%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS128+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 12:59:45 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 5 unt; 2 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 189 ( 76 ~; 68 |; 35 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 76 ( 62 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rr(X,Y)
=> ca_Cx4(Y) )
& ! [Y] :
( rr(X,Y)
=> cd(Y) )
& ? [Y] :
( cexcomp(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ca_Cx4(X)
<=> ? [Y0] : ra_Px4(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] :
( ca_Cx4xcomp(X)
<=> ~ ? [Y] : ra_Px4(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( ca_Cx4xcomp(X)
<=> ( cexcomp(X)
& cd(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
cUnsatisfiable(i2003_11_14_17_22_31584),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) )
& ? [Y] :
( cexcomp(Y)
& rr(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X] :
( ( ? [Y] :
( ~ ca_Cx4(Y)
& rr(X,Y) )
| ? [Y] :
( ~ cd(Y)
& rr(X,Y) )
| ! [Y] :
( ~ cexcomp(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ! [Y] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) )
& ? [Y] :
( cexcomp(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [X] :
( ? [Y] :
( ~ ca_Cx4(Y)
& rr(X,Y) )
| ? [Y] :
( ~ cd(Y)
& rr(X,Y) )
| ! [Y] :
( ~ cexcomp(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) )
& ? [Y] :
( cexcomp(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
( ! [X] :
( ( ~ ca_Cx4(sK2_skl(X))
& rr(X,sK2_skl(X)) )
| ( ~ cd(sK1_skl(X))
& rr(X,sK1_skl(X)) )
| ! [Y] :
( ~ cexcomp(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y] :
( ca_Cx4(Y)
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) )
& cexcomp(sK0_skl(X))
& rr(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))],[f22]) ).
fof(f24,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] :
( cexcomp(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( cd(X1)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ca_Cx4(X1)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px4(X,Y0)
| ca_Cx4(X) )
& ( ? [Y0] : ra_Px4(X,Y0)
| ~ ca_Cx4(X) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f57,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px4(X,Y0)
| ca_Cx4(X) )
& ! [X] :
( ? [Y0] : ra_Px4(X,Y0)
| ~ ca_Cx4(X) ) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px4(X,Y0)
| ca_Cx4(X) )
& ! [X] :
( ra_Px4(X,sK7_skl(X))
| ~ ca_Cx4(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(Y0,sK7_skl(X))],[f57]) ).
fof(f59,plain,
! [X0] :
( ra_Px4(X0,sK7_skl(X0))
| ~ ca_Cx4(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f61,plain,
! [X] :
( ca_Cx4xcomp(X)
<=> ! [Y] : ~ ra_Px4(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f62,plain,
! [X] :
( ( ? [Y] : ra_Px4(X,Y)
| ca_Cx4xcomp(X) )
& ( ! [Y] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
( ! [X] :
( ? [Y] : ra_Px4(X,Y)
| ca_Cx4xcomp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [X] :
( ra_Px4(X,sK8_skl(X))
| ca_Cx4xcomp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px4(X,Y)
| ~ ca_Cx4xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(Y,sK8_skl(X))],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ ra_Px4(X0,X1)
| ~ ca_Cx4xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
! [X] :
( ( ~ cexcomp(X)
| ~ cd(X)
| ca_Cx4xcomp(X) )
& ( ( cexcomp(X)
& cd(X) )
| ~ ca_Cx4xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f68,plain,
( ! [X] :
( ~ cexcomp(X)
| ~ cd(X)
| ca_Cx4xcomp(X) )
& ! [X] :
( ( cexcomp(X)
& cd(X) )
| ~ ca_Cx4xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f71,plain,
! [X0] :
( ~ cexcomp(X0)
| ~ cd(X0)
| ca_Cx4xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f72,plain,
cUnsatisfiable(i2003_11_14_17_22_31584),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f76,plain,
! [X0,X1] :
( ~ ra_Px4(X0,X1)
| ~ cexcomp(X0)
| ~ cd(X0) ),
inference(resolution,[status(thm)],[f71,f65]) ).
fof(f78,plain,
! [X0] :
( ~ ca_Cx4(X0)
| ~ cexcomp(X0)
| ~ cd(X0) ),
inference(resolution,[status(thm)],[f76,f59]) ).
fof(f79,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| ~ cUnsatisfiable(X1)
| ~ cexcomp(X0)
| ~ cd(X0) ),
inference(resolution,[status(thm)],[f78,f27]) ).
fof(f81,plain,
! [X0,X1] :
( ~ rr(X1,X0)
| ~ cUnsatisfiable(X1)
| ~ cexcomp(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f26]) ).
fof(f83,plain,
! [X0] :
( ~ rr(i2003_11_14_17_22_31584,X0)
| ~ cexcomp(X0) ),
inference(resolution,[status(thm)],[f81,f72]) ).
fof(f84,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
| ~ cexcomp(sK0_skl(i2003_11_14_17_22_31584)) ),
inference(resolution,[status(thm)],[f83,f24]) ).
fof(f85,definition,
( sQ0_spl
<=> cexcomp(sK0_skl(i2003_11_14_17_22_31584)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( sQ0_spl
| ~ cexcomp(sK0_skl(i2003_11_14_17_22_31584)) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ1_spl
<=> cUnsatisfiable(i2003_11_14_17_22_31584) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( sQ1_spl
| ~ cUnsatisfiable(i2003_11_14_17_22_31584) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f84,f85,f88]) ).
fof(f92,plain,
( sQ0_spl
| ~ cUnsatisfiable(i2003_11_14_17_22_31584) ),
inference(resolution,[status(thm)],[f87,f25]) ).
fof(f95,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f72]) ).
fof(f96,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f95]) ).
fof(f97,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f72]) ).
fof(f98,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f99,plain,
$false,
inference(sat_refutation,[status(thm)],[f91,f96,f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS128+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.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 22:56:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.030975 seconds
% 0.10/0.41 % CPU time: 0.079977 seconds
% 0.10/0.41 % Total memory used: 2.175 MB
% 0.10/0.41 % Net memory used: 2.120 MB
%------------------------------------------------------------------------------