%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS096+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 : n018.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 12:59:40 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 4 unt; 4 def)
% Number of atoms : 132 ( 16 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 159 ( 63 ~; 58 |; 30 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 51 ( 39 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] :
( cc(X)
=> ~ cd(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
cUnsatisfiable(i2003_11_14_17_20_18265),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,plain,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f50,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
( ! [X] :
( ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) )
| ~ cUnsatisfiable(X) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
( ! [X] :
( ( sK2_skl(X) != sK3_skl(X)
& rr(X,sK3_skl(X))
& rr(X,sK2_skl(X)) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| cUnsatisfiable(X) )
& ! [X] :
( ( ! [Y0,Y1] :
( Y0 = Y1
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
& cd(sK1_skl(X))
& rr(X,sK1_skl(X))
& cc(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]),skolemize(Y,sK0_skl(X)),skolemize(Y,sK1_skl(X)),skolemize(Y0,sK2_skl(X)),skolemize(Y1,sK3_skl(X))],[f51]) ).
fof(f53,plain,
! [X0] :
( rr(X0,sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0] :
( cc(sK0_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X0] :
( rr(X0,sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
! [X0] :
( cd(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ rr(X0,X2)
| ~ rr(X0,X1)
| ~ cUnsatisfiable(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f61,plain,
! [X] :
( ~ cd(X)
| ~ cc(X) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f62,plain,
! [X0] :
( ~ cd(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
cUnsatisfiable(i2003_11_14_17_20_18265),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f64,plain,
! [X0] :
( ~ cc(sK1_skl(X0))
| ~ cUnsatisfiable(X0) ),
inference(resolution,[status(thm)],[f56,f62]) ).
fof(f65,plain,
! [X0,X1] :
( X0 = X1
| ~ rr(i2003_11_14_17_20_18265,X1)
| ~ rr(i2003_11_14_17_20_18265,X0) ),
inference(resolution,[status(thm)],[f57,f63]) ).
fof(f66,plain,
! [X0] :
( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| X0 = sK1_skl(i2003_11_14_17_20_18265)
| ~ rr(i2003_11_14_17_20_18265,X0) ),
inference(resolution,[status(thm)],[f65,f55]) ).
fof(f68,definition,
! [X0] :
( sQ0_spl
<=> ( X0 = sK1_skl(i2003_11_14_17_20_18265)
| ~ rr(i2003_11_14_17_20_18265,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f69,plain,
! [X0] :
( ~ sQ0_spl
| X0 = sK1_skl(i2003_11_14_17_20_18265)
| ~ rr(i2003_11_14_17_20_18265,X0) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,definition,
( sQ1_spl
<=> cUnsatisfiable(i2003_11_14_17_20_18265) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( sQ1_spl
| ~ cUnsatisfiable(i2003_11_14_17_20_18265) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f68,f71]) ).
fof(f79,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f63]) ).
fof(f80,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( ~ sQ0_spl
| ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| sK0_skl(i2003_11_14_17_20_18265) = sK1_skl(i2003_11_14_17_20_18265) ),
inference(resolution,[status(thm)],[f69,f53]) ).
fof(f87,definition,
( sQ4_spl
<=> sK0_skl(i2003_11_14_17_20_18265) = sK1_skl(i2003_11_14_17_20_18265) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ4_spl
| sK0_skl(i2003_11_14_17_20_18265) = sK1_skl(i2003_11_14_17_20_18265) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f82,f87,f71,f68]) ).
fof(f93,plain,
( ~ sQ4_spl
| ~ cc(sK0_skl(i2003_11_14_17_20_18265))
| ~ cUnsatisfiable(i2003_11_14_17_20_18265) ),
inference(paramodulation,[status(thm)],[f88,f64]) ).
fof(f99,definition,
( sQ6_spl
<=> cc(sK0_skl(i2003_11_14_17_20_18265)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ6_spl
| ~ cc(sK0_skl(i2003_11_14_17_20_18265)) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f93,f71,f99,f87]) ).
fof(f109,plain,
( sQ6_spl
| ~ cUnsatisfiable(i2003_11_14_17_20_18265) ),
inference(resolution,[status(thm)],[f101,f54]) ).
fof(f110,plain,
( sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f109,f71,f99]) ).
fof(f111,plain,
$false,
inference(sat_refutation,[status(thm)],[f74,f80,f90,f102,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS096+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:55:45 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.029410 seconds
% 0.12/0.38 % CPU time: 0.070846 seconds
% 0.12/0.38 % Total memory used: 1.820 MB
% 0.12/0.38 % Net memory used: 1.747 MB
%------------------------------------------------------------------------------