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Vampire---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SCT239_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n005.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 12:37:18 PM UTC 2026

% Result   : Theorem 6.50s 2.16s
% Output   : Refutation 6.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   29 (  15 unt;   0 typ;   2 def)
%            Number of atoms       :   57 (  11 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :   51 (  23   ~;  16   |;   8   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   4 prp; 0-3 aty)
%            Number of functors    :   42 (  42 usr;   6 con; 0-5 aty)
%            Number of variables   :   36 (   0 sgn  30   !;   6   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    arrow_411405190le_alt: $tType ).

tff(type_def_6,type,
    arrow_159774573e_indi: $tType ).

tff(type_def_7,type,
    bool: $tType ).

tff(type_def_8,type,
    list: $tType > $tType ).

tff(type_def_9,type,
    fun: ( $tType * $tType ) > $tType ).

tff(type_def_10,type,
    product_prod: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    append: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_1,type,
    butlast: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_2,type,
    dropWhile: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).

tff(func_def_3,type,
    hd: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_4,type,
    insert: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_5,type,
    last: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_6,type,
    linorder_insort_key: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 * list(X0) ) > list(X0) ) ).

tff(func_def_7,type,
    linorder_sort_key: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X0) ) ).

tff(func_def_8,type,
    cons: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_9,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_10,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_11,type,
    list_rec: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).

tff(func_def_12,type,
    maps: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).

tff(func_def_13,type,
    rev: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_14,type,
    rotate1: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_15,type,
    splice: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_16,type,
    takeWhile: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).

tff(func_def_17,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_18,type,
    fFalse: bool ).

tff(func_def_19,type,
    fTrue: bool ).

tff(func_def_20,type,
    f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_21,type,
    sK0: arrow_411405190le_alt ).

tff(func_def_22,type,
    sK1: arrow_411405190le_alt ).

tff(func_def_23,type,
    sK2: arrow_411405190le_alt ).

tff(func_def_24,type,
    sK3: ( arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_411405190le_alt ).

tff(func_def_25,type,
    sK4: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_26,type,
    sK5: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_27,type,
    sK6: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_28,type,
    sK7: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_29,type,
    sK8: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_30,type,
    sK9: 
      !>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).

tff(func_def_31,type,
    sK10: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_32,type,
    sK11: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_33,type,
    sK12: 
      !>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_34,type,
    sK13: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).

tff(func_def_35,type,
    sK14: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_36,type,
    sK15: 
      !>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).

tff(func_def_37,type,
    sK16: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_38,type,
    sK17: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(pred_def_1,type,
    linorder: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_3,type,
    arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_4,type,
    equal_equal: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_5,type,
    distinct: 
      !>[X0: $tType] : ( list(X0) > $o ) ).

tff(pred_def_6,type,
    list_ex1: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_7,type,
    null: 
      !>[X0: $tType] : ( list(X0) > $o ) ).

tff(pred_def_8,type,
    pp: bool > $o ).

tff(f1,axiom,
    ? [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X3,cons(arrow_411405190le_alt,X4,cons(arrow_411405190le_alt,X5,nil(arrow_411405190le_alt))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_alt3) ).

tff(f8,axiom,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
      ( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
    <=> ( ( X3 != X2 )
        & distinct(X0,cons(X0,X3,X1))
        & distinct(X0,cons(X0,X2,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_distinct__length__2__or__more) ).

tff(f104,axiom,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ( X0 != X1 )
     => thesis ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f105,conjecture,
    thesis,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

tff(f106,negated_conjecture,
    ~ thesis,
    inference(negated_conjecture,[status(cth)],[f105]) ).

tff(f107,plain,
    ? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,X1,cons(arrow_411405190le_alt,X2,nil(arrow_411405190le_alt))))),
    inference(rectify,[],[f1]) ).

tff(f109,plain,
    ~ thesis,
    inference(flattening,[],[f106]) ).

tff(f149,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( thesis
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f104]) ).

tff(f150,plain,
    distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK0,cons(arrow_411405190le_alt,sK1,cons(arrow_411405190le_alt,sK2,nil(arrow_411405190le_alt))))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f107]) ).

tff(f154,plain,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
      ( ( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
        | ( X2 = X3 )
        | ~ distinct(X0,cons(X0,X3,X1))
        | ~ distinct(X0,cons(X0,X2,X1)) )
      & ( ( ( X3 != X2 )
          & distinct(X0,cons(X0,X3,X1))
          & distinct(X0,cons(X0,X2,X1)) )
        | ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ) ),
    inference(nnf_transformation,[],[f8]) ).

