%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL644+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 : Fri Sep 25 02:02:24 PM UTC 2026
% Result : Theorem 4.00s 0.97s
% Output : Proof 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 229 ( 0 equ)
% Maximal formula atoms : 53 ( 14 avg)
% Number of connectives : 333 ( 120 ~; 115 |; 98 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-1 aty)
% Number of variables : 71 ( 7 sgn 50 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,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',main) ).
fof(f0_neg,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)],[f0]) ).
fof(f0_nnf,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(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y,X] :
( p1(sk9)
& ( p1(X)
| ~ r1(sk9,X) )
& ~ p1(sk9)
& r1(sk0,sk9)
& p1(sk8)
& ( p1(X)
| ~ r1(sk8,X) )
& ~ p1(sk8)
& r1(sk0,sk8)
& ( ( p1(sk7)
& ( p1(X)
| ~ r1(sk7,X) )
& p1(sk7)
& ~ p2(sk7)
& ~ p1(sk7)
& ( p2(X)
| ~ r1(sk7,X) )
& p2(sk7)
& r1(sk0,sk7) )
| ( p1(sk6)
& ( p1(Y)
| ~ r1(sk6,Y) )
& p1(sk6)
& ~ p2(sk6)
& r1(sk5,sk6)
& ~ p1(sk5)
& ( p2(X)
| ~ r1(sk5,X) )
& p2(sk5)
& r1(sk0,sk5) )
| ( p1(sk3)
& ( p1(X)
| ~ r1(sk3,X) )
& p1(sk3)
& ~ p2(sk3)
& ~ p1(sk4)
& ( p2(Y)
| ~ r1(sk4,Y) )
& p2(sk4)
& r1(sk3,sk4)
& r1(sk0,sk3) )
| ~ p1(Y)
| ( ~ p1(sk2(Y))
& r1(Y,sk2(Y)) )
| ~ p1(Y)
| p2(Y)
| ~ r1(sk0,Y)
| p1(Y)
| ( ~ p2(sk1(Y))
& r1(Y,sk1(Y)) )
| ~ p2(Y)
| ~ r1(sk0,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5,sk6,sk7,sk8,sk9])],[f0_nnf]) ).
cnf(c154,plain,
( def50(X0)
| ~ def51(X1,X0) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47,def48,def49,def50,def51])],[f0_sk]) ).
cnf(c156,plain,
def51(X1,X0),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47,def48,def49,def50,def51])],[f0_sk]) ).
cnf(p186,plain,
def50(X0),
inference(resolution,[status(thm)],[c154,c156]) ).
cnf(c151,plain,
( def49(X0)
| ~ def50(X0) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47,def48,def49,def50,def51])],[f0_sk]) ).
cnf(p188,plain,
def49(X0),
inference(resolution,[status(thm)],[p186,c151]) ).
cnf(c148,plain,
( p1(sk9)
| ~ def49(X0) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47,def48,def49,def50,def51])],[f0_sk]) ).
cnf(p192,plain,
p1(sk9),
inference(resolution,[status(thm)],[p188,c148]) ).
cnf(c150,plain,
( def47
| ~ def50(X0) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47,def48,def49,def50,def51])],[f0_sk]) ).
cnf(p187,plain,
def47,
inference(resolution,[status(thm)],[p186,c150]) ).
cnf(c142,plain,
( ~ p1(sk9)
| ~ def47 ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47,def48,def49,def50,def51])],[f0_sk]) ).
cnf(p189,plain,
~ p1(sk9),
inference(resolution,[status(thm)],[p187,c142]) ).
cnf(p198,plain,
$false,
inference(resolution,[status(thm)],[p192,p189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL644+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 23:54:43 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.00/0.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.00/0.97 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------