%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS181+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:59:52 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 7 unt; 2 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 106 ( 40 ~; 37 |; 21 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 69 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S1)
=> status(Ax,C,S2) )
<=> isa(S1,S2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [S1,S2] :
( ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) )
<=> nota(S1,S2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [S1,S2,S3] :
( ( nota(S1,S3)
& isa(S1,S2) )
=> nota(S2,S3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [S1,S2,S3] :
( ( nota(S1,S3)
& isa(S1,S2) )
=> nota(S2,S3) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f22,plain,
! [S1,S2] :
( ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) )
<=> isa(S1,S2) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [S1,S2] :
( ( ~ isa(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ( isa(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ! [S1,S2] :
( ~ isa(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ! [S1,S2] :
( isa(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [S1,S2] :
( ~ isa(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) )
& ! [S1,S2] :
( isa(S1,S2)
| ( ~ status(sK2_skl(S2,S1),sK3_skl(S2,S1),S2)
& status(sK2_skl(S2,S1),sK3_skl(S2,S1),S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(Ax,sK2_skl(S2,S1)),skolemize(C,sK3_skl(S2,S1))],[f24]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ isa(X2,X3)
| status(X0,X1,X3)
| ~ status(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [S1,S2] :
( ( ~ nota(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f30,plain,
( ! [S1,S2] :
( ~ nota(S1,S2)
| ? [Ax,C] :
( ~ status(Ax,C,S2)
& status(Ax,C,S1) ) )
& ! [S1,S2] :
( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( ! [S1,S2] :
( ~ nota(S1,S2)
| ( ~ status(sK4_skl(S2,S1),sK5_skl(S2,S1),S2)
& status(sK4_skl(S2,S1),sK5_skl(S2,S1),S1) ) )
& ! [S1,S2] :
( nota(S1,S2)
| ! [Ax,C] :
( status(Ax,C,S2)
| ~ status(Ax,C,S1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(Ax,sK4_skl(S2,S1)),skolemize(C,sK5_skl(S2,S1))],[f30]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( nota(X2,X3)
| status(X0,X1,X3)
| ~ status(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ nota(X1,X0)
| status(sK4_skl(X0,X1),sK5_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1] :
( ~ nota(X1,X0)
| ~ status(sK4_skl(X0,X1),sK5_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f82,plain,
? [S1,S2,S3] :
( ~ nota(S2,S3)
& nota(S1,S3)
& isa(S1,S2) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f83,plain,
? [S2,S3] :
( ~ nota(S2,S3)
& ? [S1] :
( nota(S1,S3)
& isa(S1,S2) ) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f84,plain,
( ~ nota(sK29_skl,sK30_skl)
& nota(sK31_skl,sK30_skl)
& isa(sK31_skl,sK29_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl]),skolemize(S2,sK29_skl),skolemize(S3,sK30_skl),skolemize(S1,sK31_skl)],[f83]) ).
fof(f85,plain,
isa(sK31_skl,sK29_skl),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
nota(sK31_skl,sK30_skl),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f87,plain,
~ nota(sK29_skl,sK30_skl),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f88,plain,
! [X0,X1,X2,X3,X4] :
( ~ isa(X4,X3)
| ~ status(X0,X1,X4)
| nota(X3,X2)
| status(X0,X1,X2) ),
inference(resolution,[status(thm)],[f32,f28]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ status(X0,X1,sK31_skl)
| nota(sK29_skl,X2)
| status(X0,X1,X2) ),
inference(resolution,[status(thm)],[f88,f85]) ).
fof(f100,plain,
status(sK4_skl(sK30_skl,sK31_skl),sK5_skl(sK30_skl,sK31_skl),sK31_skl),
inference(resolution,[status(thm)],[f33,f86]) ).
fof(f110,plain,
! [X0] :
( nota(sK29_skl,X0)
| status(sK4_skl(sK30_skl,sK31_skl),sK5_skl(sK30_skl,sK31_skl),X0) ),
inference(resolution,[status(thm)],[f100,f89]) ).
fof(f112,plain,
( ~ nota(sK31_skl,sK30_skl)
| nota(sK29_skl,sK30_skl) ),
inference(resolution,[status(thm)],[f110,f34]) ).
fof(f115,definition,
( sQ0_spl
<=> nota(sK29_skl,sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ0_spl
| nota(sK29_skl,sK30_skl) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
( sQ1_spl
<=> nota(sK31_skl,sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ1_spl
| ~ nota(sK31_skl,sK30_skl) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f112,f115,f118]) ).
fof(f129,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f87]) ).
fof(f130,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f86]) ).
fof(f132,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
$false,
inference(sat_refutation,[status(thm)],[f121,f130,f132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS181+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 22:53:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.042861 seconds
% 0.12/0.43 % CPU time: 0.091274 seconds
% 0.12/0.43 % Total memory used: 10.015 MB
% 0.12/0.43 % Net memory used: 9.736 MB
%------------------------------------------------------------------------------