%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 11:58:49 AM UTC 2026
% Result : Theorem 0.24s 0.56s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 14 unt; 4 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 21 ~; 15 |; 0 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(f43,conjecture,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f44,negated_conjecture,
~ and_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ and_1,
inference(flattening,[],[f44]) ).
fof(f47,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
=> and_1 ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f57,plain,
( and_1
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f59,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f64,plain,
( and_1
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f57]) ).
fof(f67,plain,
( and_1
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f69,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f85,plain,
~ and_1,
inference(cnf_transformation,[],[f45]) ).
fof(f119,definition,
( spl2_9
<=> kn2 ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f123,definition,
( spl2_10
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( ~ spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f69,f123,f119]) ).
fof(f135,definition,
( spl2_13
<=> is_a_theorem(implies(and(sK0,sK1),sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f137,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| spl2_13 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,definition,
( spl2_14
<=> and_1 ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f142,plain,
( ~ spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f67,f139,f135]) ).
fof(f159,plain,
~ spl2_14,
inference(avatar_split_clause,[],[f85,f139]) ).
fof(f165,plain,
spl2_9,
inference(avatar_split_clause,[],[f79,f119]) ).
fof(f168,plain,
( $false
| ~ spl2_10
| spl2_13 ),
inference(forward_subsumption_resolution,[],[f137,f124]) ).
fof(f169,plain,
( ~ spl2_10
| spl2_13 ),
inference(avatar_contradiction_clause,[],[f168]) ).
cnf(s5,plain,
( ~ spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f125]) ).
cnf(s7,plain,
( ~ spl2_13
| spl2_14 ),
inference(sat_conversion,[],[f142]) ).
cnf(s10,plain,
~ spl2_14,
inference(sat_conversion,[],[f159]) ).
cnf(s16,plain,
spl2_9,
inference(sat_conversion,[],[f165]) ).
cnf(s22,plain,
( ~ spl2_10
| spl2_13 ),
inference(sat_conversion,[],[f169]) ).
cnf(s25,plain,
~ spl2_13,
inference(rat,[],[s7,s10]) ).
cnf(s26,plain,
~ spl2_10,
inference(rat,[],[s22,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s5,s26,s16]) ).
fof(f170,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 27 15:54:18 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.24/0.50 Running first-order model finding
% 0.24/0.50 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
% 0.24/0.56 % (3231902)Will run a generic schedule for satisfiability detection.
% 0.24/0.56 % (3231907)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2429880402_2999 on theBenchmark for (2999ds/0Mi)
% 0.24/0.56 % TRYING [1]
% 0.24/0.56 % TRYING [2]
% 0.24/0.56 % TRYING [3]
% 0.24/0.56 % (3231908)% WARNING: option uhcvi not known.
% 0.24/0.56 % TRYING [4]
% 0.24/0.56 % (3231910)dis+10_1_sil=32000:sp=arity:random_seed=4151060052:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.56 % (3231908)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2828058968:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.56 % (3231909)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=49545805:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.56 % (3231911)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3158128459:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.24/0.56 % (3231912)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3119220388:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.24/0.56 % (3231910) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3231902-3231910"...
% 0.24/0.56 % (3231909) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3231902-3231909"...
% 0.24/0.56 % (3231908) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3231902-3231908"...
% 0.24/0.56 % (3231911) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3231902-3231911"...
% 0.24/0.56 % (3231912) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3231902-3231912"...
% 0.24/0.56 % (3231913)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3676061496:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.24/0.56 % (3231910)...printing done.
% 0.24/0.56 % (3231909)...printing done.
% 0.24/0.56 % (3231908)...printing done.
% 0.24/0.56 % (3231911)...printing done.
% 0.24/0.56 % (3231912)...printing done.
% 0.24/0.56 % (3231910)Refutation found. Thanks to Tanya!
% 0.24/0.56 % SZS status Theorem for theBenchmark
% 0.24/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.56 % (3231910)------------------------------
% 0.24/0.56 % (3231910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.56 % (3231910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.56 % (3231910)CaDiCaL version: 2.1.3
% 0.24/0.56 % (3231910)Termination reason: Refutation
% 0.24/0.56 % (3231910)Time elapsed: 0.004 s
% 0.24/0.56 % (3231910)Peak memory usage: 12 MB
% 0.24/0.56 % (3231910)Instructions burned: 2 (million)
% 0.24/0.56 % (3231902)Success in time 0.042 s
% 0.24/0.56 % Vampire exiting
%------------------------------------------------------------------------------