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Vampire---5.0.1.UNS-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SWC223-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/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 01:03:00 PM UTC 2026

% Result   : Unsatisfiable 6.21s 1.67s
% Output   : Refutation 6.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   46 (  11 unt;   1 def)
%            Number of atoms       :  158 (  37 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  230 ( 118   ~; 111   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   2 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   58 (   0 sgn  58   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).

fof(f71,axiom,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).

fof(f74,axiom,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).

fof(f77,axiom,
    ! [X0] :
      ( ssList(tl(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).

fof(f78,axiom,
    ! [X0] :
      ( ssItem(hd(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause78) ).

fof(f86,axiom,
    ! [X0,X1] :
      ( ssList(cons(X0,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).

fof(f107,axiom,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | ~ ssList(X0)
      | nil = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).

fof(f125,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | app(cons(X0,nil),X1) = cons(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).

fof(f126,plain,
    ! [X0,X1] :
      ( cons(X0,X1) = app(cons(X0,nil),X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(reorient_equations,[],[f125]) ).

fof(f202,negated_conjecture,
    ssList(sk3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).

fof(f205,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).

fof(f206,negated_conjecture,
    nil != sk1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

fof(f207,negated_conjecture,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | app(app(X1,cons(X0,nil)),X2) != sk1
      | ssItem(sk5(X2,X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).

fof(f208,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | sk1 != app(app(X1,cons(X0,nil)),X2)
      | ssItem(sk5(X2,X1,X0)) ),
    inference(reorient_equations,[],[f207]) ).

fof(f209,negated_conjecture,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | app(app(X1,cons(X0,nil)),X2) != sk1
      | memberP(X1,sk5(X2,X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).

fof(f210,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | sk1 != app(app(X1,cons(X0,nil)),X2)
      | memberP(X1,sk5(X2,X1,X0)) ),
    inference(reorient_equations,[],[f209]) ).

fof(f223,plain,
    nil != sk3,
    inference(definition_unfolding,[],[f206,f205]) ).

fof(f224,plain,
    ! [X2,X0,X1] :
      ( sk3 != app(app(X1,cons(X0,nil)),X2)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssItem(X0)
      | ssItem(sk5(X2,X1,X0)) ),
    inference(definition_unfolding,[],[f208,f205]) ).

fof(f225,plain,
    ! [X2,X0,X1] :
      ( sk3 != app(app(X1,cons(X0,nil)),X2)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssItem(X0)
      | memberP(X1,sk5(X2,X1,X0)) ),
    inference(definition_unfolding,[],[f210,f205]) ).

fof(f264,definition,
    ( spl0_2
  <=> ssList(nil) ),
    introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).

fof(f265,plain,
    ( ssList(nil)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f300,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f8,f264]) ).

fof(f301,plain,
    ! [X0,X1] :
      ( app(cons(X0,nil),X1) != sk3
      | ~ ssList(nil)
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ssItem(sk5(X1,nil,X0))
      | ~ ssList(cons(X0,nil)) ),
    inference(superposition,[],[f224,f74]) ).

fof(f302,plain,
    ! [X0,X1] :
      ( app(cons(X0,nil),X1) != sk3
      | ~ ssList(nil)
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ssItem(sk5(X1,nil,X0)) ),
    inference(forward_subsumption_resolution,[],[f301,f86]) ).

fof(f303,plain,
    ( ! [X0,X1] :
        ( app(cons(X0,nil),X1) != sk3
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | ssItem(sk5(X1,nil,X0)) )
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[],[f302,f265]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( app(cons(X0,nil),X1) != sk3
      | ~ ssList(nil)
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | memberP(nil,sk5(X1,nil,X0))
      | ~ ssList(cons(X0,nil)) ),
    inference(superposition,[],[f225,f74]) ).

fof(f306,plain,
    ! [X0,X1] :
      ( app(cons(X0,nil),X1) != sk3
      | ~ ssList(nil)
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | memberP(nil,sk5(X1,nil,X0)) ),
    inference(forward_subsumption_resolution,[],[f305,f86]) ).

fof(f307,plain,
    ( ! [X0,X1] :
        ( app(cons(X0,nil),X1) != sk3
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | memberP(nil,sk5(X1,nil,X0)) )
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[],[f306,f265]) ).

fof(f318,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | memberP(nil,sk5(X1,nil,X0))
        | ~ ssList(X1)
        | ~ ssItem(X0) )
    | ~ spl0_2 ),
    inference(superposition,[],[f307,f126]) ).

fof(f319,plain,
    ( ! [X0,X1] :
        ( memberP(nil,sk5(X1,nil,X0))
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | cons(X0,X1) != sk3 )
    | ~ spl0_2 ),
    inference(duplicate_literal_removal,[],[f318]) ).

fof(f320,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssItem(X1)
        | cons(X1,X0) != sk3
        | ~ ssItem(sk5(X0,nil,X1)) )
    | ~ spl0_2 ),
    inference(resolution,[],[f319,f71]) ).

