%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:02:22 PM UTC 2026
% Result : Theorem 3.42s 1.07s
% Output : Proof 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 295 ( 0 equ)
% Maximal formula atoms : 69 ( 19 avg)
% Number of connectives : 495 ( 215 ~; 166 |; 114 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 48 ( 0 sgn 40 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,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/sandbox/benchmark/theBenchmark.p',main) ).
fof(f0_neg,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)],[f0]) ).
fof(f0_nnf,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(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y,X] :
( p100(sk0)
& ~ p101(sk0)
& ( ~ p101(sk0)
| p100(sk0) )
& ( ~ p102(sk0)
| p101(sk0) )
& ( ~ p100(sk0)
| ( ( ~ p1(sk0)
| ~ p100(Y)
| p1(Y)
| ~ r1(sk0,Y) )
& ( p1(sk0)
| ~ p100(Y)
| ~ p1(Y)
| ~ r1(sk0,Y) ) ) )
& ( ~ p101(sk0)
| ( ( ~ p2(sk0)
| ~ p101(Y)
| p2(Y)
| ~ r1(sk0,Y) )
& ( p2(sk0)
| ~ p101(Y)
| ~ p2(Y)
| ~ r1(sk0,Y) ) ) )
& ( ~ p100(sk0)
| p101(sk0)
| ( p101(sk4)
& ~ p102(sk4)
& p2(sk4)
& r1(sk0,sk4)
& p101(sk3)
& ~ p102(sk3)
& ~ p2(sk3)
& r1(sk0,sk3) ) )
& ( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ~ p100(X)
| p1(X)
| ~ r1(Y,X) )
& ( p1(Y)
| ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ~ p101(X)
| p2(X)
| ~ r1(Y,X) )
& ( p2(Y)
| ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) )
& ( ~ p100(Y)
| p101(Y)
| ( p101(sk2(Y))
& ~ p102(sk2(Y))
& p2(sk2(Y))
& r1(Y,sk2(Y))
& p101(sk1(Y))
& ~ p102(sk1(Y))
& ~ p2(sk1(Y))
& r1(Y,sk1(Y)) ) ) )
| ~ r1(sk0,Y) )
& ( p2(Y)
| ~ r1(sk0,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4])],[f0_nnf]) ).
cnf(c15,plain,
( ~ p100(sk0)
| p101(sk0)
| r1(sk0,sk3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c30,plain,
p100(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p35,plain,
( p101(sk0)
| r1(sk0,sk3) ),
inference(resolution,[status(thm)],[c15,c30]) ).
cnf(c0,plain,
( p2(X1)
| ~ r1(sk0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p36,plain,
( p2(sk3)
| p101(sk0) ),
inference(resolution,[status(thm)],[p35,c0]) ).
cnf(c29,plain,
~ p101(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p38,plain,
p2(sk3),
inference(resolution,[status(thm)],[p36,c29]) ).
cnf(c16,plain,
( ~ p100(sk0)
| p101(sk0)
| ~ p2(sk3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p39,plain,
( ~ p100(sk0)
| p101(sk0) ),
inference(resolution,[status(thm)],[p38,c16]) ).
cnf(p40,plain,
p101(sk0),
inference(resolution,[status(thm)],[p39,c30]) ).
cnf(p41,plain,
$false,
inference(resolution,[status(thm)],[p40,c29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 23:50:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.42/1.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/1.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------