%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL542+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 26.50s 8.89s
% Output : Proof 26.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 20 unt; 0 def)
% Number of atoms : 72 ( 5 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 61 ( 26 ~; 22 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 4 sgn 21 !; 5 ?)
% 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(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f85_nnf,plain,
op_strict_implies,
inference(nnf_transformation,[status(thm)],[f85]) ).
cnf(c143,plain,
op_strict_implies,
inference(cnf_transformation,[status(esa)],[f85_nnf]) ).
cnf(p238,plain,
strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(resolution,[status(thm)],[c132,c143]) ).
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',km4b_necessitation) ).
fof(f77_nnf,plain,
necessitation,
inference(nnf_transformation,[status(thm)],[f77]) ).
cnf(c135,plain,
necessitation,
inference(cnf_transformation,[status(esa)],[f77_nnf]) ).
cnf(p161,plain,
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c78,c135]) ).
fof(f6,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
fof(f6_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(implies(and(sk13,sk14),sk13))
| and_1 )
& ( is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f6_nnf]) ).
cnf(c15,plain,
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f39,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f39_nnf,plain,
and_1,
inference(nnf_transformation,[status(thm)],[f39]) ).
cnf(c68,plain,
and_1,
inference(cnf_transformation,[status(esa)],[f39_nnf]) ).
cnf(p152,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c15,c68]) ).
cnf(p169,plain,
is_a_theorem(necessarily(implies(and(X0,X1),X0))),
inference(resolution,[status(thm)],[p161,p152]) ).
cnf(p243,plain,
is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(superposition,[status(thm)],[p238,p169]) ).
fof(f63,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m2) ).
fof(f63_nnf,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [X,Y] :
( ( ~ is_a_theorem(strict_implies(and(sk78,sk79),sk78))
| axiom_m2 )
& ( is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk78,sk79])],[f63_nnf]) ).
cnf(c113,plain,
( ~ is_a_theorem(strict_implies(and(sk78,sk79),sk78))
| axiom_m2 ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(p278,plain,
axiom_m2,
inference(resolution,[status(thm)],[p243,c113]) ).
fof(f88,conjecture,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f88_neg,negated_conjecture,
~ axiom_m2,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f88_nnf,plain,
~ axiom_m2,
inference(nnf_transformation,[status(thm)],[f88_neg]) ).
fof(f88_sk,plain,
~ axiom_m2,
inference(skolemisation,[status(esa)],[f88_nnf]) ).
cnf(c146,plain,
~ axiom_m2,
inference(cnf_transformation,[status(esa)],[f88_sk]) ).
cnf(p279,plain,
$false,
inference(resolution,[status(thm)],[p278,c146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/5.39 % Computer : n015.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Wed Sep 23 23:45:02 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.50/8.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.50/8.89 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------