%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS101+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 : n012.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 12:59:41 PM UTC 2026
% Result : Unsatisfiable 0.05s 5.54s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 4 unt; 1 def)
% Number of atoms : 181 ( 24 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 237 ( 90 ~; 87 |; 52 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 97 ( 74 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ ! [Z0,Z1] :
( ( rs(Y,Z1)
& rs(Y,Z0) )
=> Z0 = Z1 )
& rr(X,Y) )
& ! [Y] :
( rr(X,Y)
=> ( cc(Y)
| ~ ? [Z0,Z1] :
( Z0 != Z1
& rs(Y,Z1)
& rs(Y,Z0) ) ) )
& ! [Y] :
( rr(X,Y)
=> cd(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( cc(X)
=> ~ cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
cUnsatisfiable(i2003_11_14_17_20_36582),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ? [Z0,Z1] :
( Z0 != Z1
& rs(Y,Z1)
& rs(Y,Z0) )
& rr(X,Y) )
& ! [Y] :
( cc(Y)
| ! [Z0,Z1] :
( Z0 = Z1
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f58,definition,
! [Y] :
( sP0_prd(Y)
<=> ( cc(Y)
| ! [Z0,Z1] :
( Z0 = Z1
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f59,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ? [Z0,Z1] :
( Z0 != Z1
& rs(Y,Z1)
& rs(Y,Z0) )
& rr(X,Y) )
& ! [Y] :
( sP0_prd(Y)
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) ) ) ),
inference(formula_renaming,[status(thm)],[f57,f58]) ).
fof(f60,plain,
! [X] :
( ( ! [Y] :
( ! [Z0,Z1] :
( Z0 = Z1
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ rr(X,Y) )
| ? [Y] :
( ~ sP0_prd(Y)
& rr(X,Y) )
| ? [Y] :
( ~ cd(Y)
& rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ? [Y] :
( ? [Z0,Z1] :
( Z0 != Z1
& rs(Y,Z1)
& rs(Y,Z0) )
& rr(X,Y) )
& ! [Y] :
( sP0_prd(Y)
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
( ! [X] :
( ! [Y] :
( ! [Z0,Z1] :
( Z0 = Z1
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ rr(X,Y) )
| ? [Y] :
( ~ sP0_prd(Y)
& rr(X,Y) )
| ? [Y] :
( ~ cd(Y)
& rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ? [Y] :
( ? [Z0,Z1] :
( Z0 != Z1
& rs(Y,Z1)
& rs(Y,Z0) )
& rr(X,Y) )
& ! [Y] :
( sP0_prd(Y)
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [X] :
( ! [Y] :
( ! [Z0,Z1] :
( Z0 = Z1
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ rr(X,Y) )
| ( ~ sP0_prd(sK4_skl(X))
& rr(X,sK4_skl(X)) )
| ( ~ cd(sK3_skl(X))
& rr(X,sK3_skl(X)) )
| cUnsatisfiable(X) )
& ! [X] :
( ( sK1_skl(X) != sK2_skl(X)
& rs(sK0_skl(X),sK2_skl(X))
& rs(sK0_skl(X),sK1_skl(X))
& rr(X,sK0_skl(X))
& ! [Y] :
( sP0_prd(Y)
| ~ rr(X,Y) )
& ! [Y] :
( cd(Y)
| ~ rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(Y,sK0_skl(X)),skolemize(Z0,sK1_skl(X)),skolemize(Z1,sK2_skl(X)),skolemize(Y,sK3_skl(X)),skolemize(Y,sK4_skl(X))],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( cd(X1)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( sP0_prd(X1)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f66,plain,
! [X0] :
( rs(sK0_skl(X0),sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f67,plain,
! [X0] :
( rs(sK0_skl(X0),sK2_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f68,plain,
! [X0] :
( sK1_skl(X0) != sK2_skl(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f73,plain,
! [X] :
( ~ cd(X)
| ~ cc(X) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f74,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
cUnsatisfiable(i2003_11_14_17_20_36582),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f76,plain,
! [Y] :
( ( ( ~ cc(Y)
& ? [Z0,Z1] :
( Z0 != Z1
& rs(Y,Z1)
& rs(Y,Z0) ) )
| sP0_prd(Y) )
& ( cc(Y)
| ! [Z0,Z1] :
( Z0 = Z1
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ sP0_prd(Y) ) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f77,plain,
( ! [Y] :
( ( ~ cc(Y)
& ? [Z0,Z1] :
( Z0 != Z1
& rs(Y,Z1)
& rs(Y,Z0) ) )
| sP0_prd(Y) )
& ! [Y] :
( cc(Y)
| ! [Z0,Z1] :
( Z0 = Z1
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ sP0_prd(Y) ) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f78,plain,
( ! [Y] :
( ( ~ cc(Y)
& sK5_skl(Y) != sK6_skl(Y)
& rs(Y,sK6_skl(Y))
& rs(Y,sK5_skl(Y)) )
| sP0_prd(Y) )
& ! [Y] :
( cc(Y)
| ! [Z0,Z1] :
( Z0 = Z1
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ sP0_prd(Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(Z0,sK5_skl(Y)),skolemize(Z1,sK6_skl(Y))],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( cc(X0)
| X1 = X2
| ~ rs(X0,X2)
| ~ rs(X0,X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f85,plain,
! [X0] :
( cd(sK0_skl(X0))
| ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f65,f63]) ).
fof(f86,plain,
! [X0] :
( cd(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sP0_prd(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f64,f65]) ).
fof(f88,plain,
! [X0] :
( sP0_prd(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| cc(sK0_skl(X0))
| X1 = sK2_skl(X0)
| ~ rs(sK0_skl(X0),X1)
| ~ sP0_prd(sK0_skl(X0)) ),
inference(resolution,[status(thm)],[f79,f67]) ).
fof(f93,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| cc(sK0_skl(X0))
| X1 = sK2_skl(X0)
| ~ rs(sK0_skl(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f88]) ).
fof(f96,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ cUnsatisfiable(X0)
| cc(sK0_skl(X0))
| sK1_skl(X0) = sK2_skl(X0) ),
inference(resolution,[status(thm)],[f93,f66]) ).
fof(f99,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cc(sK0_skl(X0))
| sK1_skl(X0) = sK2_skl(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f96]) ).
fof(f100,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| cc(sK0_skl(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f68]) ).
fof(f104,plain,
! [X0] :
( ~ cd(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f100,f74]) ).
fof(f105,plain,
! [X0] : ~ cUnsatisfiable(X0),
inference(forward_subsumption_resolution,[status(thm)],[f104,f86]) ).
fof(f108,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f75,f105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KRS101+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/5.52 % Computer : n012.cluster.edu
% 0.05/5.52 % Model : x86_64 x86_64
% 0.05/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.52 % Memory : 8046.5625MB
% 0.05/5.52 % OS : Linux 6.8.0-71-generic
% 0.05/5.52 % CPULimit : 300
% 0.05/5.52 % WCLimit : 300
% 0.05/5.52 % DateTime : Sun Sep 20 22:53:31 UTC 2026
% 0.05/5.52 % CPUTime :
% 0.05/5.52 % Drodi V4.1.1
% 0.05/5.54 % Refutation found
% 0.05/5.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.05/5.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.05/5.55 % Elapsed time: 0.024590 seconds
% 0.05/5.55 % CPU time: 0.054313 seconds
% 0.05/5.55 % Total memory used: 2.465 MB
% 0.05/5.55 % Net memory used: 2.371 MB
%------------------------------------------------------------------------------