%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:02:15 PM UTC 2026
% Result : Theorem 24.25s 3.92s
% Output : Proof 24.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 92 ( 33 ~; 38 |; 16 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f0_nnf,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( ~ is_a_theorem(sk1)
& is_a_theorem(implies(sk0,sk1))
& is_a_theorem(sk0) )
| modus_ponens )
& ( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| ~ modus_ponens ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f34,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f34_nnf,plain,
modus_ponens,
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c63,plain,
modus_ponens,
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(p147,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c0,c63]) ).
fof(f51,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(Y)
& is_a_theorem(X) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adjunction) ).
fof(f51_nnf,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(Y)
& is_a_theorem(X) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [X,Y] :
( ( ( ~ is_a_theorem(and(sk58,sk59))
& is_a_theorem(sk59)
& is_a_theorem(sk58) )
| adjunction )
& ( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ adjunction ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk58,sk59])],[f51_nnf]) ).
cnf(c87,plain,
( is_a_theorem(sk59)
| adjunction ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p318,plain,
( adjunction
| is_a_theorem(X0)
| ~ is_a_theorem(implies(sk59,X0)) ),
inference(resolution,[status(thm)],[p147,c87]) ).
cnf(c86,plain,
( is_a_theorem(sk58)
| adjunction ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p317,plain,
( adjunction
| is_a_theorem(X0)
| ~ is_a_theorem(implies(sk58,X0)) ),
inference(resolution,[status(thm)],[p147,c86]) ).
fof(f8,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f8_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(sk17,implies(sk18,and(sk17,sk18))))
| and_3 )
& ( is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17,sk18])],[f8_nnf]) ).
cnf(c19,plain,
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f41,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f41_nnf,plain,
and_3,
inference(nnf_transformation,[status(thm)],[f41]) ).
cnf(c70,plain,
and_3,
inference(cnf_transformation,[status(esa)],[f41_nnf]) ).
cnf(p159,plain,
is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[c19,c70]) ).
cnf(p473,plain,
( adjunction
| is_a_theorem(implies(X0,and(sk58,X0))) ),
inference(resolution,[status(thm)],[p317,p159]) ).
cnf(p544,plain,
( adjunction
| adjunction
| is_a_theorem(and(sk58,sk59)) ),
inference(resolution,[status(thm)],[p318,p473]) ).
cnf(p579,plain,
( adjunction
| is_a_theorem(and(sk58,sk59)) ),
inference(factoring,[status(thm)],[p544]) ).
cnf(c88,plain,
( ~ is_a_theorem(and(sk58,sk59))
| adjunction ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p580,plain,
( adjunction
| adjunction ),
inference(resolution,[status(thm)],[p579,c88]) ).
cnf(p585,plain,
adjunction,
inference(factoring,[status(thm)],[p580]) ).
fof(f88,conjecture,
adjunction,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f88_neg,negated_conjecture,
~ adjunction,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f88_nnf,plain,
~ adjunction,
inference(nnf_transformation,[status(thm)],[f88_neg]) ).
fof(f88_sk,plain,
~ adjunction,
inference(skolemisation,[status(esa)],[f88_nnf]) ).
cnf(c146,plain,
~ adjunction,
inference(cnf_transformation,[status(esa)],[f88_sk]) ).
cnf(p586,plain,
$false,
inference(resolution,[status(thm)],[p585,c146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.34 % Computer : n015.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 23:44:39 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.25/3.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.25/3.92 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------