%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL538+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 11:58:53 AM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 87 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 26 ~; 24 |; 10 &)
% ( 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+3.ax',km4b_axiom_M) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f90,negated_conjecture,
~ modus_ponens_strict_implies,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ modus_ponens_strict_implies,
inference(flattening,[],[f90]) ).
fof(f94,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f96,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(f112,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(f117,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f112]) ).
fof(f118,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f117]) ).
fof(f137,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,[],[f96]) ).
fof(f138,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(X0)
& is_a_theorem(strict_implies(X0,X1)) ) ),
inference(flattening,[],[f137]) ).
fof(f140,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f94]) ).
fof(f144,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f146,plain,
( modus_ponens_strict_implies
| ( ~ is_a_theorem(sK1)
& is_a_theorem(sK0)
& is_a_theorem(strict_implies(sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f138]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f118]) ).
fof(f168,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f184,plain,
( modus_ponens_strict_implies
| is_a_theorem(strict_implies(sK0,sK1)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f185,plain,
( modus_ponens_strict_implies
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f186,plain,
( modus_ponens_strict_implies
| ~ is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f188,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f140]) ).
fof(f192,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f144]) ).
fof(f197,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f202,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f205,plain,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[],[f91]) ).
fof(f207,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(global_subsumption,[],[f192,f202]) ).
fof(f211,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption,[],[f188,f197]) ).
fof(f213,plain,
is_a_theorem(strict_implies(sK0,sK1)),
inference(global_subsumption,[],[f184,f205]) ).
fof(f214,plain,
is_a_theorem(sK0),
inference(global_subsumption,[],[f185,f205]) ).
fof(f215,plain,
~ is_a_theorem(sK1),
inference(global_subsumption,[],[f186,f205]) ).
fof(f234,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(global_subsumption,[],[f147,f168]) ).
fof(f434,plain,
! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f234,f211]) ).
fof(f470,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f434,f207]) ).
fof(f542,plain,
is_a_theorem(implies(sK0,sK1)),
inference(resolution,[],[f470,f213]) ).
fof(f563,plain,
( ~ is_a_theorem(sK0)
| is_a_theorem(sK1) ),
inference(resolution,[],[f542,f234]) ).
fof(f564,plain,
is_a_theorem(sK1),
inference(forward_subsumption_resolution,[],[f563,f214]) ).
fof(f565,plain,
$false,
inference(forward_subsumption_resolution,[],[f564,f215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 15:57:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.44 % (3134882)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (3134889)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2228449749:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.44 % (3134888)% WARNING: option uhcvi not known.
% 0.09/0.44 % (3134889) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3134882-3134889"...
% 0.09/0.44 % (3134889)...printing done.
% 0.09/0.44 % (3134889)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (3134889)------------------------------
% 0.09/0.44 % (3134889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (3134889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (3134889)CaDiCaL version: 2.1.3
% 0.09/0.44 % (3134889)Termination reason: Refutation
% 0.09/0.44 % (3134889)Time elapsed: 0.005 s
% 0.09/0.44 % (3134889)Peak memory usage: 12 MB
% 0.09/0.44 % (3134889)Instructions burned: 13 (million)
% 0.09/0.44 % (3134882)Success in time 0.036 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------