )
& ! [X] :
( ra_Px1(X,sK3_skl(X))
| ~ cdxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y0,sK3_skl(X))],[f44]) ).
fof(f46,plain,
! [X0] :
( ra_Px1(X0,sK3_skl(X0))
| ~ cdxcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f63,plain,
! [X] :
( ( ~ cc(X)
| ~ cd(X)
| ca_Ax3(X) )
& ( ( cc(X)
& cd(X) )
| ~ ca_Ax3(X) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f64,plain,
( ! [X] :
( ~ cc(X)
| ~ cd(X)
| ca_Ax3(X) )
& ! [X] :
( ( cc(X)
& cd(X) )
| ~ ca_Ax3(X) ) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
! [X0] :
( cd(X0)
| ~ ca_Ax3(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0] :
( cc(X0)
| ~ ca_Ax3(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
cUnsatisfiable(i2003_11_14_17_22_10903),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
! [X0] :
( ca_Ax3(X0)
| ~ rr(i2003_11_14_17_22_10903,X0) ),
inference(resolution,[status(thm)],[f28,f68]) ).
fof(f70,plain,
! [X0] :
( cc(X0)
| ~ rr(i2003_11_14_17_22_10903,X0) ),
inference(resolution,[status(thm)],[f69,f66]) ).
fof(f71,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_10903)
| cc(sK0_skl(i2003_11_14_17_22_10903)) ),
inference(resolution,[status(thm)],[f70,f26]) ).
fof(f72,definition,
( sQ0_spl
<=> cc(sK0_skl(i2003_11_14_17_22_10903)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( ~ sQ0_spl
| cc(sK0_skl(i2003_11_14_17_22_10903)) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,definition,
( sQ1_spl
<=> cUnsatisfiable(i2003_11_14_17_22_10903) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ1_spl
| ~ cUnsatisfiable(i2003_11_14_17_22_10903) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f72,f75]) ).
fof(f79,plain,
( ~ sQ0_spl
| cdxcomp(sK0_skl(i2003_11_14_17_22_10903)) ),
inference(resolution,[status(thm)],[f73,f32]) ).
fof(f82,plain,
! [X0] :
( ~ cd(X0)
| ~ cdxcomp(X0) ),
inference(resolution,[status(thm)],[f46,f41]) ).
fof(f83,plain,
( ~ sQ0_spl
| ~ cd(sK0_skl(i2003_11_14_17_22_10903)) ),
inference(resolution,[status(thm)],[f82,f79]) ).
fof(f86,plain,
( ~ sQ0_spl
| ~ ca_Ax3(sK0_skl(i2003_11_14_17_22_10903)) ),
inference(resolution,[status(thm)],[f83,f65]) ).
fof(f88,plain,
( ~ sQ0_spl
| ~ rr(i2003_11_14_17_22_10903,sK0_skl(i2003_11_14_17_22_10903)) ),
inference(resolution,[status(thm)],[f86,f69]) ).
fof(f91,plain,
( ~ sQ0_spl
| ~ cUnsatisfiable(i2003_11_14_17_22_10903) ),
inference(resolution,[status(thm)],[f88,f26]) ).
fof(f92,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f68]) ).
fof(f93,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f92]) ).
fof(f94,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f68]) ).
fof(f95,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f96,plain,
$false,
inference(sat_refutation,[status(thm)],[f78,f93,f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS124+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n003.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Sun Sep 20 22:55:46 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.53 % Drodi V4.1.1
% 0.10/0.54 % Refutation found
% 0.10/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.55 % Elapsed time: 0.028093 seconds
% 0.10/0.55 % CPU time: 0.072356 seconds
% 0.10/0.55 % Total memory used: 1.751 MB
% 0.10/0.55 % Net memory used: 1.714 MB
%------------------------------------------------------------------------------