tff(f155,plain,
    ! [X0: $tType,X1: list(X0),X2: X0,X3: X0] :
      ( ( distinct(X0,cons(X0,X3,cons(X0,X2,X1)))
        | ( X2 = X3 )
        | ~ distinct(X0,cons(X0,X3,X1))
        | ~ distinct(X0,cons(X0,X2,X1)) )
      & ( ( ( X3 != X2 )
          & distinct(X0,cons(X0,X3,X1))
          & distinct(X0,cons(X0,X2,X1)) )
        | ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ) ),
    inference(flattening,[],[f154]) ).

tff(f206,plain,
    distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,sK0,cons(arrow_411405190le_alt,sK1,cons(arrow_411405190le_alt,sK2,nil(arrow_411405190le_alt))))),
    inference(cnf_transformation,[],[f150]) ).

tff(f215,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: list(X0)] :
      ( ( X2 != X3 )
      | ~ distinct(X0,cons(X0,X3,cons(X0,X2,X1))) ),
    inference(cnf_transformation,[],[f155]) ).

tff(f369,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( thesis
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f149]) ).

tff(f370,plain,
    ~ thesis,
    inference(cnf_transformation,[],[f109]) ).

tff(f373,plain,
    ! [X0: $tType,X3: X0,X1: list(X0)] : ~ distinct(X0,cons(X0,X3,cons(X0,X3,X1))),
    inference(equality_resolution,[],[f215]) ).

tff(f428,definition,
    ( spl18_1
  <=> ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ( X0 = X1 ) ),
    introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).

tff(f429,plain,
    ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ( X0 = X1 )
    | ~ spl18_1 ),
    inference(avatar_component_clause,[],[f428]) ).

tff(f431,definition,
    ( spl18_2
  <=> thesis ),
    introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).

tff(f434,plain,
    ( spl18_1
    | spl18_2 ),
    inference(avatar_split_clause,[],[f369,f431,f428]) ).

tff(f435,plain,
    ~ spl18_2,
    inference(avatar_split_clause,[],[f370,f431]) ).

tff(f482,plain,
    ( ! [X0: arrow_411405190le_alt] : distinct(arrow_411405190le_alt,cons(arrow_411405190le_alt,X0,cons(arrow_411405190le_alt,sK1,cons(arrow_411405190le_alt,sK2,nil(arrow_411405190le_alt)))))
    | ~ spl18_1 ),
    inference(superposition,[],[f206,f429]) ).

tff(f518,plain,
    ( $false
    | ~ spl18_1 ),
    inference(resolution,[],[f482,f373]) ).

tff(f523,plain,
    ~ spl18_1,
    inference(avatar_contradiction_clause,[],[f518]) ).

cnf(s1,plain,
    ( spl18_1
    | spl18_2 ),
    inference(sat_conversion,[],[f434]) ).

cnf(s2,plain,
    ~ spl18_2,
    inference(sat_conversion,[],[f435]) ).

cnf(s3,plain,
    ~ spl18_1,
    inference(sat_conversion,[],[f523]) ).

cnf(s4,plain,
    $false,
    inference(rat,[],[s1,s2,s3]) ).

