%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL644+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 01:08:18 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 23 ( 3 unt; 15 def)
% Number of atoms : 1043 ( 0 equ)
% Maximal formula atoms : 225 ( 45 avg)
% Number of connectives : 1535 ( 515 ~; 540 |; 465 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 12 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-1 aty)
% Number of variables : 367 ( 289 !; 78 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X] :
~ ( ~ ( ~ ( ! [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) ) )
| ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) ) )
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) ) )
| p5(Y)
| ~ r1(X,Y) )
| ~ ( ~ ( ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p2(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X) )
| p3(X)
| ~ r1(Y,X) )
| p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| ! [X] :
( p2(X)
| ~ ( ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p3(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X) )
| p4(X)
| ~ r1(Y,X) )
| p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| ! [X] :
( p3(X)
| ~ ( ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p4(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X) )
| p5(X)
| ~ r1(Y,X) )
| p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| ! [X] :
( p4(X)
| ~ ( ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p5(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X) )
| p6(X)
| ~ r1(Y,X) )
| p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| ! [X] :
( p5(X)
| ~ ( ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(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) )
| 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) ) )
| ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) ) )
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) ) )
| p5(Y)
| ~ r1(X,Y) )
| ~ ( ~ ( ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p2(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X) )
| p3(X)
| ~ r1(Y,X) )
| p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| ! [X] :
( p2(X)
| ~ ( ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y) )
| p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ ( ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p3(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X) )
| p4(X)
| ~ r1(Y,X) )
| p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| ! [X] :
( p3(X)
| ~ ( ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y) )
| p4(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ ( ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p4(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X) )
| p5(X)
| ~ r1(Y,X) )
| p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| ! [X] :
( p4(X)
| ~ ( ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y) )
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p4(Y)
| ~ ( ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| ~ r1(X,Y) ) )
| ~ ( ~ ( ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ! [X] :
( ~ ( p5(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X) )
| p6(X)
| ~ r1(Y,X) )
| p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y) )
| ~ r1(X,Y) )
& ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| ! [X] :
( p5(X)
| ~ ( ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) )
| ! [Y] :
( ~ ( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y) )
| p6(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ~ ( ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(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)
& ~ 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) ) )
& ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& ~ p5(Y)
& r1(X,Y) )
& ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& ~ p5(Y)
& r1(X,Y) )
& ( ? [Y] :
( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& ~ p3(Y)
& ~ p2(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p2(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X)
& ~ p3(X)
& r1(Y,X) )
& ~ p2(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& r1(X,Y) )
| ? [Y] :
( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& ~ p3(Y)
& ? [X] :
( ~ p2(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p2(Y)
| ? [X] :
( ~ p2(X)
& r1(Y,X) )
| ~ p2(Y)
| p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ? [X] :
( ~ p3(X)
& r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& ~ p4(Y)
& ~ p3(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p3(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X)
& ~ p4(X)
& r1(Y,X) )
& ~ p3(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& r1(X,Y) )
| ? [Y] :
( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& ~ p4(Y)
& ? [X] :
( ~ p3(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p3(Y)
| ? [X] :
( ~ p3(X)
& r1(Y,X) )
| ~ p3(Y)
| p4(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ? [X] :
( ~ p4(X)
& r1(Y,X) )
| ~ p4(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& ~ p5(Y)
& ~ p4(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p4(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X)
& ~ p5(X)
& r1(Y,X) )
& ~ p4(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& r1(X,Y) )
| ? [Y] :
( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& ~ p5(Y)
& ? [X] :
( ~ p4(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p4(Y)
| ? [X] :
( ~ p4(X)
& r1(Y,X) )
| ~ p4(Y)
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p4(Y)
