%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL454+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 : n014.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 0.24s 0.56s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 102 ( 33 unt; 10 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 197 ( 88 ~; 85 |; 2 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 16 usr; 16 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 70 !; 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(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
fof(f53,conjecture,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f54,negated_conjecture,
~ r1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ r1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
=> r1 ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f60,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f67,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f68,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f71,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(f72,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f71]) ).
fof(f73,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f68]) ).
fof(f77,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f67]) ).
fof(f84,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(ennf_transformation,[],[f60]) ).
fof(f88,plain,
( r1
| ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
( r1
| ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f73]) ).
fof(f98,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f77]) ).
fof(f106,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[],[f84]) ).
fof(f110,plain,
( r1
| ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f119,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f121,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f122,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f129,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f137,plain,
~ r1,
inference(cnf_transformation,[],[f55]) ).
fof(f138,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| modus_ponens ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f140,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| implies_1 ),
inference(consistent_polarity_flipping,[],[f98]) ).
fof(f141,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| implies_2 ),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f146,plain,
( ~ r1
| ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f153,plain,
~ modus_ponens,
inference(consistent_polarity_flipping,[],[f119]) ).
fof(f155,plain,
~ implies_1,
inference(consistent_polarity_flipping,[],[f121]) ).
fof(f156,plain,
~ implies_2,
inference(consistent_polarity_flipping,[],[f122]) ).
fof(f162,plain,
r1,
inference(consistent_polarity_flipping,[],[f137]) ).
fof(f204,definition,
( spl1_11
<=> is_a_theorem(implies(or(sK0,sK0),sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f206,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| spl1_11 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f208,definition,
( spl1_12
<=> r1 ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f210,plain,
( ~ r1
| spl1_12 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f211,plain,
( ~ spl1_11
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f146,f208,f204]) ).
fof(f237,definition,
( spl1_19
<=> or_3 ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f239,plain,
( ~ or_3
| spl1_19 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f241,definition,
( spl1_20
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition]) ).
fof(f242,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f243,plain,
( ~ spl1_19
| spl1_20 ),
inference(avatar_split_clause,[],[f106,f241,f237]) ).
fof(f293,definition,
( spl1_33
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[spl1_33])],[avatar_definition]) ).
fof(f295,plain,
( implies_2
| ~ spl1_33 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f297,definition,
( spl1_34
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_34])],[avatar_definition]) ).
fof(f298,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl1_34 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( spl1_33
| spl1_34 ),
inference(avatar_split_clause,[],[f141,f297,f293]) ).
fof(f301,definition,
( spl1_35
<=> implies_1 ),
introduced(definition,[new_symbols(definition,[spl1_35])],[avatar_definition]) ).
fof(f303,plain,
( implies_1
| ~ spl1_35 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f305,definition,
( spl1_36
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[spl1_36])],[avatar_definition]) ).
fof(f306,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ spl1_36 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f307,plain,
( spl1_35
| spl1_36 ),
inference(avatar_split_clause,[],[f140,f305,f301]) ).
fof(f325,definition,
( spl1_41
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_41])],[avatar_definition]) ).
fof(f327,plain,
( modus_ponens
| ~ spl1_41 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f329,definition,
( spl1_42
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_42])],[avatar_definition]) ).
fof(f330,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl1_42 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f331,plain,
( spl1_41
| spl1_42 ),
inference(avatar_split_clause,[],[f138,f329,f325]) ).
fof(f340,plain,
( $false
| spl1_12 ),
inference(resolution,[],[f210,f162]) ).
fof(f341,plain,
spl1_12,
inference(avatar_contradiction_clause,[],[f340]) ).
fof(f348,plain,
( $false
| spl1_19 ),
inference(resolution,[],[f239,f129]) ).
fof(f349,plain,
spl1_19,
inference(avatar_contradiction_clause,[],[f348]) ).
fof(f362,plain,
( $false
| ~ spl1_33 ),
inference(resolution,[],[f295,f156]) ).
fof(f363,plain,
~ spl1_33,
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f364,plain,
( $false
| ~ spl1_35 ),
inference(resolution,[],[f303,f155]) ).
fof(f365,plain,
~ spl1_35,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f370,plain,
( $false
| ~ spl1_41 ),
inference(resolution,[],[f327,f153]) ).
fof(f371,plain,
~ spl1_41,
inference(avatar_contradiction_clause,[],[f370]) ).
