%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL527+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 : 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 11:58:52 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 24 unt; 8 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 165 ( 71 ~; 66 |; 10 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 12 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 38 !; 4 ?)
% 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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f52,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(f88,conjecture,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f89,negated_conjecture,
~ adjunction,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ adjunction,
inference(flattening,[],[f89]) ).
fof(f94,plain,
( ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(X1) )
=> is_a_theorem(and(X0,X1)) )
=> adjunction ),
inference(unused_predicate_definition_removal,[],[f52]) ).
fof(f102,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f110,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(f115,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f110]) ).
fof(f116,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f115]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f102]) ).
fof(f135,plain,
( adjunction
| ? [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
& is_a_theorem(X0)
& is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f136,plain,
( adjunction
| ? [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
& is_a_theorem(X0)
& is_a_theorem(X1) ) ),
inference(flattening,[],[f135]) ).
fof(f143,plain,
( adjunction
| ( ~ is_a_theorem(and(sK0,sK1))
& is_a_theorem(sK0)
& is_a_theorem(sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f136]) ).
fof(f144,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f116]) ).
fof(f152,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f165,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f172,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f181,plain,
( adjunction
| is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f182,plain,
( adjunction
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f183,plain,
( adjunction
| ~ is_a_theorem(and(sK0,sK1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f200,plain,
~ adjunction,
inference(cnf_transformation,[],[f90]) ).
fof(f201,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| modus_ponens ),
inference(consistent_polarity_flipping,[],[f144]) ).
fof(f204,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| and_3 ),
inference(consistent_polarity_flipping,[],[f152]) ).
fof(f212,plain,
~ modus_ponens,
inference(consistent_polarity_flipping,[],[f165]) ).
fof(f215,plain,
~ and_3,
inference(consistent_polarity_flipping,[],[f172]) ).
fof(f222,plain,
( ~ adjunction
| ~ is_a_theorem(and(sK0,sK1)) ),
inference(consistent_polarity_flipping,[],[f183]) ).
fof(f223,plain,
( ~ adjunction
| is_a_theorem(sK0) ),
inference(consistent_polarity_flipping,[],[f182]) ).
fof(f224,plain,
( ~ adjunction
| is_a_theorem(sK1) ),
inference(consistent_polarity_flipping,[],[f181]) ).
fof(f226,plain,
adjunction,
inference(consistent_polarity_flipping,[],[f200]) ).
fof(f276,definition,
( spl2_13
<=> is_a_theorem(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f280,definition,
( spl2_14
<=> adjunction ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f282,plain,
( ~ adjunction
| spl2_14 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f283,plain,
( spl2_13
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f224,f280,f276]) ).
fof(f285,definition,
( spl2_15
<=> is_a_theorem(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f288,plain,
( spl2_15
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f223,f280,f285]) ).
fof(f290,definition,
( spl2_16
<=> is_a_theorem(and(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f292,plain,
( ~ is_a_theorem(and(sK0,sK1))
| spl2_16 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f293,plain,
( ~ spl2_16
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f222,f280,f290]) ).
fof(f375,definition,
( spl2_37
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl2_37])],[avatar_definition]) ).
fof(f377,plain,
( and_3
| ~ spl2_37 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f379,definition,
( spl2_38
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl2_38])],[avatar_definition]) ).
fof(f380,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl2_38 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f381,plain,
( spl2_37
| spl2_38 ),
inference(avatar_split_clause,[],[f204,f379,f375]) ).
fof(f439,definition,
( spl2_53
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl2_53])],[avatar_definition]) ).
fof(f441,plain,
( modus_ponens
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f443,definition,
( spl2_54
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_54])],[avatar_definition]) ).
fof(f444,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl2_54 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
( spl2_53
| spl2_54 ),
inference(avatar_split_clause,[],[f201,f443,f439]) ).
fof(f458,plain,
( $false
| spl2_14 ),
inference(resolution,[],[f282,f226]) ).
fof(f459,plain,
spl2_14,
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f480,plain,
( $false
| ~ spl2_37 ),
inference(resolution,[],[f377,f215]) ).
fof(f481,plain,
~ spl2_37,
inference(avatar_contradiction_clause,[],[f480]) ).
