%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS126+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 : n010.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 0.11s 0.79s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 26 ~; 20 |; 6 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 38 ( 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( cUnsatisfiable(X)
=> cd1xcomp(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( cUnsatisfiable(X)
=> cd1(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( cd1(X)
<=> ? [Y0] : ra_Px2(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( cd1xcomp(X)
<=> ~ ? [Y] : ra_Px2(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
cUnsatisfiable(i2003_11_14_17_22_23554),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0] :
( cd1xcomp(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [X] :
( cd1(X)
| ~ cUnsatisfiable(X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0] :
( cd1(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f37,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px2(X,Y0)
| cd1(X) )
& ( ? [Y0] : ra_Px2(X,Y0)
| ~ cd1(X) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px2(X,Y0)
| cd1(X) )
& ! [X] :
( ? [Y0] : ra_Px2(X,Y0)
| ~ cd1(X) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [X] :
( ! [Y0] : ~ ra_Px2(X,Y0)
| cd1(X) )
& ! [X] :
( ra_Px2(X,sK2_skl(X))
| ~ cd1(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y0,sK2_skl(X))],[f38]) ).
fof(f40,plain,
! [X0] :
( ra_Px2(X0,sK2_skl(X0))
| ~ cd1(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X] :
( cd1xcomp(X)
<=> ! [Y] : ~ ra_Px2(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
! [X] :
( ( ? [Y] : ra_Px2(X,Y)
| cd1xcomp(X) )
& ( ! [Y] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [X] :
( ? [Y] : ra_Px2(X,Y)
| cd1xcomp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
( ! [X] :
( ra_Px2(X,sK3_skl(X))
| cd1xcomp(X) )
& ! [X] :
( ! [Y] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ~ ra_Px2(X0,X1)
| ~ cd1xcomp(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f52,plain,
cUnsatisfiable(i2003_11_14_17_22_23554),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f53,plain,
! [X0] :
( ~ cd1xcomp(X0)
| ~ cd1(X0) ),
inference(resolution,[status(thm)],[f40,f46]) ).
fof(f54,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| ~ cd1(X0) ),
inference(resolution,[status(thm)],[f53,f21]) ).
fof(f55,plain,
! [X0] : ~ cUnsatisfiable(X0),
inference(forward_subsumption_resolution,[status(thm)],[f54,f23]) ).
fof(f57,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f52,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS126+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.77 % Computer : n010.cluster.edu
% 0.11/0.77 % Model : x86_64 x86_64
% 0.11/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.77 % Memory : 8046.5625MB
% 0.11/0.77 % OS : Linux 6.8.0-71-generic
% 0.11/0.77 % CPULimit : 300
% 0.11/0.77 % WCLimit : 300
% 0.11/0.77 % DateTime : Sun Sep 20 22:54:13 UTC 2026
% 0.11/0.77 % CPUTime :
% 0.11/0.77 % Drodi V4.1.1
% 0.11/0.79 % Refutation found
% 0.11/0.79 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.80 % Elapsed time: 0.029668 seconds
% 0.15/0.80 % CPU time: 0.069262 seconds
% 0.15/0.80 % Total memory used: 1.322 MB
% 0.15/0.80 % Net memory used: 1.301 MB
%------------------------------------------------------------------------------