fof(f461,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) )
| ~ spl1_34
| ~ spl1_42 ),
inference(resolution,[],[f298,f330]) ).
fof(f528,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl1_34
| ~ spl1_42 ),
inference(resolution,[],[f461,f330]) ).
fof(f837,plain,
( ! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl1_20
| ~ spl1_34
| ~ spl1_42 ),
inference(resolution,[],[f242,f528]) ).
fof(f1069,plain,
( ~ is_a_theorem(implies(sK0,sK0))
| spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_42 ),
inference(resolution,[],[f837,f206]) ).
fof(f1077,plain,
( ~ is_a_theorem(implies(sK0,implies(sK0,sK0)))
| spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_42 ),
inference(resolution,[],[f1069,f461]) ).
fof(f1083,plain,
( $false
| spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_36
| ~ spl1_42 ),
inference(resolution,[],[f1077,f306]) ).
fof(f1090,plain,
( spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_36
| ~ spl1_42 ),
inference(avatar_contradiction_clause,[],[f1083]) ).
cnf(s6,plain,
( ~ spl1_11
| ~ spl1_12 ),
inference(sat_conversion,[],[f211]) ).
cnf(s10,plain,
( ~ spl1_19
| spl1_20 ),
inference(sat_conversion,[],[f243]) ).
cnf(s17,plain,
( spl1_33
| spl1_34 ),
inference(sat_conversion,[],[f299]) ).
cnf(s18,plain,
( spl1_35
| spl1_36 ),
inference(sat_conversion,[],[f307]) ).
cnf(s21,plain,
( spl1_41
| spl1_42 ),
inference(sat_conversion,[],[f331]) ).
cnf(s26,plain,
spl1_12,
inference(sat_conversion,[],[f341]) ).
cnf(s30,plain,
spl1_19,
inference(sat_conversion,[],[f349]) ).
cnf(s37,plain,
~ spl1_33,
inference(sat_conversion,[],[f363]) ).
cnf(s38,plain,
~ spl1_35,
inference(sat_conversion,[],[f365]) ).
cnf(s41,plain,
~ spl1_41,
inference(sat_conversion,[],[f371]) ).
cnf(s48,plain,
( spl1_11
| ~ spl1_20
| ~ spl1_34
| ~ spl1_36
| ~ spl1_42 ),
inference(sat_conversion,[],[f1090]) ).
cnf(s49,plain,
spl1_42,
inference(rat,[],[s21,s41]) ).
cnf(s52,plain,
spl1_36,
inference(rat,[],[s18,s38]) ).
cnf(s53,plain,
spl1_34,
inference(rat,[],[s17,s37]) ).
cnf(s60,plain,
spl1_20,
inference(rat,[],[s10,s30]) ).
cnf(s61,plain,
spl1_11,
inference(rat,[],[s48,s49,s52,s53,s60]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s6,s26,s61]) ).
fof(f1091,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.41 % Computer : n014.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 15:44:46 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.46 Running first-order model finding
% 0.16/0.46 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
% 0.24/0.56 % (963312)Will run a generic schedule for satisfiability detection.
% 0.24/0.56 % (963321)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3331957164:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.24/0.56 % (963317)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2020442816_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 % (963318)% WARNING: option uhcvi not known.
% 0.24/0.56 % (963322)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3632550084:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.24/0.56 % (963320)dis+10_1_sil=32000:sp=arity:random_seed=4016715984:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.56 % (963323)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1213336246:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.24/0.56 % (963319)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4200059861:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.56 % (963318)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1334976622:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.56 % TRYING [4]
% 0.24/0.56 % TRYING [5]
% 0.24/0.56 % (963323) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-963312-963323"...
% 0.24/0.56 % (963323)...printing done.
% 0.24/0.56 % (963323)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
% 0.24/0.57 % (963323)------------------------------
% 0.24/0.57 % (963323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.57 % (963323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.57 % (963323)CaDiCaL version: 2.1.3
% 0.24/0.57 % (963323)Termination reason: Refutation
% 0.24/0.57 % (963323)Time elapsed: 0.045 s
% 0.24/0.57 % (963323)Peak memory usage: 13 MB
% 0.24/0.57 % (963323)Instructions burned: 38 (million)
% 0.24/0.57 % (963312)Success in time 0.087 s
% 0.24/0.57 % Vampire exiting
%------------------------------------------------------------------------------