%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL540+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 : n004.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 11:58:54 AM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : Refutation 0.16s
% 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 : 163 ( 69 ~; 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(f89,conjecture,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f90,negated_conjecture,
~ adjunction,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ adjunction,
inference(flattening,[],[f90]) ).
fof(f96,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(f104,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f112,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(f117,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f112]) ).
fof(f118,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f117]) ).
fof(f126,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f104]) ).
fof(f137,plain,
( adjunction
| ? [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
& is_a_theorem(X0)
& is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f138,plain,
( adjunction
| ? [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
& is_a_theorem(X0)
& is_a_theorem(X1) ) ),
inference(flattening,[],[f137]) ).
fof(f146,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)],[f138]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f118]) ).
fof(f155,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f126]) ).
fof(f168,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f175,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f184,plain,
( adjunction
| is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f185,plain,
( adjunction
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f186,plain,
( adjunction
| ~ is_a_theorem(and(sK0,sK1)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f205,plain,
~ adjunction,
inference(cnf_transformation,[],[f91]) ).
fof(f206,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(X0)
| is_a_theorem(implies(X0,X1))
| modus_ponens ),
inference(consistent_polarity_flipping,[],[f147]) ).
fof(f214,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| and_3 ),
inference(consistent_polarity_flipping,[],[f155]) ).
fof(f223,plain,
~ modus_ponens,
inference(consistent_polarity_flipping,[],[f168]) ).
fof(f226,plain,
~ and_3,
inference(consistent_polarity_flipping,[],[f175]) ).
fof(f230,plain,
( ~ adjunction
| is_a_theorem(and(sK0,sK1)) ),
inference(consistent_polarity_flipping,[],[f186]) ).
fof(f231,plain,
( ~ adjunction
| ~ is_a_theorem(sK0) ),
inference(consistent_polarity_flipping,[],[f185]) ).
fof(f232,plain,
( ~ adjunction
| ~ is_a_theorem(sK1) ),
inference(consistent_polarity_flipping,[],[f184]) ).
fof(f241,plain,
adjunction,
inference(consistent_polarity_flipping,[],[f205]) ).
fof(f299,definition,
( spl2_15
<=> is_a_theorem(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f303,definition,
( spl2_16
<=> adjunction ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f305,plain,
( ~ adjunction
| spl2_16 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f306,plain,
( ~ spl2_15
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f232,f303,f299]) ).
fof(f308,definition,
( spl2_17
<=> is_a_theorem(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f311,plain,
( ~ spl2_17
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f231,f303,f308]) ).
fof(f313,definition,
( spl2_18
<=> is_a_theorem(and(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f315,plain,
( is_a_theorem(and(sK0,sK1))
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,plain,
( spl2_18
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f230,f303,f313]) ).
fof(f398,definition,
( spl2_39
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl2_39])],[avatar_definition]) ).
fof(f400,plain,
( and_3
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f402,definition,
( spl2_40
<=> ! [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl2_40])],[avatar_definition]) ).
fof(f403,plain,
( ! [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl2_40 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f404,plain,
( spl2_39
| spl2_40 ),
inference(avatar_split_clause,[],[f214,f402,f398]) ).
fof(f462,definition,
( spl2_55
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl2_55])],[avatar_definition]) ).
fof(f464,plain,
( modus_ponens
| ~ spl2_55 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f466,definition,
( spl2_56
<=> ! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(X0)
| is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_56])],[avatar_definition]) ).
fof(f467,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(X1) )
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f468,plain,
( spl2_55
| spl2_56 ),
inference(avatar_split_clause,[],[f206,f466,f462]) ).
fof(f483,plain,
( $false
| spl2_16 ),
inference(resolution,[],[f305,f241]) ).
fof(f484,plain,
spl2_16,
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f505,plain,
( $false
| ~ spl2_39 ),
inference(resolution,[],[f400,f226]) ).
fof(f506,plain,
~ spl2_39,
inference(avatar_contradiction_clause,[],[f505]) ).