| ? [X] :
( ~ p5(X)
& r1(Y,X) )
| ~ p5(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& ~ p6(Y)
& ~ p5(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& r1(X,Y) )
| ? [Y] :
( ? [X] :
( p5(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X)
& ~ p6(X)
& r1(Y,X) )
& ~ p5(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& r1(X,Y) )
| ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& ~ p6(Y)
& ? [X] :
( ~ p5(X)
& ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X)
& r1(Y,X) )
& r1(X,Y) )
| ! [Y] :
( ~ p5(Y)
| ? [X] :
( ~ p5(X)
& r1(Y,X) )
| ~ p5(Y)
| p6(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ? [X] :
( ~ p6(X)
& r1(Y,X) )
| ~ p6(Y)
| ~ r1(X,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [Y,X] :
( sP0_prd(X,Y)
<=> ( ~ p6(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,definition,
! [Y,X] :
( sP1_prd(X,Y)
<=> ( ~ p5(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f6,definition,
! [X] :
( sP2_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p5(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X)
& ~ p6(X)
& r1(Y,X) )
& ~ p5(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& r1(X,Y) )
| ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& ~ p6(Y)
& ? [X] :
( ~ p5(X)
& ! [Y] :
( p6(Y)
| ~ r1(X,Y) )
& p6(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f7,definition,
! [Y,X] :
( sP3_prd(X,Y)
<=> ( ~ p5(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f8,definition,
! [Y,X] :
( sP4_prd(X,Y)
<=> ( ~ p4(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f9,definition,
! [X] :
( sP5_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p4(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X)
& ~ p5(X)
& r1(Y,X) )
& ~ p4(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& r1(X,Y) )
| ? [Y] :
( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& ~ p5(Y)
& ? [X] :
( ~ p4(X)
& ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
& p5(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f10,definition,
! [Y,X] :
( sP6_prd(X,Y)
<=> ( ~ p4(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f11,definition,
! [Y,X] :
( sP7_prd(X,Y)
<=> ( ~ p3(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f12,definition,
! [X] :
( sP8_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p3(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X)
& ~ p4(X)
& r1(Y,X) )
& ~ p3(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& r1(X,Y) )
| ? [Y] :
( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& ~ p4(Y)
& ? [X] :
( ~ p3(X)
& ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
& p4(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f13,definition,
! [Y,X] :
( sP9_prd(X,Y)
<=> ( ~ p3(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f14,definition,
! [Y,X] :
( sP10_prd(X,Y)
<=> ( ~ p2(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f15,definition,
! [X] :
( sP11_prd(X)
<=> ( ? [Y] :
( ? [X] :
( p2(X)
& ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
& p2(X)
& ~ p3(X)
& r1(Y,X) )
& ~ p2(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& r1(X,Y) )
| ? [Y] :
( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& ~ p3(Y)
& ? [X] :
( ~ p2(X)
& ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
& p3(X)
& r1(Y,X) )
& r1(X,Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f16,definition,
! [Y,X] :
( sP12_prd(X,Y)
<=> ( ~ p2(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f17,definition,
! [Y,X] :
( sP13_prd(X,Y)
<=> ( ~ p1(X)
& r1(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP13_prd])],[]) ).
fof(f18,definition,
! [X] :
( sP14_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,[sP14_prd])],[]) ).
fof(f19,plain,
? [X] :
( ( ? [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) )
| sP14_prd(X)
| ! [Y] :
( ~ p1(Y)
| ? [X] : sP13_prd(X,Y)
| ~ p1(Y)
| p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ? [X] : sP12_prd(X,Y)
| ~ p2(Y)
| ~ r1(X,Y) ) )
& ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& ~ p5(Y)
& r1(X,Y) )
& ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& ~ p5(Y)
& r1(X,Y) )
& ( ? [Y] :
( p2(Y)
& ! [X] :
( p2(X)
| ~ r1(Y,X) )
& p2(Y)
& ~ p3(Y)
& ~ p2(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& r1(X,Y) )
| sP11_prd(X)
| ! [Y] :
( ~ p2(Y)
| ? [X] : sP10_prd(X,Y)
| ~ p2(Y)
| p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ? [X] : sP9_prd(X,Y)
| ~ p3(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p3(Y)
& ! [X] :
( p3(X)
| ~ r1(Y,X) )
& p3(Y)
& ~ p4(Y)
& ~ p3(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& r1(X,Y) )
| sP8_prd(X)
| ! [Y] :
( ~ p3(Y)
| ? [X] : sP7_prd(X,Y)
| ~ p3(Y)
| p4(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ? [X] : sP6_prd(X,Y)
| ~ p4(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p4(Y)
& ! [X] :
( p4(X)
| ~ r1(Y,X) )
& p4(Y)
& ~ p5(Y)
& ~ p4(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& r1(X,Y) )
| sP5_prd(X)
| ! [Y] :
( ~ p4(Y)
| ? [X] : sP4_prd(X,Y)
| ~ p4(Y)
| p5(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p4(Y)
| ? [X] : sP3_prd(X,Y)
| ~ p5(Y)
| ~ r1(X,Y) ) )
& ( ? [Y] :
( p5(Y)
& ! [X] :
( p5(X)
| ~ r1(Y,X) )
& p5(Y)
& ~ p6(Y)
& ~ p5(Y)
& ! [X] :
( p6(X)
| ~ r1(Y,X) )
& p6(Y)
& r1(X,Y) )
| sP2_prd(X)
| ! [Y] :
( ~ p5(Y)
| ? [X] : sP1_prd(X,Y)
| ~ p5(Y)
| p6(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ? [X] : sP0_prd(X,Y)
| ~ p6(Y)
| ~ r1(X,Y) ) ) ),
inference(formula_renaming,[status(thm)],[f3,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9,f8,f7,f6,f5,f4]) ).
