%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL525+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 02:02:13 PM UTC 2026
% Result : Theorem 26.12s 3.98s
% Output : Proof 26.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 19 unt; 0 def)
% Number of atoms : 107 ( 5 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 99 ( 36 ~; 41 |; 16 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 21 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(f50,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
fof(f50_nnf,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
| modus_ponens_strict_implies )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens_strict_implies ) ),
inference(nnf_transformation,[status(thm)],[f50]) ).
fof(f50_sk,plain,
! [X,Y] :
( ( ( ~ is_a_theorem(sk57)
& is_a_theorem(strict_implies(sk56,sk57))
& is_a_theorem(sk56) )
| modus_ponens_strict_implies )
& ( is_a_theorem(Y)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X)
| ~ modus_ponens_strict_implies ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk56,sk57])],[f50_nnf]) ).
cnf(c83,plain,
( is_a_theorem(strict_implies(sk56,sk57))
| modus_ponens_strict_implies ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(p297,plain,
( modus_ponens_strict_implies
| is_a_theorem(X0)
| ~ is_a_theorem(implies(strict_implies(sk56,sk57),X0)) ),
inference(resolution,[status(thm)],[p146,c83]) ).
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(f54,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f54_nnf,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),X))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
! [X] :
( ( ~ is_a_theorem(implies(necessarily(sk64),sk64))
| axiom_M )
& ( is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk64])],[f54_nnf]) ).
cnf(c94,plain,
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
fof(f79,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f79_nnf,plain,
axiom_M,
inference(nnf_transformation,[status(thm)],[f79]) ).
cnf(c137,plain,
axiom_M,
inference(cnf_transformation,[status(esa)],[f79_nnf]) ).
cnf(p150,plain,
is_a_theorem(implies(necessarily(X0),X0)),
inference(resolution,[status(thm)],[c94,c137]) ).
cnf(p230,plain,
is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[p228,p150]) ).
cnf(p1106,plain,
( modus_ponens_strict_implies
| is_a_theorem(implies(sk56,sk57)) ),
inference(resolution,[status(thm)],[p297,p230]) ).
cnf(c82,plain,
( is_a_theorem(sk56)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(p294,plain,
( modus_ponens_strict_implies
| is_a_theorem(X0)
| ~ is_a_theorem(implies(sk56,X0)) ),
inference(resolution,[status(thm)],[p146,c82]) ).
cnf(p1112,plain,
( modus_ponens_strict_implies
| is_a_theorem(sk57)
| modus_ponens_strict_implies ),
inference(resolution,[status(thm)],[p1106,p294]) ).
cnf(p1114,plain,
( is_a_theorem(sk57)
| modus_ponens_strict_implies ),
inference(factoring,[status(thm)],[p1112]) ).
cnf(c84,plain,
( ~ is_a_theorem(sk57)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[status(esa)],[f50_sk]) ).
cnf(p1115,plain,
( modus_ponens_strict_implies
| modus_ponens_strict_implies ),
inference(resolution,[status(thm)],[p1114,c84]) ).
cnf(p1119,plain,
modus_ponens_strict_implies,
inference(factoring,[status(thm)],[p1115]) ).
fof(f87,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f87_neg,negated_conjecture,
~ modus_ponens_strict_implies,
inference(negated_conjecture,[status(cth)],[f87]) ).
fof(f87_nnf,plain,
~ modus_ponens_strict_implies,
inference(nnf_transformation,[status(thm)],[f87_neg]) ).
fof(f87_sk,plain,
~ modus_ponens_strict_implies,
inference(skolemisation,[status(esa)],[f87_nnf]) ).
cnf(c145,plain,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(p1126,plain,
$false,
inference(resolution,[status(thm)],[p1119,c145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL525+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n013.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 23:38:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.12/3.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.12/3.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------