tff(f524,plain,
    $false,
    inference(avatar_sat_refutation,[],[s4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : SCT239_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.44  % Computer : n005.cluster.edu
% 0.16/0.44  % Model    : x86_64 x86_64
% 0.16/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44  % Memory   : 8046.5625MB
% 0.16/0.44  % OS       : Linux 6.8.0-71-generic
% 0.16/0.44  % CPULimit : 300
% 0.16/0.44  % WCLimit  : 300
% 0.16/0.44  % DateTime : Mon Sep 28 00:01:17 UTC 2026
% 0.16/0.44  % CPUTime  : 
% 0.16/0.44  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 3.72/1.84  % (309124)Detected formulas, will run a generic FOF schedule.
% 3.72/1.84  % (309138)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=2415318995:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.72/1.84  % (309137)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=653024244:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.72/1.84  % (309143)dis-21_1_sil=8000:lcm=predicate:random_seed=1751468629: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)
% 3.72/1.84  % (309142)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3761011869:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.72/1.84  % (309141)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2909472266:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.72/1.84  % (309140)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3928043414:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.72/1.84  % (309139)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=438720840:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.72/1.84  % (309141)Refutation not found, incomplete strategy
% 3.72/1.84  % (309141)------------------------------
% 3.72/1.84  % (309141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.84  % (309141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.84  % (309140)Refutation not found, incomplete strategy
% 3.72/1.84  % (309140)------------------------------
% 3.72/1.84  % (309140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.84  % (309141)CaDiCaL version: 2.1.3
% 3.72/1.84  % (309141)Termination reason: Refutation not found, incomplete strategy
% 3.72/1.84  % (309141)Time elapsed: 0.001 s
% 3.72/1.84  % (309140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.84  % (309141)Peak memory usage: 87 MB
% 3.72/1.84  % (309140)CaDiCaL version: 2.1.3
% 3.72/1.84  % (309140)Termination reason: Refutation not found, incomplete strategy
% 3.72/1.84  % (309140)Time elapsed: 0.001 s
% 3.72/1.84  % (309140)Peak memory usage: 88 MB
% 3.72/1.84  % (309139)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.72/1.84  % (309142)First to succeed.
% 3.72/1.84  % (309142)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-309124"
% 3.72/1.84  % (309143)Instruction limit reached! 
% 3.72/1.84  % (309143)------------------------------
% 3.72/1.84  % (309143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.84  % (309143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.84  % (309143)CaDiCaL version: 2.1.3
% 3.72/1.84  % (309143)Termination reason: Instruction limit
% 3.72/1.84  % (309143)Termination phase: Saturation
% 3.72/1.84  % (309143)Time elapsed: 0.115 s
% 3.72/1.84  % (309143)Peak memory usage: 89 MB
% 3.72/1.84  % (309143)Instructions burned: 129 (million)
% 3.72/1.84  % Exception at run slice level
% 3.72/1.84  User error: GNN currently only supports monomorphic FOL.
% 3.72/1.84  % (309155)lrs+10_1_sil=8000:sp=occurrence:random_seed=2608360658:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.72/1.84  % (309155)Refutation not found, incomplete strategy
% 3.72/1.84  % (309155)------------------------------
% 3.72/1.84  % (309155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.84  % (309155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.84  % (309155)CaDiCaL version: 2.1.3
% 3.72/1.84  % (309155)Termination reason: Refutation not found, incomplete strategy
% 3.72/1.84  % (309155)Time elapsed: 0.002 s
% 3.72/1.84  % (309155)Peak memory usage: 88 MB
% 3.72/1.84  % (309140)------------------------------
% 3.72/1.84  % (309140)------------------------------
% 3.72/1.84  % (309141)------------------------------
% 3.72/1.84  % (309141)------------------------------
% 3.72/1.84  % (309157)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2617059755:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 3.72/1.84  % (309157)Refutation not found, incomplete strategy
% 3.72/1.84  % (309157)------------------------------
% 6.50/2.16  % (309157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.50/2.16  % (309157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.50/2.16  % (309157)CaDiCaL version: 2.1.3
% 6.50/2.16  % (309157)Termination reason: Refutation not found, incomplete strategy
% 6.50/2.16  % (309157)Time elapsed: 0.002 s
% 6.50/2.16  % (309157)Peak memory usage: 88 MB
% 6.50/2.16  % (309157)Instructions burned: 1 (million)
% 6.50/2.16  % Exception at run slice level
% 6.50/2.16  User error: GNN currently only supports monomorphic FOL.
% 6.50/2.16  % (309142)Refutation found. Thanks to Tanya!
% 6.50/2.16  % SZS status Theorem for theBenchmark
% 6.50/2.16  % SZS output start Proof for theBenchmark
% See solution above
% 6.50/2.16  % (309142)------------------------------
% 6.50/2.16  % (309142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.50/2.16  % (309142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.50/2.16  % (309142)CaDiCaL version: 2.1.3
% 6.50/2.16  % (309142)Termination reason: Refutation
% 6.50/2.16  % (309142)Time elapsed: 0.022 s
% 6.50/2.16  % (309142)Peak memory usage: 90 MB
% 6.50/2.16  % (309142)Instructions burned: 20 (million)
% 6.50/2.16  % (309142)------------------------------
% 6.50/2.16  % (309142)------------------------------
% 6.50/2.16  % (309124)Success in time 0.815 s
% 6.50/2.16  % Vampire exiting
%------------------------------------------------------------------------------