%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS071+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:59:37 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 13 unt; 6 def)
% Number of atoms : 242 ( 54 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 296 ( 112 ~; 118 |; 55 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 78 ( 60 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1,Y2] :
( ( rr(X,Y2)
& rr(X,Y1)
& rr(X,Y0) )
=> ( Y1 = Y2
| Y0 = Y2
| Y0 = Y1 ) )
& ? [Y] :
( cp3(Y)
& rr(X,Y) )
& ? [Y] :
( cp2(Y)
& rr(X,Y) )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] :
( cp1(X)
=> ~ ( cp5(X)
| cp3(X)
| cp2(X)
| cp4(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] :
( cp2(X)
=> ~ ( cp5(X)
| cp3(X)
| cp4(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
cUnsatisfiable(i2003_11_14_17_18_39380),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1,Y2] :
( Y1 = Y2
| Y0 = Y2
| Y0 = Y1
| ~ rr(X,Y2)
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cp3(Y)
& rr(X,Y) )
& ? [Y] :
( cp2(Y)
& rr(X,Y) )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f74,plain,
! [X] :
( ( ? [Y0,Y1,Y2] :
( Y1 != Y2
& Y0 != Y2
& Y0 != Y1
& rr(X,Y2)
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ! [Y0,Y1,Y2] :
( Y1 = Y2
| Y0 = Y2
| Y0 = Y1
| ~ rr(X,Y2)
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cp3(Y)
& rr(X,Y) )
& ? [Y] :
( cp2(Y)
& rr(X,Y) )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
( ! [X] :
( ? [Y0,Y1,Y2] :
( Y1 != Y2
& Y0 != Y2
& Y0 != Y1
& rr(X,Y2)
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y0,Y1,Y2] :
( Y1 = Y2
| Y0 = Y2
| Y0 = Y1
| ~ rr(X,Y2)
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cp3(Y)
& rr(X,Y) )
& ? [Y] :
( cp2(Y)
& rr(X,Y) )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f76,plain,
( ! [X] :
( ( sK4_skl(X) != sK5_skl(X)
& sK3_skl(X) != sK5_skl(X)
& sK3_skl(X) != sK4_skl(X)
& rr(X,sK5_skl(X))
& rr(X,sK4_skl(X))
& rr(X,sK3_skl(X)) )
| ! [Y] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y0,Y1,Y2] :
( Y1 = Y2
| Y0 = Y2
| Y0 = Y1
| ~ rr(X,Y2)
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& cp3(sK2_skl(X))
& rr(X,sK2_skl(X))
& cp2(sK1_skl(X))
& rr(X,sK1_skl(X))
& cp1(sK0_skl(X))
& rr(X,sK0_skl(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X)),skolemize(Y,sK2_skl(X)),skolemize(Y0,sK3_skl(X)),skolemize(Y1,sK4_skl(X)),skolemize(Y2,sK5_skl(X))],[f75]) ).
fof(f77,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0] :
( cp1(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
! [X0] :
( rr(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [X0] :
( cp2(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,plain,
! [X0] :
( rr(X0,sK2_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f82,plain,
! [X0] :
( cp3(sK2_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| X1 = X3
| X1 = X2
| ~ rr(X0,X3)
| ~ rr(X0,X2)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f90,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp3(X)
& ~ cp2(X)
& ~ cp4(X) )
| ~ cp1(X) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f92,plain,
! [X0] :
( ~ cp2(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f93,plain,
! [X0] :
( ~ cp3(X0)
| ~ cp1(X0) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f95,plain,
! [X] :
( ( ~ cp5(X)
& ~ cp3(X)
& ~ cp4(X) )
| ~ cp2(X) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f97,plain,
! [X0] :
( ~ cp3(X0)
| ~ cp2(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f108,plain,
cUnsatisfiable(i2003_11_14_17_18_39380),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f109,plain,
cp1(sK0_skl(i2003_11_14_17_18_39380)),
inference(resolution,[status(thm)],[f78,f108]) ).
fof(f111,plain,
~ cp3(sK0_skl(i2003_11_14_17_18_39380)),
inference(resolution,[status(thm)],[f109,f93]) ).
fof(f112,plain,
~ cp2(sK0_skl(i2003_11_14_17_18_39380)),
inference(resolution,[status(thm)],[f109,f92]) ).
fof(f114,plain,
cp2(sK1_skl(i2003_11_14_17_18_39380)),
inference(resolution,[status(thm)],[f80,f108]) ).
fof(f116,plain,
~ cp3(sK1_skl(i2003_11_14_17_18_39380)),
inference(resolution,[status(thm)],[f114,f97]) ).
fof(f118,plain,
cp3(sK2_skl(i2003_11_14_17_18_39380)),
inference(resolution,[status(thm)],[f82,f108]) ).
fof(f121,plain,
! [X0,X1,X2] :
( X1 = X2
| X0 = X2
| X0 = X1
| ~ rr(i2003_11_14_17_18_39380,X2)
| ~ rr(i2003_11_14_17_18_39380,X1)
| ~ rr(i2003_11_14_17_18_39380,X0) ),
inference(resolution,[status(thm)],[f83,f108]) ).
