%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL531+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 : n002.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 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 96 ( 34 unt; 12 def)
% Number of atoms : 201 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 187 ( 82 ~; 76 |; 2 &)
% ( 17 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 62 !; 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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
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(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(f66,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f89,negated_conjecture,
~ axiom_m4,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m4,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
=> axiom_m4 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f95,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f102,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f106,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
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(f120,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f106]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f102]) ).
fof(f134,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f95]) ).
fof(f138,plain,
( axiom_m4
| ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f91]) ).
fof(f140,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f142,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f138]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f116]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f151,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f164,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f167,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f171,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f179,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f134]) ).
fof(f183,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
inference(cnf_transformation,[],[f142]) ).
fof(f185,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f140]) ).
fof(f188,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f194,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
~ axiom_m4,
inference(cnf_transformation,[],[f90]) ).
fof(f207,definition,
( spl1_3
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f211,definition,
( spl1_4
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f212,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f213,plain,
( ~ spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f185,f211,f207]) ).
fof(f223,definition,
( spl1_7
<=> is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f225,plain,
( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| spl1_7 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f227,definition,
( spl1_8
<=> axiom_m4 ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f230,plain,
( ~ spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f183,f227,f223]) ).
fof(f256,definition,
( spl1_15
<=> necessitation ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f260,definition,
( spl1_16
<=> ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f261,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f262,plain,
( ~ spl1_15
| spl1_16 ),
inference(avatar_split_clause,[],[f179,f260,f256]) ).
fof(f336,definition,
( spl1_35
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl1_35])],[avatar_definition]) ).
fof(f340,definition,
( spl1_36
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl1_36])],[avatar_definition]) ).
fof(f341,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl1_36 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f342,plain,
( ~ spl1_35
| spl1_36 ),
inference(avatar_split_clause,[],[f151,f340,f336]) ).
fof(f368,definition,
( spl1_43
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[spl1_43])],[avatar_definition]) ).
fof(f372,definition,
( spl1_44
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_44])],[avatar_definition]) ).
fof(f373,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl1_44 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f374,plain,
( ~ spl1_43
| spl1_44 ),
inference(avatar_split_clause,[],[f147,f372,f368]) ).
fof(f400,definition,
( spl1_51
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_51])],[avatar_definition]) ).
fof(f404,definition,
( spl1_52
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_52])],[avatar_definition]) ).
fof(f405,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl1_52 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f406,plain,
( ~ spl1_51
| spl1_52 ),
inference(avatar_split_clause,[],[f143,f404,f400]) ).
fof(f407,plain,
~ spl1_8,
inference(avatar_split_clause,[],[f197,f227]) ).
fof(f411,plain,
spl1_51,
inference(avatar_split_clause,[],[f164,f400]) ).
fof(f414,plain,
spl1_43,
inference(avatar_split_clause,[],[f167,f368]) ).
fof(f418,plain,
spl1_35,
inference(avatar_split_clause,[],[f171,f336]) ).
fof(f427,plain,
spl1_15,
inference(avatar_split_clause,[],[f188,f256]) ).
fof(f431,plain,
spl1_3,
inference(avatar_split_clause,[],[f194,f207]) ).
fof(f434,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) )
| ~ spl1_4
| ~ spl1_16 ),
inference(superposition,[],[f261,f212]) ).
fof(f465,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl1_44
| ~ spl1_52 ),
inference(resolution,[],[f373,f405]) ).
fof(f671,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ spl1_36
| ~ spl1_44
| ~ spl1_52 ),
inference(resolution,[],[f465,f341]) ).
fof(f708,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ spl1_4
| ~ spl1_16
| ~ spl1_36
| ~ spl1_44
| ~ spl1_52 ),
inference(resolution,[],[f671,f434]) ).
fof(f717,plain,
( $false
| ~ spl1_4
| spl1_7
| ~ spl1_16
| ~ spl1_36
| ~ spl1_44
| ~ spl1_52 ),
inference(resolution,[],[f708,f225]) ).
fof(f722,plain,
( ~ spl1_4
| spl1_7
| ~ spl1_16
| ~ spl1_36
| ~ spl1_44
| ~ spl1_52 ),
inference(avatar_contradiction_clause,[],[f717]) ).
cnf(s2,plain,
( ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f213]) ).
cnf(s4,plain,
( ~ spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f230]) ).
cnf(s8,plain,
( ~ spl1_15
| spl1_16 ),
inference(sat_conversion,[],[f262]) ).
cnf(s18,plain,
( ~ spl1_35
| spl1_36 ),
inference(sat_conversion,[],[f342]) ).
cnf(s22,plain,
( ~ spl1_43
| spl1_44 ),
inference(sat_conversion,[],[f374]) ).
cnf(s26,plain,
( ~ spl1_51
| spl1_52 ),
inference(sat_conversion,[],[f406]) ).
cnf(s27,plain,
~ spl1_8,
inference(sat_conversion,[],[f407]) ).
cnf(s31,plain,
spl1_51,
inference(sat_conversion,[],[f411]) ).
cnf(s34,plain,
spl1_43,
inference(sat_conversion,[],[f414]) ).
cnf(s38,plain,
spl1_35,
inference(sat_conversion,[],[f418]) ).
cnf(s47,plain,
spl1_15,
inference(sat_conversion,[],[f427]) ).
cnf(s53,plain,
spl1_3,
inference(sat_conversion,[],[f431]) ).
cnf(s58,plain,
( ~ spl1_4
| spl1_7
| ~ spl1_16
| ~ spl1_36
| ~ spl1_44
| ~ spl1_52 ),
inference(sat_conversion,[],[f722]) ).
cnf(s59,plain,
spl1_52,
inference(rat,[],[s26,s31]) ).
cnf(s63,plain,
spl1_44,
inference(rat,[],[s22,s34]) ).
cnf(s67,plain,
spl1_36,
inference(rat,[],[s18,s38]) ).
cnf(s77,plain,
spl1_16,
inference(rat,[],[s8,s47]) ).
cnf(s81,plain,
~ spl1_7,
inference(rat,[],[s4,s27]) ).
cnf(s82,plain,
~ spl1_4,
inference(rat,[],[s58,s59,s63,s67,s77,s81]) ).
cnf(s84,plain,
$false,
inference(rat,[],[s2,s82,s53]) ).
fof(f723,plain,
$false,
inference(avatar_sat_refutation,[],[s84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 15:59:06 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.47 % (3706678)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3706692)dis+10_1_sil=32000:sp=arity:random_seed=4258779043:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (3706690)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3706689)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2007627542_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (3706692) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3706678-3706692"...
% 0.17/0.47 % (3706690)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1118241782:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (3706691)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=647057303:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3706693)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3568979724:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (3706695)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2643079:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (3706692)...printing done.
% 0.17/0.47 % (3706694)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4092828537:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (3706692)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (3706692)------------------------------
% 0.17/0.47 % (3706692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3706692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3706692)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3706692)Termination reason: Refutation
% 0.17/0.47 % (3706692)Time elapsed: 0.007 s
% 0.17/0.47 % (3706692)Peak memory usage: 13 MB
% 0.17/0.47 % (3706692)Instructions burned: 16 (million)
% 0.17/0.47 % (3706678)Success in time 0.039 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------