%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL451+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 : n003.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 11:58:43 AM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 42 ( 19 ~; 15 |; 0 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(f19,axiom,
( cn1
<=> ! [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',cn1) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(f53,conjecture,
cn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn1) ).
fof(f54,negated_conjecture,
~ cn1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ cn1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> cn1 ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f66,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(f81,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f66]) ).
fof(f91,plain,
( cn1
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f95,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f91]) ).
fof(f101,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f81]) ).
fof(f111,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f122,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f135,plain,
~ cn1,
inference(cnf_transformation,[],[f55]) ).
fof(f161,definition,
( spl3_7
<=> is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f163,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| spl3_7 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl3_8
<=> cn1 ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f168,plain,
( ~ spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f111,f165,f161]) ).
fof(f242,definition,
( spl3_27
<=> implies_3 ),
introduced(definition,[new_symbols(definition,[spl3_27])],[avatar_definition]) ).
fof(f246,definition,
( spl3_28
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[spl3_28])],[avatar_definition]) ).
fof(f247,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ spl3_28 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( ~ spl3_27
| spl3_28 ),
inference(avatar_split_clause,[],[f101,f246,f242]) ).
fof(f289,plain,
~ spl3_8,
inference(avatar_split_clause,[],[f135,f165]) ).
fof(f297,plain,
spl3_27,
inference(avatar_split_clause,[],[f122,f242]) ).
fof(f355,plain,
( $false
| spl3_7
| ~ spl3_28 ),
inference(resolution,[],[f247,f163]) ).
fof(f360,plain,
( spl3_7
| ~ spl3_28 ),
inference(avatar_contradiction_clause,[],[f355]) ).
cnf(s4,plain,
( ~ spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s14,plain,
( ~ spl3_27
| spl3_28 ),
inference(sat_conversion,[],[f248]) ).
cnf(s20,plain,
~ spl3_8,
inference(sat_conversion,[],[f289]) ).
cnf(s28,plain,
spl3_27,
inference(sat_conversion,[],[f297]) ).
cnf(s42,plain,
( spl3_7
| ~ spl3_28 ),
inference(sat_conversion,[],[f360]) ).
cnf(s48,plain,
spl3_28,
inference(rat,[],[s14,s28]) ).
cnf(s49,plain,
spl3_7,
inference(rat,[],[s42,s48]) ).
cnf(s59,plain,
$false,
inference(rat,[],[s4,s20,s49]) ).
fof(f363,plain,
$false,
inference(avatar_sat_refutation,[],[s59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n003.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 15:46:56 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 Running first-order model finding
% 0.13/0.40 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
% 0.13/0.46 % (734237)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (734244)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1658537174:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.46 % (734242)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2807690660_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.46 % (734245)dis+10_1_sil=32000:sp=arity:random_seed=1018792450:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.46 % (734246)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4251267453:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.46 % (734247)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2800516166:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.46 % (734248)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1081294273:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.46 % TRYING [1]
% 0.13/0.46 % TRYING [2]
% 0.13/0.46 % (734246) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-734237-734246"...
% 0.13/0.46 % (734243)% WARNING: option uhcvi not known.
% 0.13/0.46 % TRYING [3]
% 0.13/0.46 % (734245) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-734237-734245"...
% 0.13/0.46 % (734247) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-734237-734247"...
% 0.13/0.46 % (734246)...printing done.
% 0.13/0.46 % (734245)...printing done.
% 0.13/0.46 % (734247)...printing done.
% 0.13/0.46 % (734245)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (734245)------------------------------
% 0.13/0.46 % (734245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (734245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (734245)CaDiCaL version: 2.1.3
% 0.13/0.46 % (734245)Termination reason: Refutation
% 0.13/0.46 % (734245)Time elapsed: 0.005 s
% 0.13/0.46 % (734245)Peak memory usage: 12 MB
% 0.13/0.46 % (734245)Instructions burned: 6 (million)
% 0.13/0.46 % (734237)Success in time 0.042 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------