%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL531+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 : n013.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 02:02:14 PM UTC 2026
% Result : Theorem 27.02s 4.03s
% Output : Proof 27.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 28 unt; 0 def)
% Number of atoms : 121 ( 5 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 45 ~; 41 |; 17 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 30 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f74,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f74_nnf,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [X,Y] :
( strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c132,plain,
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
fof(f84,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f84_nnf,plain,
op_strict_implies,
inference(nnf_transformation,[status(thm)],[f84]) ).
cnf(c142,plain,
op_strict_implies,
inference(cnf_transformation,[status(esa)],[f84_nnf]) ).
cnf(p228,plain,
strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(resolution,[status(thm)],[c132,c142]) ).
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]) ).
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]) ).
cnf(p146,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c63,c0]) ).
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(p158,plain,
is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[c19,c70]) ).
cnf(p323,plain,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,and(X0,X1))),X2)) ),
inference(resolution,[status(thm)],[p146,p158]) ).
fof(f4,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f4_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(implies(sk8,implies(sk8,sk9)),implies(sk8,sk9)))
| implies_2 )
& ( is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f4_nnf]) ).
cnf(c11,plain,
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f37,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f37_nnf,plain,
implies_2,
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c66,plain,
implies_2,
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(p152,plain,
is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[c11,c66]) ).
cnf(p1461,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[p323,p152]) ).
fof(f49,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f49_nnf,plain,
( ( ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [X] :
( ( ( ~ is_a_theorem(necessarily(sk55))
& is_a_theorem(sk55) )
| necessitation )
& ( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X)
| ~ necessitation ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk55])],[f49_nnf]) ).
cnf(c78,plain,
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
fof(f77,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_necessitation) ).
fof(f77_nnf,plain,
necessitation,
inference(nnf_transformation,[status(thm)],[f77]) ).
cnf(c135,plain,
necessitation,
inference(cnf_transformation,[status(esa)],[f77_nnf]) ).
cnf(p160,plain,
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c78,c135]) ).
cnf(p1469,plain,
is_a_theorem(necessarily(implies(X0,and(X0,X0)))),
inference(resolution,[status(thm)],[p1461,p160]) ).
cnf(p1475,plain,
is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[p228,p1469]) ).
fof(f65,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m4) ).
fof(f65_nnf,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,and(X,X)))
| axiom_m4 )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [X] :
( ( ~ is_a_theorem(strict_implies(sk83,and(sk83,sk83)))
| axiom_m4 )
& ( is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk83])],[f65_nnf]) ).
cnf(c117,plain,
( ~ is_a_theorem(strict_implies(sk83,and(sk83,sk83)))
| axiom_m4 ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(p1481,plain,
axiom_m4,
inference(resolution,[status(thm)],[p1475,c117]) ).
fof(f87,conjecture,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f87_neg,negated_conjecture,
~ axiom_m4,
inference(negated_conjecture,[status(cth)],[f87]) ).
fof(f87_nnf,plain,
~ axiom_m4,
inference(nnf_transformation,[status(thm)],[f87_neg]) ).
fof(f87_sk,plain,
~ axiom_m4,
inference(skolemisation,[status(esa)],[f87_nnf]) ).
cnf(c145,plain,
~ axiom_m4,
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(p1491,plain,
$false,
inference(resolution,[status(thm)],[p1481,c145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Wed Sep 23 23:39:20 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.02/4.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.02/4.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------