%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL644+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 : n014.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 01:08:17 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 3 unt; 3 def)
% Number of atoms : 251 ( 0 equ)
% Maximal formula atoms : 53 ( 22 avg)
% Number of connectives : 367 ( 127 ~; 124 |; 113 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 12 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 91 ( 69 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) ) )
| p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) ) )
| p1(Y)
| ~ r1(X,Y) )
| ~ ( ~ ( ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p1(X)
& ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& p1(X) )
| p2(X)
| ~ r1(Y,X) )
| p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| ! [X] :
( p1(X)
| ~ ( ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) ) )
| p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) ) )
| p1(Y)
| ~ r1(X,Y) )
| ~ ( ~ ( ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p1(X)
& ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& p1(X) )
| p2(X)
| ~ r1(Y,X) )
| p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| ! [X] :
( p1(X)
| ~ ( ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y) )
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ~ ( ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| ~ r1(X,Y) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X] :
( ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ p1(Y)
& r1(X,Y) )
& ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ p1(Y)
& r1(X,Y) )
& ( ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y)
& ~ p2(Y)
& ~ p1(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p1(X)
& ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& p1(X)
& ~ p2(X)
& r1(Y,X) )
& ~ p1(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& r1(X,Y) )
| ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y)
& ~ p2(Y)
& ? [X] :
( ~ p1(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p1(Y)
| ? [X] :
( ~ p1(X)
& r1(Y,X) )
| ~ p1(Y)
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ? [X] :
( ~ p2(X)
& r1(Y,X) )
| ~ p2(Y)
| ~ r1(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [Y,X] :
( sP0_prd(X,Y)
<=> ( ~ p2(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,definition,
! [Y,X] :
( sP1_prd(X,Y)
<=> ( ~ p1(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f6,definition,
! [X] :
( sP2_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p1(X)
& ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
& p1(X)
& ~ p2(X)
& r1(Y,X) )
& ~ p1(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& r1(X,Y) )
| ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y)
& ~ p2(Y)
& ? [X] :
( ~ p1(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f7,plain,
? [X] :
( ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ p1(Y)
& r1(X,Y) )
& ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ p1(Y)
& r1(X,Y) )
& ( ? [Y] :
( p1(Y)
& ! [X] :
( p1(X)
| ~ r1(Y,X) )
& p1(Y)
& ~ p2(Y)
& ~ p1(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& r1(X,Y) )
| sP2_prd(X)
| ! [Y] :
( ~ p1(Y)
| ? [X] : sP1_prd(X,Y)
| ~ p1(Y)
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ? [X] : sP0_prd(X,Y)
| ~ p2(Y)
| ~ r1(X,Y) ) ) ),
inference(formula_renaming,[status(thm)],[f3,f6,f5,f4]) ).
fof(f8,plain,
( p1(sK5_skl)
& ! [X] :
( p1(X)
| ~ r1(sK5_skl,X) )
& ~ p1(sK5_skl)
& r1(sK0_skl,sK5_skl)
& p1(sK4_skl)
& ! [X] :
( p1(X)
| ~ r1(sK4_skl,X) )
& ~ p1(sK4_skl)
& r1(sK0_skl,sK4_skl)
& ( ( p1(sK3_skl)
& ! [X] :
( p1(X)
| ~ r1(sK3_skl,X) )
& p1(sK3_skl)
& ~ p2(sK3_skl)
& ~ p1(sK3_skl)
& ! [X] :
( p2(X)
| ~ r1(sK3_skl,X) )
& p2(sK3_skl)
& r1(sK0_skl,sK3_skl) )
| sP2_prd(sK0_skl)
| ! [Y] :
( ~ p1(Y)
| sP1_prd(sK2_skl(Y),Y)
| ~ p1(Y)
| p2(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p1(Y)
| sP0_prd(sK1_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,sK5_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y)),skolemize(X,sK2_skl(Y)),skolemize(Y,sK3_skl),skolemize(Y,sK4_skl),skolemize(Y,sK5_skl)],[f7]) ).
fof(f18,plain,
~ p1(sK4_skl),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
p1(sK4_skl),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f110,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL644+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n014.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 00:43:05 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.039657 seconds
% 0.12/0.40 % CPU time: 0.109261 seconds
% 0.12/0.40 % Total memory used: 16.111 MB
% 0.12/0.40 % Net memory used: 15.993 MB
%------------------------------------------------------------------------------