fof(f521,plain,
( $false
| ~ spl2_55 ),
inference(resolution,[],[f464,f223]) ).
fof(f522,plain,
~ spl2_55,
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f528,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,and(X0,X1)))
| is_a_theorem(X0) )
| ~ spl2_40
| ~ spl2_56 ),
inference(resolution,[],[f467,f403]) ).
fof(f543,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X1)
| is_a_theorem(X0) )
| ~ spl2_40
| ~ spl2_56 ),
inference(resolution,[],[f528,f467]) ).
fof(f548,plain,
( is_a_theorem(sK1)
| is_a_theorem(sK0)
| ~ spl2_18
| ~ spl2_40
| ~ spl2_56 ),
inference(resolution,[],[f543,f315]) ).
fof(f551,plain,
( spl2_17
| spl2_15
| ~ spl2_18
| ~ spl2_40
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f548,f466,f402,f313,f299,f308]) ).
cnf(s8,plain,
( ~ spl2_15
| ~ spl2_16 ),
inference(sat_conversion,[],[f306]) ).
cnf(s9,plain,
( ~ spl2_16
| ~ spl2_17 ),
inference(sat_conversion,[],[f311]) ).
cnf(s10,plain,
( ~ spl2_16
| spl2_18 ),
inference(sat_conversion,[],[f316]) ).
cnf(s21,plain,
( spl2_39
| spl2_40 ),
inference(sat_conversion,[],[f404]) ).
cnf(s29,plain,
( spl2_55
| spl2_56 ),
inference(sat_conversion,[],[f468]) ).
cnf(s37,plain,
spl2_16,
inference(sat_conversion,[],[f484]) ).
cnf(s48,plain,
~ spl2_39,
inference(sat_conversion,[],[f506]) ).
cnf(s56,plain,
~ spl2_55,
inference(sat_conversion,[],[f522]) ).
cnf(s57,plain,
( spl2_15
| spl2_17
| ~ spl2_18
| ~ spl2_40
| ~ spl2_56 ),
inference(sat_conversion,[],[f551]) ).
cnf(s58,plain,
spl2_56,
inference(rat,[],[s29,s56]) ).
cnf(s66,plain,
spl2_40,
inference(rat,[],[s21,s48]) ).
cnf(s77,plain,
spl2_18,
inference(rat,[],[s10,s37]) ).
cnf(s78,plain,
~ spl2_17,
inference(rat,[],[s9,s37]) ).
cnf(s79,plain,
spl2_15,
inference(rat,[],[s57,s58,s66,s77,s78]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s8,s37,s79]) ).
fof(f552,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 % Computer : n004.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Sun Sep 27 15:58:07 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.45 Running first-order model finding
% 0.10/0.45 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
% 0.16/0.50 % (3695497)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (3695507)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2438501959:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (3695503)% WARNING: option uhcvi not known.
% 0.16/0.50 % (3695502)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=416185261_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (3695503)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2882638506:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (3695504)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2244716955:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (3695505)dis+10_1_sil=32000:sp=arity:random_seed=4129039518:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (3695506)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2547176616:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (3695508)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=135338389:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % TRYING [2]
% 0.16/0.50 % TRYING [3]
% 0.16/0.50 % (3695508) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3695497-3695508"...
% 0.16/0.50 % (3695508)...printing done.
% 0.16/0.50 % (3695506) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3695497-3695506"...
% 0.16/0.50 % (3695508)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (3695508)------------------------------
% 0.16/0.50 % (3695508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (3695508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (3695508)CaDiCaL version: 2.1.3
% 0.16/0.50 % (3695508)Termination reason: Refutation
% 0.16/0.50 % (3695508)Time elapsed: 0.006 s
% 0.16/0.50 % (3695508)Peak memory usage: 12 MB
% 0.16/0.50 % (3695508)Instructions burned: 7 (million)
% 0.16/0.50 % (3695497)Success in time 0.042 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------