fof(f124,plain,
! [X0,X1] :
( ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| sK2_skl(i2003_11_14_17_18_39380) = X1
| X0 = X1
| X0 = sK2_skl(i2003_11_14_17_18_39380)
| ~ rr(i2003_11_14_17_18_39380,X1)
| ~ rr(i2003_11_14_17_18_39380,X0) ),
inference(resolution,[status(thm)],[f121,f81]) ).
fof(f138,definition,
( sQ2_spl
<=> cUnsatisfiable(i2003_11_14_17_18_39380) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ2_spl
| ~ cUnsatisfiable(i2003_11_14_17_18_39380) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f142,definition,
! [X0,X1] :
( sQ3_spl
<=> ( sK2_skl(i2003_11_14_17_18_39380) = X1
| X0 = X1
| X0 = sK2_skl(i2003_11_14_17_18_39380)
| ~ rr(i2003_11_14_17_18_39380,X1)
| ~ rr(i2003_11_14_17_18_39380,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ3_spl
| sK2_skl(i2003_11_14_17_18_39380) = X1
| X0 = X1
| X0 = sK2_skl(i2003_11_14_17_18_39380)
| ~ rr(i2003_11_14_17_18_39380,X1)
| ~ rr(i2003_11_14_17_18_39380,X0) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( ~ sQ2_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f124,f142,f138]) ).
fof(f171,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f108]) ).
fof(f172,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f180,definition,
( sQ10_spl
<=> sK1_skl(i2003_11_14_17_18_39380) = sK2_skl(i2003_11_14_17_18_39380) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ10_spl
| sK1_skl(i2003_11_14_17_18_39380) = sK2_skl(i2003_11_14_17_18_39380) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f184,definition,
( sQ11_spl
<=> sK0_skl(i2003_11_14_17_18_39380) = sK2_skl(i2003_11_14_17_18_39380) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ11_spl
| sK0_skl(i2003_11_14_17_18_39380) = sK2_skl(i2003_11_14_17_18_39380) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f189,plain,
( ~ sQ10_spl
| ~ cp3(sK2_skl(i2003_11_14_17_18_39380)) ),
inference(backward_demodulation,[status(thm)],[f181,f116]) ).
fof(f193,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f118]) ).
fof(f194,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f205,definition,
( sQ12_spl
<=> sK0_skl(i2003_11_14_17_18_39380) = sK1_skl(i2003_11_14_17_18_39380) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ12_spl
| sK0_skl(i2003_11_14_17_18_39380) = sK1_skl(i2003_11_14_17_18_39380) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f218,plain,
( ~ sQ11_spl
| ~ cp3(sK2_skl(i2003_11_14_17_18_39380)) ),
inference(backward_demodulation,[status(thm)],[f185,f111]) ).
fof(f222,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f118]) ).
fof(f223,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f231,plain,
! [X0] :
( ~ sQ3_spl
| ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| sK2_skl(i2003_11_14_17_18_39380) = sK1_skl(i2003_11_14_17_18_39380)
| X0 = sK1_skl(i2003_11_14_17_18_39380)
| X0 = sK2_skl(i2003_11_14_17_18_39380)
| ~ rr(i2003_11_14_17_18_39380,X0) ),
inference(resolution,[status(thm)],[f143,f79]) ).
fof(f234,definition,
! [X0] :
( sQ13_spl
<=> ( X0 = sK1_skl(i2003_11_14_17_18_39380)
| X0 = sK2_skl(i2003_11_14_17_18_39380)
| ~ rr(i2003_11_14_17_18_39380,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f235,plain,
! [X0] :
( ~ sQ13_spl
| X0 = sK1_skl(i2003_11_14_17_18_39380)
| X0 = sK2_skl(i2003_11_14_17_18_39380)
| ~ rr(i2003_11_14_17_18_39380,X0) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f231,f234,f180,f138,f142]) ).
fof(f244,plain,
( ~ sQ13_spl
| ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| sK0_skl(i2003_11_14_17_18_39380) = sK1_skl(i2003_11_14_17_18_39380)
| sK0_skl(i2003_11_14_17_18_39380) = sK2_skl(i2003_11_14_17_18_39380) ),
inference(resolution,[status(thm)],[f235,f77]) ).
fof(f247,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f244,f184,f205,f138,f234]) ).
fof(f252,plain,
( ~ sQ12_spl
| ~ cp2(sK1_skl(i2003_11_14_17_18_39380)) ),
inference(backward_demodulation,[status(thm)],[f206,f112]) ).
fof(f255,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f114]) ).
fof(f256,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f255]) ).
fof(f257,plain,
$false,
inference(sat_refutation,[status(thm)],[f145,f172,f194,f223,f237,f247,f256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS071+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 22:52:51 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.41 % Elapsed time: 0.037447 seconds
% 0.11/0.41 % CPU time: 0.095491 seconds
% 0.11/0.41 % Total memory used: 3.121 MB
% 0.11/0.41 % Net memory used: 3.007 MB
%------------------------------------------------------------------------------