%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS099+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 : n019.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 0.08s 0.55s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 4 unt; 2 def)
% Number of atoms : 147 ( 45 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 198 ( 71 ~; 60 |; 59 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-1 aty)
% Number of variables : 90 ( 65 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( ( rtt(X,Y1)
& rtt(X,Y0) )
=> Y0 = Y1 )
& ! [Y0,Y1] :
( ( rtt(X,Y1)
& rtt(X,Y0) )
=> Y0 = Y1 )
& ! [Y] :
( rtt(X,Y)
=> ca(Y) )
& ? [Y0,Y1,Y2] :
( Y1 != Y2
& Y0 != Y2
& Y0 != Y1
& rtt(X,Y2)
& rtt(X,Y1)
& rtt(X,Y0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
cUnsatisfiable(i2003_11_14_17_20_29215),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) )
& ! [Y0,Y1] :
( Y0 = Y1
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) )
& ! [Y] :
( ca(Y)
| ~ rtt(X,Y) )
& ? [Y0,Y1,Y2] :
( Y1 != Y2
& Y0 != Y2
& Y0 != Y1
& rtt(X,Y2)
& rtt(X,Y1)
& rtt(X,Y0) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f55,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( ca(Y)
| ~ rtt(X,Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f56,definition,
! [X,Y0,Y1] :
( sP1_prd(Y1,Y0,X)
<=> ( Y0 = Y1
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f57,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) )
& ! [Y0,Y1] : sP1_prd(Y1,Y0,X)
& ! [Y] : sP0_prd(Y,X)
& ? [Y0,Y1,Y2] :
( Y1 != Y2
& Y0 != Y2
& Y0 != Y1
& rtt(X,Y2)
& rtt(X,Y1)
& rtt(X,Y0) ) ) ),
inference(formula_renaming,[status(thm)],[f54,f56,f55]) ).
fof(f58,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rtt(X,Y1)
& rtt(X,Y0) )
| ? [Y0,Y1] : ~ sP1_prd(Y1,Y0,X)
| ? [Y] : ~ sP0_prd(Y,X)
| ! [Y0,Y1,Y2] :
( Y1 = Y2
| Y0 = Y2
| Y0 = Y1
| ~ rtt(X,Y2)
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) )
| cUnsatisfiable(X) )
& ( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) )
& ! [Y0,Y1] : sP1_prd(Y1,Y0,X)
& ! [Y] : sP0_prd(Y,X)
& ? [Y0,Y1,Y2] :
( Y1 != Y2
& Y0 != Y2
& Y0 != Y1
& rtt(X,Y2)
& rtt(X,Y1)
& rtt(X,Y0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
( ! [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rtt(X,Y1)
& rtt(X,Y0) )
| ? [Y0,Y1] : ~ sP1_prd(Y1,Y0,X)
| ? [Y] : ~ sP0_prd(Y,X)
| ! [Y1,Y2] :
( Y1 = Y2
| ! [Y0] :
( Y0 = Y2
| Y0 = Y1
| ~ rtt(X,Y2)
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) ) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) )
& ! [Y0,Y1] : sP1_prd(Y1,Y0,X)
& ! [Y] : sP0_prd(Y,X)
& ? [Y1,Y2] :
( Y1 != Y2
& ? [Y0] :
( Y0 != Y2
& Y0 != Y1
& rtt(X,Y2)
& rtt(X,Y1)
& rtt(X,Y0) ) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
( ! [X] :
( ( sK6_skl(X) != sK7_skl(X)
& rtt(X,sK7_skl(X))
& rtt(X,sK6_skl(X)) )
| ~ sP1_prd(sK5_skl(X),sK4_skl(X),X)
| ~ sP0_prd(sK3_skl(X),X)
| ! [Y1,Y2] :
( Y1 = Y2
| ! [Y0] :
( Y0 = Y2
| Y0 = Y1
| ~ rtt(X,Y2)
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) ) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rtt(X,Y1)
| ~ rtt(X,Y0) )
& ! [Y0,Y1] : sP1_prd(Y1,Y0,X)
& ! [Y] : sP0_prd(Y,X)
& sK0_skl(X) != sK1_skl(X)
& sK2_skl(X) != sK1_skl(X)
& sK2_skl(X) != sK0_skl(X)
& rtt(X,sK1_skl(X))
& rtt(X,sK0_skl(X))
& rtt(X,sK2_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(Y1,sK0_skl(X)),skolemize(Y2,sK1_skl(X)),skolemize(Y0,sK2_skl(X)),skolemize(Y,sK3_skl(X)),skolemize(Y0,sK4_skl(X)),skolemize(Y1,sK5_skl(X)),skolemize(Y0,sK6_skl(X)),skolemize(Y1,sK7_skl(X))],[f59]) ).
fof(f62,plain,
! [X0] :
( rtt(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
! [X0] :
( rtt(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f66,plain,
! [X0] :
( sK0_skl(X0) != sK1_skl(X0)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f69,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rtt(X0,X2)
| ~ rtt(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f77,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f91,plain,
! [X0,X1] :
( ~ cUnsatisfiable(X0)
| X1 = sK1_skl(X0)
| ~ rtt(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f69,f63]) ).
fof(f95,plain,
! [X0,X1] :
( X1 = sK1_skl(X0)
| ~ rtt(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f91]) ).
fof(f109,plain,
! [X0] :
( ~ cUnsatisfiable(X0)
| sK0_skl(X0) = sK1_skl(X0)
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f95,f62]) ).
fof(f112,plain,
! [X0] :
( sK0_skl(X0) = sK1_skl(X0)
| ~ cUnsatisfiable(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f109]) ).
fof(f113,plain,
! [X0] : ~ cUnsatisfiable(X0),
inference(forward_subsumption_resolution,[status(thm)],[f112,f66]) ).
fof(f117,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f77,f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS099+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.52 % Computer : n019.cluster.edu
% 0.08/0.52 % Model : x86_64 x86_64
% 0.08/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.52 % Memory : 8046.5625MB
% 0.08/0.52 % OS : Linux 6.8.0-71-generic
% 0.08/0.52 % CPULimit : 300
% 0.08/0.52 % WCLimit : 300
% 0.08/0.52 % DateTime : Sun Sep 20 22:53:54 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.53 % Drodi V4.1.1
% 0.08/0.55 % Refutation found
% 0.08/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.56 % Elapsed time: 0.033630 seconds
% 0.14/0.56 % CPU time: 0.080461 seconds
% 0.14/0.56 % Total memory used: 2.540 MB
% 0.14/0.56 % Net memory used: 2.444 MB
%------------------------------------------------------------------------------