%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 11:52:53 AM UTC 2026
% Result : Theorem 3.39s 1.32s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 24 unt; 8 def)
% Number of atoms : 123 ( 5 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 105 ( 47 ~; 41 |; 0 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f72,axiom,
( axiom_m10
<=> ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m10) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_necessitation) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
axiom_m10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m10_axiom_m10) ).
fof(f89,negated_conjecture,
~ axiom_m10,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m10,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_m10 ),
inference(unused_predicate_definition_removal,[],[f72]) ).
fof(f92,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f95,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f134,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f95]) ).
fof(f137,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(ennf_transformation,[],[f92]) ).
fof(f138,plain,
( axiom_m10
| ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(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_m10
| ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f138]) ).
fof(f179,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f134]) ).
fof(f182,plain,
! [X0] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[],[f137]) ).
fof(f183,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(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(f191,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f194,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
~ axiom_m10,
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(possibly(sK0),necessarily(possibly(sK0)))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f225,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| spl1_7 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f227,definition,
( spl1_8
<=> axiom_m10 ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f230,plain,
( ~ spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f183,f227,f223]) ).
fof(f232,definition,
( spl1_9
<=> axiom_5 ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f236,definition,
( spl1_10
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f237,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( ~ spl1_9
| spl1_10 ),
inference(avatar_split_clause,[],[f182,f236,f232]) ).
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(f407,plain,
~ spl1_8,
inference(avatar_split_clause,[],[f197,f227]) ).
fof(f458,plain,
spl1_15,
inference(avatar_split_clause,[],[f188,f256]) ).
fof(f467,plain,
spl1_9,
inference(avatar_split_clause,[],[f191,f232]) ).
fof(f471,plain,
spl1_3,
inference(avatar_split_clause,[],[f194,f207]) ).
fof(f491,plain,
( ! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl1_4
| ~ spl1_16 ),
inference(superposition,[],[f261,f212]) ).
fof(f509,plain,
( ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0))))
| ~ spl1_4
| spl1_7
| ~ spl1_16 ),
inference(resolution,[],[f491,f225]) ).
fof(f510,plain,
( $false
| ~ spl1_4
| spl1_7
| ~ spl1_10
| ~ spl1_16 ),
inference(forward_subsumption_resolution,[],[f509,f237]) ).
fof(f511,plain,
( ~ spl1_4
| spl1_7
| ~ spl1_10
| ~ spl1_16 ),
inference(avatar_contradiction_clause,[],[f510]) ).
cnf(s2,plain,
( ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f213]) ).
cnf(s4,plain,
( ~ spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f230]) ).
cnf(s5,plain,
( ~ spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f238]) ).
cnf(s8,plain,
( ~ spl1_15
| spl1_16 ),
inference(sat_conversion,[],[f262]) ).
cnf(s27,plain,
~ spl1_8,
inference(sat_conversion,[],[f407]) ).
cnf(s61,plain,
spl1_15,
inference(sat_conversion,[],[f458]) ).
cnf(s67,plain,
spl1_9,
inference(sat_conversion,[],[f467]) ).
cnf(s69,plain,
spl1_3,
inference(sat_conversion,[],[f471]) ).
cnf(s78,plain,
( ~ spl1_4
| spl1_7
| ~ spl1_10
| ~ spl1_16 ),
inference(sat_conversion,[],[f511]) ).
cnf(s97,plain,
spl1_16,
inference(rat,[],[s8,s61]) ).
cnf(s100,plain,
spl1_10,
inference(rat,[],[s5,s67]) ).
cnf(s101,plain,
~ spl1_7,
inference(rat,[],[s4,s27]) ).
cnf(s102,plain,
~ spl1_4,
inference(rat,[],[s78,s97,s100,s101]) ).
cnf(s104,plain,
$false,
inference(rat,[],[s2,s102,s69]) ).
fof(f512,plain,
$false,
inference(avatar_sat_refutation,[],[s104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 16:00:07 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.39/1.32 % (3709073)Detected formulas, will run a generic FOF schedule.
% 3.39/1.32 % (3709079)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=789821627:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/1.32 % (3709083)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1391027728:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/1.32 % (3709082)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3983208957:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/1.32 % (3709081)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=539400540:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/1.32 % (3709080)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2933501594:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/1.32 % (3709078)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2840280204:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/1.32 % (3709082)Refutation not found, incomplete strategy
% 3.39/1.32 % (3709082)------------------------------
% 3.39/1.32 % (3709082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.32 % (3709082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.32 % (3709081)Refutation not found, incomplete strategy
% 3.39/1.32 % (3709081)------------------------------
% 3.39/1.32 % (3709081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.32 % (3709082)CaDiCaL version: 2.1.3
% 3.39/1.32 % (3709082)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.32 % (3709082)Time elapsed: 0.001 s
% 3.39/1.32 % (3709082)Peak memory usage: 86 MB
% 3.39/1.32 % (3709081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.32 % (3709081)CaDiCaL version: 2.1.3
% 3.39/1.32 % (3709081)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.32 % (3709081)Time elapsed: 0.001 s
% 3.39/1.32 % (3709081)Peak memory usage: 87 MB
% 3.39/1.32 % (3709083)First to succeed.
% 3.39/1.32 % (3709083)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3709073"
% 3.39/1.32 % (3709084)dis-21_1_sil=8000:lcm=predicate:random_seed=356698189:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.39/1.32 % (3709084)Refutation not found, incomplete strategy
% 3.39/1.32 % (3709084)------------------------------
% 3.39/1.32 % (3709084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.32 % (3709084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.32 % (3709084)CaDiCaL version: 2.1.3
% 3.39/1.32 % (3709084)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.32 % (3709084)Time elapsed: 0.002 s
% 3.39/1.32 % (3709084)Peak memory usage: 88 MB
% 3.39/1.32 % (3709084)Instructions burned: 1 (million)
% 3.39/1.32 % (3709082)------------------------------
% 3.39/1.32 % (3709082)------------------------------
% 3.39/1.32 % (3709081)------------------------------
% 3.39/1.32 % (3709081)------------------------------
% 3.39/1.32 % (3709084)------------------------------
% 3.39/1.32 % (3709084)------------------------------
% 3.39/1.32 % (3709083)Refutation found. Thanks to Tanya!
% 3.39/1.32 % SZS status Theorem for theBenchmark
% 3.39/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.32 % (3709083)------------------------------
% 3.39/1.32 % (3709083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.32 % (3709083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.32 % (3709083)CaDiCaL version: 2.1.3
% 3.39/1.32 % (3709083)Termination reason: Refutation
% 3.39/1.32 % (3709083)Time elapsed: 0.007 s
% 3.39/1.32 % (3709083)Peak memory usage: 90 MB
% 3.39/1.32 % (3709083)Instructions burned: 8 (million)
% 3.39/1.32 % (3709083)------------------------------
% 3.39/1.32 % (3709083)------------------------------
% 3.39/1.32 % (3709073)Success in time 0.411 s
% 3.39/1.32 % Vampire exiting
%------------------------------------------------------------------------------