%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 01:08:05 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 7 unt; 7 def)
% Number of atoms : 319 ( 0 equ)
% Maximal formula atoms : 31 ( 6 avg)
% Number of connectives : 504 ( 233 ~; 195 |; 69 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 165 ( 131 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( p1(X)
| ~ r1(Y,X) )
| p1(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ! [X] :
( $false
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ! [Y] :
( ~ ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ~ p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( p1(X)
| ~ r1(Y,X) )
| p1(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ! [X] :
( $false
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ! [Y] :
( ~ ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ~ p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X] :
( ? [Y] :
( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ p1(Y)
& r1(X,Y) )
& ! [Y] :
( ? [X] :
( $true
& r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ? [X] :
( ~ p1(X)
& r1(Y,X) )
| ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ? [X] :
( ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
& r1(Y,X) )
| ! [X] :
( ! [Y] :
( ? [X] :
( p1(X)
& r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ p1(Y)
| ! [X] :
( ? [Y] :
( p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( p1(Y)
| ! [X] :
( ? [Y] :
( ~ p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [Y,X] :
( sP0_prd(X,Y)
<=> ( p1(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
? [X] :
( ? [Y] :
( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ p1(Y)
& r1(X,Y) )
& ! [Y] :
( ? [X] :
( $true
& r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ? [X] :
( ~ p1(X)
& r1(Y,X) )
| ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ? [X] :
( ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
& r1(Y,X) )
| ! [X] :
( ! [Y] :
( ? [X] : sP0_prd(X,Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ p1(Y)
| ! [X] :
( ? [Y] :
( p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( p1(Y)
| ! [X] :
( ? [Y] :
( ~ p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
? [X] :
( ? [Y] :
( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ p1(Y)
& r1(X,Y) )
& ! [Y] :
( ( $true
& ? [X] : r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ? [X] :
( ~ p1(X)
& r1(Y,X) )
| ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ? [X] :
( ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
& r1(Y,X) )
| ! [X] :
( ! [Y] :
( ? [X] : sP0_prd(X,Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ p1(Y)
| ! [X] :
( ? [Y] :
( p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
& ! [Y] :
( p1(Y)
| ! [X] :
( ? [Y] :
( ~ p1(Y)
& r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f7,plain,
( ! [X] :
( p1(X)
| ~ r1(sK7_skl,X) )
& ~ p1(sK7_skl)
& r1(sK0_skl,sK7_skl)
& ! [Y] :
( ( $true
& r1(Y,sK6_skl(Y)) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( ( ~ p1(sK5_skl(Y))
& r1(Y,sK5_skl(Y)) )
| ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( ( ! [Y] :
( ~ p1(Y)
| ~ r1(sK4_skl(Y),Y) )
& r1(Y,sK4_skl(Y)) )
| ! [X] :
( ! [Y] :
( sP0_prd(sK3_skl(Y,X,Y),Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( ~ p1(Y)
| ! [X] :
( ( p1(sK2_skl(X,Y))
& r1(X,sK2_skl(X,Y)) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( p1(Y)
| ! [X] :
( ( ~ p1(sK1_skl(X,Y))
& r1(X,sK1_skl(X,Y)) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl(X,Y)),skolemize(Y,sK2_skl(X,Y)),skolemize(X,sK3_skl(Y,X,Y)),skolemize(X,sK4_skl(Y)),skolemize(X,sK5_skl(Y)),skolemize(X,sK6_skl(Y)),skolemize(Y,sK7_skl)],[f6]) ).
fof(f8,plain,
? [X] :
( ? [Y] :
( ! [X] :
( p1(X)
| ~ r1(sK7_skl,X) )
& ~ p1(sK7_skl)
& r1(sK0_skl,sK7_skl) )
& ! [Y] :
( ? [X] : r1(Y,sK6_skl(Y))
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( ? [X] :
( ~ p1(sK5_skl(Y))
& r1(Y,sK5_skl(Y)) )
| ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( ? [X] :
( ! [Y] :
( ~ p1(Y)
| ~ r1(sK4_skl(Y),Y) )
& r1(Y,sK4_skl(Y)) )
| ! [X] :
( ! [Y] :
( ? [X] : sP0_prd(sK3_skl(Y,X,Y),Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( ~ p1(Y)
| ! [X] :
( ? [Y] :
( p1(sK2_skl(X,Y))
& r1(X,sK2_skl(X,Y)) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) )
& ! [Y] :
( p1(Y)
| ! [X] :
( ? [Y] :
( ~ p1(sK1_skl(X,Y))
& r1(X,sK1_skl(X,Y)) )
| ~ r1(Y,X) )
| ~ r1(sK0_skl,Y) ) ),
inference(true_and_false_simplification,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( p1(X0)
| r1(X1,sK1_skl(X1,X0))
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( p1(X0)
| ~ p1(sK1_skl(X1,X0))
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f15,plain,
! [X0,X1,X2] :
( r1(X0,sK5_skl(X0))
| p1(X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ p1(sK5_skl(X0))
| p1(X2)
| ~ r1(X1,X2)
| ~ r1(X0,X1)
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f17,plain,
! [X0] :
( r1(X0,sK6_skl(X0))
| ~ r1(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
r1(sK0_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f19,plain,
~ p1(sK7_skl),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0] :
( p1(X0)
| ~ r1(sK7_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0] :
( p1(sK7_skl)
| r1(X0,sK1_skl(X0,sK7_skl))
| ~ r1(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f9,f18]) ).