fof(f20,plain,
( ( ( p1(sK17_skl)
& ! [X] :
( p1(X)
| ~ r1(sK17_skl,X) )
& p1(sK17_skl)
& ~ p2(sK17_skl)
& ~ p1(sK17_skl)
& ! [X] :
( p2(X)
| ~ r1(sK17_skl,X) )
& p2(sK17_skl)
& r1(sK0_skl,sK17_skl) )
| sP14_prd(sK0_skl)
| ! [Y] :
( ~ p1(Y)
| sP13_prd(sK16_skl(Y),Y)
| ~ p1(Y)
| p2(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p1(Y)
| sP12_prd(sK15_skl(Y),Y)
| ~ p2(Y)
| ~ r1(sK0_skl,Y) ) )
& p5(sK14_skl)
& ! [X] :
( p5(X)
| ~ r1(sK14_skl,X) )
& ~ p5(sK14_skl)
& r1(sK0_skl,sK14_skl)
& p5(sK13_skl)
& ! [X] :
( p5(X)
| ~ r1(sK13_skl,X) )
& ~ p5(sK13_skl)
& r1(sK0_skl,sK13_skl)
& ( ( p2(sK12_skl)
& ! [X] :
( p2(X)
| ~ r1(sK12_skl,X) )
& p2(sK12_skl)
& ~ p3(sK12_skl)
& ~ p2(sK12_skl)
& ! [X] :
( p3(X)
| ~ r1(sK12_skl,X) )
& p3(sK12_skl)
& r1(sK0_skl,sK12_skl) )
| sP11_prd(sK0_skl)
| ! [Y] :
( ~ p2(Y)
| sP10_prd(sK11_skl(Y),Y)
| ~ p2(Y)
| p3(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p2(Y)
| sP9_prd(sK10_skl(Y),Y)
| ~ p3(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p3(sK9_skl)
& ! [X] :
( p3(X)
| ~ r1(sK9_skl,X) )
& p3(sK9_skl)
& ~ p4(sK9_skl)
& ~ p3(sK9_skl)
& ! [X] :
( p4(X)
| ~ r1(sK9_skl,X) )
& p4(sK9_skl)
& r1(sK0_skl,sK9_skl) )
| sP8_prd(sK0_skl)
| ! [Y] :
( ~ p3(Y)
| sP7_prd(sK8_skl(Y),Y)
| ~ p3(Y)
| p4(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p3(Y)
| sP6_prd(sK7_skl(Y),Y)
| ~ p4(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p4(sK6_skl)
& ! [X] :
( p4(X)
| ~ r1(sK6_skl,X) )
& p4(sK6_skl)
& ~ p5(sK6_skl)
& ~ p4(sK6_skl)
& ! [X] :
( p5(X)
| ~ r1(sK6_skl,X) )
& p5(sK6_skl)
& r1(sK0_skl,sK6_skl) )
| sP5_prd(sK0_skl)
| ! [Y] :
( ~ p4(Y)
| sP4_prd(sK5_skl(Y),Y)
| ~ p4(Y)
| p5(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p4(Y)
| sP3_prd(sK4_skl(Y),Y)
| ~ p5(Y)
| ~ r1(sK0_skl,Y) ) )
& ( ( p5(sK3_skl)
& ! [X] :
( p5(X)
| ~ r1(sK3_skl,X) )
& p5(sK3_skl)
& ~ p6(sK3_skl)
& ~ p5(sK3_skl)
& ! [X] :
( p6(X)
| ~ r1(sK3_skl,X) )
& p6(sK3_skl)
& r1(sK0_skl,sK3_skl) )
| sP2_prd(sK0_skl)
| ! [Y] :
( ~ p5(Y)
| sP1_prd(sK2_skl(Y),Y)
| ~ p5(Y)
| p6(Y)
| ~ r1(sK0_skl,Y) )
| ! [Y] :
( p5(Y)
| sP0_prd(sK1_skl(Y),Y)
| ~ p6(Y)
| ~ 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,sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl,sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl(Y)),skolemize(X,sK2_skl(Y)),skolemize(Y,sK3_skl),skolemize(X,sK4_skl(Y)),skolemize(X,sK5_skl(Y)),skolemize(Y,sK6_skl),skolemize(X,sK7_skl(Y)),skolemize(X,sK8_skl(Y)),skolemize(Y,sK9_skl),skolemize(X,sK10_skl(Y)),skolemize(X,sK11_skl(Y)),skolemize(Y,sK12_skl),skolemize(Y,sK13_skl),skolemize(Y,sK14_skl),skolemize(X,sK15_skl(Y)),skolemize(X,sK16_skl(Y)),skolemize(Y,sK17_skl)],[f19]) ).
fof(f54,plain,
~ p5(sK13_skl),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f56,plain,
p5(sK13_skl),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f454,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f56,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL644+1.005 : 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 : n026.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 00:45:52 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % 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
% 0.17/0.51 % Elapsed time: 0.057696 seconds
% 0.17/0.51 % CPU time: 0.116098 seconds
% 0.17/0.51 % Total memory used: 10.177 MB
% 0.17/0.51 % Net memory used: 10.078 MB
%------------------------------------------------------------------------------