%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 11:58:53 AM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 53 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 17 ~; 12 |; 0 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 23 ( 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
fof(f72,axiom,
( axiom_m10
<=> ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m10) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
axiom_m10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m10_axiom_m10) ).
fof(f89,negated_conjecture,
~ axiom_m10,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m10,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_m10 ),
inference(unused_predicate_definition_removal,[],[f72]) ).
fof(f92,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f95,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f134,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f95]) ).
fof(f137,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(ennf_transformation,[],[f92]) ).
fof(f138,plain,
( axiom_m10
| ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f91]) ).
fof(f140,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f178,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f181,plain,
! [X0] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f182,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_m10 ),
inference(cnf_transformation,[],[f138]) ).
fof(f184,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f187,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f190,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f193,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f196,plain,
~ axiom_m10,
inference(cnf_transformation,[],[f90]) ).
fof(f198,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f184,f193]) ).
fof(f200,plain,
~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))),
inference(forward_subsumption_resolution,[],[f182,f196]) ).
fof(f201,plain,
! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(forward_subsumption_resolution,[],[f181,f190]) ).
fof(f204,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f178,f187]) ).
fof(f226,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f204,f198]) ).
fof(f311,plain,
~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))),
inference(resolution,[],[f226,f200]) ).
fof(f312,plain,
$false,
inference(forward_subsumption_resolution,[],[f311,f201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 15:59:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.45 % (3708628)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (3708637)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2269936217:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (3708637) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3708628-3708637"...
% 0.12/0.45 % (3708634)% WARNING: option uhcvi not known.
% 0.12/0.45 % (3708637)...printing done.
% 0.12/0.45 % (3708637)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (3708637)------------------------------
% 0.12/0.45 % (3708637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (3708637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (3708637)CaDiCaL version: 2.1.3
% 0.12/0.45 % (3708637)Termination reason: Refutation
% 0.12/0.45 % (3708637)Time elapsed: 0.003 s
% 0.12/0.45 % (3708637)Peak memory usage: 12 MB
% 0.12/0.45 % (3708637)Instructions burned: 6 (million)
% 0.12/0.45 % (3708628)Success in time 0.029 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------