%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL636+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 : n003.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 01:08:04 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 5 unt; 4 def)
% Number of atoms : 322 ( 0 equ)
% Maximal formula atoms : 69 ( 11 avg)
% Number of connectives : 521 ( 226 ~; 177 |; 114 &)
% ( 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 : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 56 ( 49 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ( ~ p101(X)
| p100(X) )
& ( ~ p102(X)
| p101(X) )
& ( ~ p100(X)
| ( ( ~ p1(X)
| ! [Y] :
( ~ p100(Y)
| p1(Y)
| ~ r1(X,Y) ) )
& ( p1(X)
| ! [Y] :
( ~ p100(Y)
| ~ p1(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ p101(X)
| ( ( ~ p2(X)
| ! [Y] :
( ~ p101(Y)
| p2(Y)
| ~ r1(X,Y) ) )
& ( p2(X)
| ! [Y] :
( ~ p101(Y)
| ~ p2(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ ( p100(X)
& ~ p101(X) )
| ( ~ ! [Y] :
( ~ ( p101(Y)
& ~ p102(Y)
& p2(Y) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ( p101(Y)
& ~ p102(Y)
& ~ p2(Y) )
| ~ r1(X,Y) ) ) )
& ! [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(f2,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ( ~ p101(X)
| p100(X) )
& ( ~ p102(X)
| p101(X) )
& ( ~ p100(X)
| ( ( ~ p1(X)
| ! [Y] :
( ~ p100(Y)
| p1(Y)
| ~ r1(X,Y) ) )
& ( p1(X)
| ! [Y] :
( ~ p100(Y)
| ~ p1(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ p101(X)
| ( ( ~ p2(X)
| ! [Y] :
( ~ p101(Y)
| p2(Y)
| ~ r1(X,Y) ) )
& ( p2(X)
| ! [Y] :
( ~ p101(Y)
| ~ p2(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ ( p100(X)
& ~ p101(X) )
| ( ~ ! [Y] :
( ~ ( p101(Y)
& ~ p102(Y)
& p2(Y) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ( p101(Y)
& ~ p102(Y)
& ~ p2(Y) )
| ~ r1(X,Y) ) ) )
& ! [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)],[f1]) ).
fof(f3,plain,
? [X] :
( p100(X)
& ~ p101(X)
& ( ~ p101(X)
| p100(X) )
& ( ~ p102(X)
| p101(X) )
& ( ~ p100(X)
| ( ( ~ p1(X)
| ! [Y] :
( ~ p100(Y)
| p1(Y)
| ~ r1(X,Y) ) )
& ( p1(X)
| ! [Y] :
( ~ p100(Y)
| ~ p1(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ p101(X)
| ( ( ~ p2(X)
| ! [Y] :
( ~ p101(Y)
| p2(Y)
| ~ r1(X,Y) ) )
& ( p2(X)
| ! [Y] :
( ~ p101(Y)
| ~ p2(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ p100(X)
| p101(X)
| ( ? [Y] :
( p101(Y)
& ~ p102(Y)
& p2(Y)
& r1(X,Y) )
& ? [Y] :
( p101(Y)
& ~ p102(Y)
& ~ p2(Y)
& r1(X,Y) ) ) )
& ! [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)],[f2]) ).
fof(f4,plain,
( p100(sK0_skl)
& ~ p101(sK0_skl)
& ( ~ p101(sK0_skl)
| p100(sK0_skl) )
& ( ~ p102(sK0_skl)
| p101(sK0_skl) )
& ( ~ p100(sK0_skl)
| ( ( ~ p1(sK0_skl)
| ! [Y] :
( ~ p100(Y)
| p1(Y)
| ~ r1(sK0_skl,Y) ) )
& ( p1(sK0_skl)
| ! [Y] :
( ~ p100(Y)
| ~ p1(Y)
| ~ r1(sK0_skl,Y) ) ) ) )
& ( ~ p101(sK0_skl)
| ( ( ~ p2(sK0_skl)
| ! [Y] :
( ~ p101(Y)
| p2(Y)
| ~ r1(sK0_skl,Y) ) )
& ( p2(sK0_skl)
| ! [Y] :
( ~ p101(Y)
| ~ p2(Y)
| ~ r1(sK0_skl,Y) ) ) ) )
& ( ~ p100(sK0_skl)
| p101(sK0_skl)
| ( p101(sK4_skl)
& ~ p102(sK4_skl)
& p2(sK4_skl)
& r1(sK0_skl,sK4_skl)
& p101(sK3_skl)
& ~ p102(sK3_skl)
& ~ p2(sK3_skl)
& r1(sK0_skl,sK3_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,sK3_skl,sK4_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y)),skolemize(X,sK2_skl(Y)),skolemize(Y,sK3_skl),skolemize(Y,sK4_skl)],[f3]) ).
fof(f5,plain,
! [X0] :
( p2(X0)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
( ~ p100(sK0_skl)
| p101(sK0_skl)
| r1(sK0_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
( ~ p100(sK0_skl)
| p101(sK0_skl)
| ~ p2(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
~ p101(sK0_skl),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f35,plain,
p100(sK0_skl),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,definition,
( sQ0_spl
<=> r1(sK0_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ0_spl
| r1(sK0_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ1_spl
<=> p101(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ1_spl
| p101(sK0_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
( sQ2_spl
<=> p100(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( sQ2_spl
| ~ p100(sK0_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f36,f39,f42]) ).
fof(f46,definition,
( sQ3_spl
<=> p2(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( sQ3_spl
| ~ p2(sK3_skl) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( ~ sQ2_spl
| sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f21,f46,f39,f42]) ).
fof(f101,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f34]) ).
fof(f102,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f103,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f35]) ).
fof(f104,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( ~ sQ0_spl
| p2(sK3_skl) ),
inference(resolution,[status(thm)],[f37,f5]) ).
fof(f114,plain,
( ~ sQ0_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f48]) ).
fof(f115,plain,
( ~ sQ0_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
$false,
inference(sat_refutation,[status(thm)],[f45,f49,f102,f104,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 00:43:15 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.045766 seconds
% 0.12/0.41 % CPU time: 0.131653 seconds
% 0.12/0.41 % Total memory used: 17.387 MB
% 0.12/0.41 % Net memory used: 17.180 MB
%------------------------------------------------------------------------------