%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL525+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 : n006.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 11:58:52 AM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 18 unt; 0 def)
% Number of atoms : 83 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 67 ( 25 ~; 23 |; 8 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f51,axiom,
( modus_ponens_strict_implies
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
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(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f89,negated_conjecture,
~ modus_ponens_strict_implies,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ modus_ponens_strict_implies,
inference(flattening,[],[f89]) ).
fof(f92,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f94,plain,
( ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) )
=> is_a_theorem(X1) )
=> modus_ponens_strict_implies ),
inference(unused_predicate_definition_removal,[],[f51]) ).
fof(f110,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f115,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f110]) ).
fof(f116,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f115]) ).
fof(f135,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f136,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) ) ),
inference(flattening,[],[f135]) ).
fof(f138,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f92]) ).
fof(f141,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f143,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f164,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f180,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f136]) ).
fof(f181,plain,
( is_a_theorem(sK0)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f136]) ).
fof(f182,plain,
( ~ is_a_theorem(sK1)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f136]) ).
fof(f184,plain,
! [X0] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f187,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f141]) ).
fof(f192,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f196,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f199,plain,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[],[f90]) ).
fof(f201,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f187,f196]) ).
fof(f204,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[],[f184,f192]) ).
fof(f206,plain,
is_a_theorem(strict_implies(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f180,f199]) ).
fof(f207,plain,
is_a_theorem(sK0),
inference(forward_subsumption_resolution,[],[f181,f199]) ).
fof(f208,plain,
~ is_a_theorem(sK1),
inference(forward_subsumption_resolution,[],[f182,f199]) ).
fof(f227,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f143,f164]) ).
fof(f241,plain,
! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f227,f204]) ).
fof(f244,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f241,f201]) ).
fof(f328,plain,
is_a_theorem(implies(sK0,sK1)),
inference(resolution,[],[f244,f206]) ).
fof(f337,plain,
( ~ is_a_theorem(sK0)
| is_a_theorem(sK1) ),
inference(resolution,[],[f328,f227]) ).
fof(f338,plain,
is_a_theorem(sK1),
inference(forward_subsumption_resolution,[],[f337,f207]) ).
fof(f339,plain,
$false,
inference(forward_subsumption_resolution,[],[f338,f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL525+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 : n006.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 15:55:56 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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 % (3131636)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (3131645)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3986017064:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (3131642)% WARNING: option uhcvi not known.
% 0.12/0.45 % (3131645) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3131636-3131645"...
% 0.12/0.45 % (3131645)...printing done.
% 0.12/0.45 % (3131645)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
% 0.12/0.46 % (3131645)------------------------------
% 0.12/0.46 % (3131645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (3131645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (3131645)CaDiCaL version: 2.1.3
% 0.12/0.46 % (3131645)Termination reason: Refutation
% 0.12/0.46 % (3131645)Time elapsed: 0.003 s
% 0.12/0.46 % (3131645)Peak memory usage: 12 MB
% 0.12/0.46 % (3131645)Instructions burned: 8 (million)
% 0.12/0.46 % (3131636)Success in time 0.033 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------