%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL130-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 11:51:18 AM UTC 2026
% Result : Unsatisfiable 3.79s 1.48s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 10 unt; 1 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 26 ~; 18 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f2,axiom,
! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_4) ).
fof(f3,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_2) ).
fof(f4,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))))
| is_a_theorem(X0) ),
inference(resolution,[],[f2,f1]) ).
fof(f5,plain,
! [X2,X3,X0,X1,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X1,X2))),equivalent(equivalent(X3,X4),equivalent(equivalent(X3,X5),equivalent(X4,X5))))),
inference(resolution,[],[f4,f2]) ).
fof(f6,plain,
! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X1,X2)))),
inference(resolution,[],[f5,f4]) ).
fof(f9,definition,
( spl0_1
<=> ! [X4,X5,X3] : is_a_theorem(equivalent(equivalent(X3,X4),equivalent(equivalent(X3,X5),equivalent(X4,X5)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f10,plain,
( ! [X3,X4,X5] : is_a_theorem(equivalent(equivalent(X3,X4),equivalent(equivalent(X3,X5),equivalent(X4,X5))))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f15,plain,
spl0_1,
inference(avatar_split_clause,[],[f6,f9]) ).
fof(f16,plain,
( ! [X2,X0,X1] :
( is_a_theorem(equivalent(equivalent(X0,X2),equivalent(X1,X2)))
| ~ is_a_theorem(equivalent(X0,X1)) )
| ~ spl0_1 ),
inference(resolution,[],[f10,f1]) ).
fof(f18,plain,
( ! [X2,X0,X1] :
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X0,X2))
| ~ is_a_theorem(equivalent(X0,X1)) )
| ~ spl0_1 ),
inference(resolution,[],[f16,f1]) ).
fof(f19,plain,
( ! [X0] :
( ~ is_a_theorem(equivalent(X0,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e))))))
| ~ is_a_theorem(equivalent(X0,a)) )
| ~ spl0_1 ),
inference(resolution,[],[f18,f3]) ).
fof(f24,plain,
( ! [X0] :
( ~ is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))),a))
| ~ is_a_theorem(equivalent(X0,a)) )
| ~ spl0_1 ),
inference(resolution,[],[f19,f16]) ).
fof(f30,plain,
( ~ is_a_theorem(equivalent(a,a))
| ~ spl0_1 ),
inference(resolution,[],[f24,f2]) ).
fof(f36,plain,
( ! [X0] :
( ~ is_a_theorem(equivalent(X0,a))
| ~ is_a_theorem(equivalent(X0,a)) )
| ~ spl0_1 ),
inference(resolution,[],[f30,f18]) ).
fof(f38,plain,
( ! [X0] : ~ is_a_theorem(equivalent(X0,a))
| ~ spl0_1 ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f45,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f38,f2]) ).
fof(f49,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f45]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f15]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f49]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f50,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL130-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n019.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 15:23:19 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.50 Running first-order theorem proving
% 0.23/0.50 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.79/1.48 % (3197493)Input is clausal, will run a generic CNF schedule.
% 3.79/1.48 % (3197504)dis-21_1_sil=8000:lcm=predicate:random_seed=2710054062:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 3.79/1.48 % (3197504)First to succeed.
% 3.79/1.48 % (3197504)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3197493"
% 3.79/1.48 % (3197503)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1307502429:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 3.79/1.48 % (3197503)Also succeeded, but the first one will report.
% 3.79/1.48 % (3197498)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3019232206:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 3.79/1.48 % (3197500)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=152480515:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 3.79/1.48 % (3197499)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=397416065:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 3.79/1.48 % (3197501)lrs+10_1_sil=8000:sp=occurrence:random_seed=3818209614:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 3.79/1.48 % (3197502)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=764224687:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 3.79/1.48 % (3197502)Also succeeded, but the first one will report.
% 3.79/1.48 % (3197501)Also succeeded, but the first one will report.
% 3.79/1.48 % (3197504)Refutation found. Thanks to Tanya!
% 3.79/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.79/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.48 % (3197504)------------------------------
% 3.79/1.48 % (3197504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.48 % (3197504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.48 % (3197504)CaDiCaL version: 2.1.3
% 3.79/1.48 % (3197504)Termination reason: Refutation
% 3.79/1.48 % (3197504)Time elapsed: 0.003 s
% 3.79/1.48 % (3197504)Peak memory usage: 89 MB
% 3.79/1.48 % (3197504)Instructions burned: 2 (million)
% 3.79/1.48 % (3197504)------------------------------
% 3.79/1.48 % (3197504)------------------------------
% 3.79/1.48 % (3197493)Success in time 0.452 s
% 3.79/1.48 % Vampire exiting
%------------------------------------------------------------------------------