%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 11:57:28 AM UTC 2026
% Result : Unsatisfiable 0.64s 0.65s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 15 unt; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 34 ~; 28 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_18) ).
fof(f3,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_35) ).
fof(f4,axiom,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_49) ).
fof(f5,axiom,
! [X0,X1] : is_a_theorem(implies(necessary(implies(X0,X1)),implies(necessary(X0),necessary(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation1) ).
fof(f6,axiom,
! [X0] : is_a_theorem(implies(necessary(X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation2) ).
fof(f7,axiom,
! [X0] :
( is_a_theorem(necessary(X0))
| ~ is_a_theorem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_of_necessitation) ).
fof(f8,negated_conjecture,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f10,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1,f2]) ).
fof(f11,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f4,f1]) ).
fof(f13,plain,
! [X0,X1] :
( is_a_theorem(implies(necessary(X0),necessary(X1)))
| ~ is_a_theorem(necessary(implies(X0,X1))) ),
inference(resolution,[],[f5,f1]) ).
fof(f16,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f3,f1]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f16,f1]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f29,f10]) ).
fof(f36,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(not(X0),not(X1)),X1))
| is_a_theorem(implies(implies(not(X0),not(X1)),X0)) ),
inference(resolution,[],[f29,f4]) ).
fof(f49,definition,
( spl0_3
<=> ! [X1] : ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f50,plain,
( ! [X1] : ~ is_a_theorem(X1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f77,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessary(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f35,f6]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,implies(not(X2),not(X1))))
| is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f35,f4]) ).
fof(f99,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f36,f10]) ).
fof(f118,plain,
! [X0,X1] :
( ~ is_a_theorem(necessary(implies(X0,X1)))
| is_a_theorem(implies(necessary(X0),X1)) ),
inference(resolution,[],[f77,f13]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,implies(not(X2),not(X0))))
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f99,f35]) ).
fof(f259,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[],[f84,f2]) ).
fof(f472,plain,
! [X0,X1] :
( is_a_theorem(implies(necessary(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f118,f7]) ).
fof(f571,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f50,f2]) ).
fof(f618,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f571]) ).
fof(f1110,plain,
~ is_a_theorem(implies(a,not(necessary(not(a))))),
inference(resolution,[],[f472,f8]) ).
fof(f1280,plain,
! [X0,X1] :
( is_a_theorem(implies(not(not(X0)),X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f156,f259]) ).
fof(f1302,definition,
( spl0_37
<=> ! [X0] : is_a_theorem(implies(not(not(X0)),X0)) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f1303,plain,
( ! [X0] : is_a_theorem(implies(not(not(X0)),X0))
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1302]) ).
fof(f1304,plain,
( spl0_3
| spl0_37 ),
inference(avatar_split_clause,[],[f1280,f1302,f49]) ).
fof(f1328,plain,
( ! [X0] : is_a_theorem(implies(not(not(necessary(X0))),X0))
| ~ spl0_37 ),
inference(resolution,[],[f1303,f77]) ).
fof(f1532,plain,
( ! [X0] : is_a_theorem(implies(X0,not(necessary(not(X0)))))
| ~ spl0_37 ),
inference(resolution,[],[f1328,f11]) ).
fof(f1724,plain,
( $false
| ~ spl0_37 ),
inference(resolution,[],[f1532,f1110]) ).
fof(f1725,plain,
~ spl0_37,
inference(avatar_contradiction_clause,[],[f1724]) ).
cnf(s33,plain,
~ spl0_3,
inference(sat_conversion,[],[f618]) ).
cnf(s64,plain,
( spl0_3
| spl0_37 ),
inference(sat_conversion,[],[f1304]) ).
cnf(s81,plain,
~ spl0_37,
inference(sat_conversion,[],[f1725]) ).
cnf(s83,plain,
spl0_3,
inference(rat,[],[s64,s81]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s33,s83]) ).
fof(f1726,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.20/0.47 % Computer : n006.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 27 15:18:10 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.48 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.53 Running first-order model finding
% 0.25/0.53 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.65 % (3084777)Will run a generic schedule for satisfiability detection.
% 0.64/0.65 % (3084784)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3937849702:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.64/0.65 % (3084782)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3970623379_2999 on theBenchmark for (2999ds/0Mi)
% 0.64/0.65 % (3084787)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3912951042:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.64/0.65 % (3084785)dis+10_1_sil=32000:sp=arity:random_seed=3429693138:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.64/0.65 % TRYING [1]
% 0.64/0.65 % TRYING [2]
% 0.64/0.65 % TRYING [3]
% 0.64/0.65 % TRYING [4]
% 0.64/0.65 % (3084786)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2239464480:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.64/0.65 % (3084783)% WARNING: option uhcvi not known.
% 0.64/0.65 % (3084783)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3313144805:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.64/0.65 % (3084788)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=27029153:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.64/0.65 % (3084785) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3084777-3084785"...
% 0.64/0.65 % (3084785)...printing done.
% 0.64/0.65 % (3084785)Refutation found. Thanks to Tanya!
% 0.64/0.65 % SZS status Unsatisfiable for theBenchmark
% 0.64/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/0.65 % (3084785)------------------------------
% 0.64/0.65 % (3084785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.65 % (3084785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.65 % (3084785)CaDiCaL version: 2.1.3
% 0.64/0.65 % (3084785)Termination reason: Refutation
% 0.64/0.65 % (3084785)Time elapsed: 0.055 s
% 0.64/0.65 % (3084785)Peak memory usage: 12 MB
% 0.64/0.65 % (3084785)Instructions burned: 51 (million)
% 0.64/0.65 % (3084777)Success in time 0.102 s
% 0.64/0.65 % Vampire exiting
%------------------------------------------------------------------------------