fof(f27,definition,
! [X0] :
( sQ0_spl
<=> ( r1(X0,sK1_skl(X0,sK7_skl))
| ~ r1(sK7_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f28,plain,
! [X0] :
( ~ sQ0_spl
| r1(X0,sK1_skl(X0,sK7_skl))
| ~ r1(sK7_skl,X0) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,definition,
( sQ1_spl
<=> p1(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f31,plain,
( ~ sQ1_spl
| p1(sK7_skl) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f26,f27,f30]) ).
fof(f34,plain,
r1(sK7_skl,sK6_skl(sK7_skl)),
inference(resolution,[status(thm)],[f17,f18]) ).
fof(f37,plain,
( ~ sQ0_spl
| r1(sK6_skl(sK7_skl),sK1_skl(sK6_skl(sK7_skl),sK7_skl)) ),
inference(resolution,[status(thm)],[f28,f34]) ).
fof(f45,plain,
! [X0,X1] :
( r1(sK7_skl,sK5_skl(sK7_skl))
| p1(X1)
| ~ r1(X0,X1)
| ~ r1(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f15,f18]) ).
fof(f46,definition,
! [X0,X1] :
( sQ3_spl
<=> ( p1(X1)
| ~ r1(X0,X1)
| ~ r1(sK7_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f47,plain,
! [X0,X1] :
( ~ sQ3_spl
| p1(X1)
| ~ r1(X0,X1)
| ~ r1(sK7_skl,X0) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
( sQ4_spl
<=> r1(sK7_skl,sK5_skl(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ4_spl
| r1(sK7_skl,sK5_skl(sK7_skl)) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f45,f46,f49]) ).
fof(f53,plain,
! [X0] :
( ~ sQ3_spl
| p1(X0)
| ~ r1(sK6_skl(sK7_skl),X0) ),
inference(resolution,[status(thm)],[f47,f34]) ).
fof(f55,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| p1(sK1_skl(sK6_skl(sK7_skl),sK7_skl)) ),
inference(resolution,[status(thm)],[f53,f37]) ).
fof(f57,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| p1(sK7_skl)
| ~ r1(sK7_skl,sK6_skl(sK7_skl))
| ~ r1(sK0_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f55,f10]) ).
fof(f59,definition,
( sQ5_spl
<=> r1(sK0_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( sQ5_spl
| ~ r1(sK0_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,definition,
( sQ6_spl
<=> r1(sK7_skl,sK6_skl(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( sQ6_spl
| ~ r1(sK7_skl,sK6_skl(sK7_skl)) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f57,f59,f62,f30,f46,f27]) ).
fof(f66,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f19]) ).
fof(f67,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f66]) ).
fof(f68,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f34]) ).
fof(f69,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f68]) ).
fof(f70,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f18]) ).
fof(f71,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( ~ sQ4_spl
| p1(sK5_skl(sK7_skl)) ),
inference(resolution,[status(thm)],[f50,f20]) ).
fof(f73,plain,
! [X0,X1] :
( ~ sQ4_spl
| p1(X1)
| ~ r1(X0,X1)
| ~ r1(sK7_skl,X0)
| ~ r1(sK0_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f72,f16]) ).
fof(f75,plain,
( ~ sQ4_spl
| sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f73,f59,f46,f49]) ).
fof(f76,plain,
$false,
inference(sat_refutation,[status(thm)],[f33,f52,f65,f67,f69,f71,f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 00:45:35 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.53 % Elapsed time: 0.069442 seconds
% 0.18/0.53 % CPU time: 0.083917 seconds
% 0.18/0.53 % Total memory used: 3.811 MB
% 0.18/0.53 % Net memory used: 3.754 MB
%------------------------------------------------------------------------------