%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 01:08:23 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 8 unt; 4 def)
% Number of atoms : 204 ( 0 equ)
% Maximal formula atoms : 37 ( 6 avg)
% Number of connectives : 310 ( 137 ~; 109 |; 60 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 38 ( 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,conjecture,
~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ ( p100(Y)
& ~ p101(Y) )
| ( ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& p2(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& ~ p2(X) )
| ~ r1(Y,X) ) ) ) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ ( p100(Y)
& ~ p101(Y) )
| ( ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& p2(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& ~ p2(X) )
| ~ r1(Y,X) ) ) ) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
? [X] :
( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X] :
( p101(X)
& ~ p102(X)
& p2(X)
& r1(Y,X) )
& ? [X] :
( p101(X)
& ~ p102(X)
& ~ p2(X)
& r1(Y,X) ) ) ) )
| ~ r1(X,Y) )
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f6,plain,
( p100(sK0_skl)
& ~ p101(sK0_skl)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p100(Y)
| p101(Y)
| ( p101(sK2_skl(Y))
& ~ p102(sK2_skl(Y))
& p2(sK2_skl(Y))
& r1(Y,sK2_skl(Y))
& p101(sK1_skl(Y))
& ~ p102(sK1_skl(Y))
& ~ p2(sK1_skl(Y))
& r1(Y,sK1_skl(Y)) ) ) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( p2(Y)
| ~ r1(sK0_skl,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y)),skolemize(X,sK2_skl(Y))],[f5]) ).
fof(f7,plain,
! [X0] :
( p2(X0)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ p100(X0)
| p101(X0)
| r1(X0,sK1_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0] :
( ~ p100(X0)
| p101(X0)
| ~ p2(sK1_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
~ p101(sK0_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
p100(sK0_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
( ~ p100(sK0_skl)
| p101(sK0_skl)
| r1(sK0_skl,sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f4,f8]) ).
fof(f26,definition,
( sQ0_spl
<=> r1(sK0_skl,sK1_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( ~ sQ0_spl
| r1(sK0_skl,sK1_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,definition,
( sQ1_spl
<=> p101(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( ~ sQ1_spl
| p101(sK0_skl) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,definition,
( sQ2_spl
<=> p100(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( sQ2_spl
| ~ p100(sK0_skl) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f24,f26,f29,f32]) ).
fof(f36,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f23]) ).
fof(f37,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( ~ sQ0_spl
| p2(sK1_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f27,f7]) ).
fof(f50,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f22]) ).
fof(f51,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f50]) ).
fof(f55,plain,
( ~ sQ0_spl
| ~ p100(sK0_skl)
| p101(sK0_skl)
| ~ r1(sK0_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f9,f39]) ).
fof(f56,definition,
( sQ6_spl
<=> r1(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ6_spl
| ~ r1(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| sQ1_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f55,f56,f29,f32,f26]) ).
fof(f60,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f4]) ).
fof(f61,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
$false,
inference(sat_refutation,[status(thm)],[f35,f37,f51,f59,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 00:46:48 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.40/0.51 % Elapsed time: 0.055962 seconds
% 0.40/0.51 % CPU time: 0.134717 seconds
% 0.40/0.51 % Total memory used: 17.087 MB
% 0.40/0.51 % Net memory used: 16.686 MB
%------------------------------------------------------------------------------