%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL546+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 : n001.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 11:58:54 AM UTC 2026
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 24 unt; 0 def)
% Number of atoms : 108 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 88 ( 38 ~; 31 |; 2 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 62 ( 61 !; 1 ?)
% 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(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
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(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(f57,axiom,
( axiom_B
<=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_B) ).
fof(f68,axiom,
( axiom_m6
<=> ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m6) ).
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+3.ax',km4b_necessitation) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
fof(f82,axiom,
axiom_B,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_axiom_B) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
axiom_m6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
fof(f90,negated_conjecture,
~ axiom_m6,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ axiom_m6,
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
=> axiom_m6 ),
inference(unused_predicate_definition_removal,[],[f68]) ).
fof(f93,plain,
( axiom_B
=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f95,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f97,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f107,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
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(f123,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f107]) ).
fof(f136,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f97]) ).
fof(f138,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f95]) ).
fof(f140,plain,
( ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(ennf_transformation,[],[f93]) ).
fof(f141,plain,
( axiom_m6
| ? [X0] : ~ is_a_theorem(strict_implies(X0,possibly(X0))) ),
inference(ennf_transformation,[],[f92]) ).
fof(f143,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f145,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf_transformation,[],[f123]) ).
fof(f166,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f170,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f181,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f183,plain,
! [X0] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f185,plain,
! [X0] :
( ~ axiom_B
| is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f140]) ).
fof(f186,plain,
( ~ is_a_theorem(strict_implies(sK0,possibly(sK0)))
| axiom_m6 ),
inference(cnf_transformation,[],[f141]) ).
fof(f188,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f191,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f193,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f195,plain,
axiom_B,
inference(cnf_transformation,[],[f82]) ).
fof(f198,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f201,plain,
~ axiom_m6,
inference(cnf_transformation,[],[f91]) ).
fof(f203,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[],[f188,f198]) ).
fof(f205,plain,
~ is_a_theorem(strict_implies(sK0,possibly(sK0))),
inference(forward_subsumption_resolution,[],[f186,f201]) ).
fof(f206,plain,
! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))),
inference(forward_subsumption_resolution,[],[f185,f195]) ).
fof(f208,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[],[f183,f193]) ).
fof(f210,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[],[f181,f191]) ).
fof(f223,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(forward_subsumption_resolution,[],[f150,f170]) ).
fof(f228,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f145,f166]) ).
fof(f233,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f210,f203]) ).
fof(f307,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f223,f228]) ).
fof(f328,plain,
~ is_a_theorem(implies(sK0,possibly(sK0))),
inference(resolution,[],[f233,f205]) ).
fof(f666,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f307,f228]) ).
fof(f1681,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,possibly(sK0)))
| ~ is_a_theorem(implies(sK0,X0)) ),
inference(resolution,[],[f666,f328]) ).
fof(f1701,plain,
~ is_a_theorem(implies(sK0,necessarily(possibly(sK0)))),
inference(resolution,[],[f1681,f208]) ).
fof(f1705,plain,
$false,
inference(forward_subsumption_resolution,[],[f1701,f206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n001.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 16:05:16 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
% 0.19/0.51 % (3750627)Will run a generic schedule for satisfiability detection.
% 0.19/0.51 % (3750634)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2212580403:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.51 % (3750633)% WARNING: option uhcvi not known.
% 0.19/0.51 % (3750632)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=420833806_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.51 % (3750633)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4154701041:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.51 % (3750635)dis+10_1_sil=32000:sp=arity:random_seed=362259851:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.51 % (3750636)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3864337324:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.51 % (3750637)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1800791511:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.51 % (3750638)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3819567115:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.51 % TRYING [1]
% 0.19/0.51 % TRYING [2]
% 0.19/0.51 % TRYING [3]
% 0.19/0.51 % TRYING [4]
% 0.19/0.51 % (3750636) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3750627-3750636"...
% 0.19/0.51 % (3750636)...printing done.
% 0.19/0.51 % (3750636)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (3750636)------------------------------
% 0.19/0.51 % (3750636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.51 % (3750636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.51 % (3750636)CaDiCaL version: 2.1.3
% 0.19/0.51 % (3750636)Termination reason: Refutation
% 0.19/0.51 % (3750636)Time elapsed: 0.038 s
% 0.19/0.51 % (3750636)Peak memory usage: 13 MB
% 0.19/0.51 % (3750636)Instructions burned: 58 (million)
% 0.19/0.51 % (3750627)Success in time 0.08 s
% 0.19/0.51 % Vampire exiting
%------------------------------------------------------------------------------