%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL686+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 : n002.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 02:02:40 PM UTC 2026
% Result : Theorem 12.13s 2.15s
% Output : Proof 12.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 173 ( 77 ~; 62 |; 34 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 42 ( 0 sgn 23 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X] : r1(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f0_nnf,plain,
! [X] : r1(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : r1(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
r1(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f2,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( $false
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f2_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] :
( $false
| ~ r1(X,Y) ) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
? [X] :
( ? [Y] :
( ! [X] :
( ( ? [Y] :
( ( ~ p1(Y)
| ~ p2(Y) )
& ( p2(Y)
| p1(Y) )
& r1(X,Y) )
& ? [Y] :
( ~ p3(Y)
& r1(X,Y) )
& ! [Y] :
( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ? [Y] :
( ~ $false
& r1(X,Y) ) )
| ~ r1(Y,X) )
& r1(X,Y) )
& ? [Y] :
( ? [X] :
( p1(X)
& r1(Y,X) )
& p3(Y)
& r1(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [X,Y] :
( ( ( ( ~ p1(sk6(X))
| ~ p2(sk6(X)) )
& ( p2(sk6(X))
| p1(sk6(X)) )
& r1(X,sk6(X))
& ~ p3(sk5(X))
& r1(X,sk5(X))
& ( ( ( ~ p1(Y)
| p2(Y) )
& ( p1(Y)
| ~ p2(Y) ) )
| ~ r1(X,Y) )
& ~ $false
& r1(X,sk4(X)) )
| ~ r1(sk3,X) )
& r1(sk0,sk3)
& p1(sk2)
& r1(sk1,sk2)
& p3(sk1)
& r1(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5,sk6])],[f2_nnf]) ).
cnf(c10,plain,
( ~ p1(X1)
| p2(X1)
| ~ r1(X0,X1)
| ~ r1(sk3,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p26,plain,
( ~ p1(X0)
| p2(X0)
| ~ r1(sk3,X0) ),
inference(resolution,[status(thm)],[c0,c10]) ).
cnf(c13,plain,
( r1(X0,sk6(X0))
| ~ r1(sk3,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p22,plain,
r1(sk3,sk6(sk3)),
inference(resolution,[status(thm)],[c0,c13]) ).
cnf(p60,plain,
( ~ p1(sk6(sk3))
| p2(sk6(sk3)) ),
inference(resolution,[status(thm)],[p26,p22]) ).
cnf(c9,plain,
( p1(X1)
| ~ p2(X1)
| ~ r1(X0,X1)
| ~ r1(sk3,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p25,plain,
( p1(X0)
| ~ p2(X0)
| ~ r1(sk3,X0) ),
inference(resolution,[status(thm)],[c0,c9]) ).
cnf(p54,plain,
( p1(sk6(sk3))
| ~ p2(sk6(sk3)) ),
inference(resolution,[status(thm)],[p25,p22]) ).
cnf(c14,plain,
( p2(sk6(X0))
| p1(sk6(X0))
| ~ r1(sk3,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p23,plain,
( p2(sk6(sk3))
| p1(sk6(sk3)) ),
inference(resolution,[status(thm)],[c0,c14]) ).
cnf(p55,plain,
( p1(sk6(sk3))
| p1(sk6(sk3)) ),
inference(resolution,[status(thm)],[p54,p23]) ).
cnf(p56,plain,
p1(sk6(sk3)),
inference(factoring,[status(thm)],[p55]) ).
cnf(p61,plain,
p2(sk6(sk3)),
inference(resolution,[status(thm)],[p60,p56]) ).
cnf(c15,plain,
( ~ p1(sk6(X0))
| ~ p2(sk6(X0))
| ~ r1(sk3,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p24,plain,
( ~ p1(sk6(sk3))
| ~ p2(sk6(sk3)) ),
inference(resolution,[status(thm)],[c0,c15]) ).
cnf(p62,plain,
~ p1(sk6(sk3)),
inference(resolution,[status(thm)],[p61,p24]) ).
cnf(p63,plain,
$false,
inference(resolution,[status(thm)],[p62,p56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 00:22:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.13/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.13/2.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------