fof(f496,plain,
( $false
| ~ spl2_53 ),
inference(resolution,[],[f441,f212]) ).
fof(f497,plain,
~ spl2_53,
inference(avatar_contradiction_clause,[],[f496]) ).
fof(f502,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) )
| ~ spl2_38
| ~ spl2_54 ),
inference(resolution,[],[f444,f380]) ).
fof(f512,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ spl2_38
| ~ spl2_54 ),
inference(resolution,[],[f502,f444]) ).
fof(f515,plain,
( ~ is_a_theorem(sK1)
| ~ is_a_theorem(sK0)
| spl2_16
| ~ spl2_38
| ~ spl2_54 ),
inference(resolution,[],[f512,f292]) ).
fof(f518,plain,
( ~ spl2_15
| ~ spl2_13
| spl2_16
| ~ spl2_38
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f515,f443,f379,f290,f276,f285]) ).
cnf(s7,plain,
( spl2_13
| ~ spl2_14 ),
inference(sat_conversion,[],[f283]) ).
cnf(s8,plain,
( ~ spl2_14
| spl2_15 ),
inference(sat_conversion,[],[f288]) ).
cnf(s9,plain,
( ~ spl2_14
| ~ spl2_16 ),
inference(sat_conversion,[],[f293]) ).
cnf(s20,plain,
( spl2_37
| spl2_38 ),
inference(sat_conversion,[],[f381]) ).
cnf(s28,plain,
( spl2_53
| spl2_54 ),
inference(sat_conversion,[],[f445]) ).
cnf(s35,plain,
spl2_14,
inference(sat_conversion,[],[f459]) ).
cnf(s46,plain,
~ spl2_37,
inference(sat_conversion,[],[f481]) ).
cnf(s54,plain,
~ spl2_53,
inference(sat_conversion,[],[f497]) ).
cnf(s55,plain,
( ~ spl2_13
| ~ spl2_15
| spl2_16
| ~ spl2_38
| ~ spl2_54 ),
inference(sat_conversion,[],[f518]) ).
cnf(s56,plain,
spl2_54,
inference(rat,[],[s28,s54]) ).
cnf(s64,plain,
spl2_38,
inference(rat,[],[s20,s46]) ).
cnf(s75,plain,
~ spl2_16,
inference(rat,[],[s9,s35]) ).
cnf(s76,plain,
spl2_15,
inference(rat,[],[s8,s35]) ).
cnf(s77,plain,
~ spl2_13,
inference(rat,[],[s55,s56,s64,s75,s76]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s7,s35,s77]) ).
fof(f519,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n006.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 15:56:11 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.44 Running first-order model finding
% 0.13/0.44 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
% 0.19/0.48 % (3132401)Will run a generic schedule for satisfiability detection.
% 0.19/0.48 % (3132414)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1614380896:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.48 % (3132410)% WARNING: option uhcvi not known.
% 0.19/0.48 % (3132409)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3114367215_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.48 % (3132413)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=56469883:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.48 % (3132410)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2362582107:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.48 % (3132411)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1435328590:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.48 % (3132412)dis+10_1_sil=32000:sp=arity:random_seed=20922007:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.48 % (3132415)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2171345185:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.48 % TRYING [1]
% 0.19/0.48 % TRYING [2]
% 0.19/0.48 % TRYING [3]
% 0.19/0.48 % (3132415) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3132401-3132415"...
% 0.19/0.48 % (3132413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3132401-3132413"...
% 0.19/0.48 % (3132415)...printing done.
% 0.19/0.48 % (3132415)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (3132415)------------------------------
% 0.19/0.48 % (3132415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.48 % (3132415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.48 % (3132415)CaDiCaL version: 2.1.3
% 0.19/0.48 % (3132415)Termination reason: Refutation
% 0.19/0.48 % (3132415)Time elapsed: 0.005 s
% 0.19/0.48 % (3132415)Peak memory usage: 12 MB
% 0.19/0.48 % (3132415)Instructions burned: 6 (million)
% 0.19/0.48 % (3132401)Success in time 0.031 s
% 0.19/0.48 % Vampire exiting
%------------------------------------------------------------------------------