fof(f321,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | ssItem(sk5(X1,nil,X0))
        | ~ ssList(X1)
        | ~ ssItem(X0) )
    | ~ spl0_2 ),
    inference(superposition,[],[f303,f126]) ).

fof(f322,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssList(X1)
        | ~ ssItem(X0)
        | ssItem(sk5(X1,nil,X0)) )
    | ~ spl0_2 ),
    inference(duplicate_literal_removal,[],[f321]) ).

fof(f323,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sk3
        | ~ ssList(X1)
        | ~ ssItem(X0) )
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[],[f322,f320]) ).

fof(f324,plain,
    ( ! [X0] :
        ( sk3 != X0
        | ~ ssList(tl(X0))
        | ~ ssItem(hd(X0))
        | ~ ssList(X0)
        | nil = X0 )
    | ~ spl0_2 ),
    inference(superposition,[],[f323,f107]) ).

fof(f325,plain,
    ( ! [X0] :
        ( sk3 != X0
        | ~ ssItem(hd(X0))
        | ~ ssList(X0)
        | nil = X0 )
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[],[f324,f77]) ).

fof(f326,plain,
    ( ! [X0] :
        ( nil = X0
        | ~ ssList(X0)
        | sk3 != X0 )
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[],[f325,f78]) ).

fof(f331,plain,
    ( ! [X0] :
        ( sk3 != X0
        | ~ ssList(X0)
        | sk3 != X0 )
    | ~ spl0_2 ),
    inference(superposition,[],[f223,f326]) ).

fof(f340,plain,
    ( ! [X0] :
        ( sk3 != X0
        | ~ ssList(X0) )
    | ~ spl0_2 ),
    inference(duplicate_literal_removal,[],[f331]) ).

fof(f341,plain,
    ( ~ ssList(sk3)
    | ~ spl0_2 ),
    inference(equality_resolution,[],[f340]) ).

fof(f342,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[],[f341,f202]) ).

fof(f343,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f342]) ).

cnf(s10,plain,
    spl0_2,
    inference(sat_conversion,[],[f300]) ).

cnf(s11,plain,
    ~ spl0_2,
    inference(sat_conversion,[],[f343]) ).

cnf(s12,plain,
    $false,
    inference(rat,[],[s10,s11]) ).

fof(f344,plain,
    $false,
    inference(avatar_sat_refutation,[],[s12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC223-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23  % Computer : n005.cluster.edu
% 0.10/0.23  % Model    : x86_64 x86_64
% 0.10/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23  % Memory   : 8046.5625MB
% 0.10/0.23  % OS       : Linux 6.8.0-71-generic
% 0.10/0.23  % CPULimit : 300
% 0.10/0.23  % WCLimit  : 300
% 0.10/0.23  % DateTime : Mon Sep 28 08:32:47 UTC 2026
% 0.10/0.24  % CPUTime  : 
% 0.10/0.24  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.29  Running first-order theorem proving
% 0.24/0.29  Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.68/1.43  % (642210)Input is clausal, will run a generic CNF schedule.
% 5.68/1.43  % (642223)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1409503489:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.68/1.43  % (642221)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=1296214816:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.68/1.43  % (642222)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3373683889:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.68/1.43  % (642226)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2173220003:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.68/1.43  % (642224)lrs+10_1_sil=8000:sp=occurrence:random_seed=1800821561:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.68/1.43  % (642227)dis-21_1_sil=8000:lcm=predicate:random_seed=3365750897:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 5.68/1.43  % (642225)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3201848733:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.68/1.43  % (642227)Instruction limit reached! 
% 5.68/1.43  % (642227)------------------------------
% 5.68/1.43  % (642227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43  % (642227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43  % (642227)CaDiCaL version: 2.1.3
% 5.68/1.43  % (642227)Termination reason: Instruction limit
% 5.68/1.43  % (642227)Termination phase: Saturation
% 5.68/1.43  % (642227)Time elapsed: 0.090 s
% 5.68/1.43  % (642227)Peak memory usage: 89 MB
% 5.68/1.43  % (642227)Instructions burned: 118 (million)
% 5.68/1.43  % (642224)Instruction limit reached! 
% 5.68/1.43  % (642224)------------------------------
% 5.68/1.43  % (642224)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43  % (642224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43  % (642224)CaDiCaL version: 2.1.3
% 5.68/1.43  % (642224)Termination reason: Instruction limit
% 5.68/1.43  % (642224)Termination phase: Saturation
% 5.68/1.43  % (642224)Time elapsed: 0.105 s
% 5.68/1.43  % (642224)Peak memory usage: 90 MB
% 5.68/1.43  % (642224)Instructions burned: 108 (million)
% 5.68/1.43  % (642225)Instruction limit reached! 
% 5.68/1.43  % (642225)------------------------------
% 5.68/1.43  % (642225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43  % (642225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43  % (642225)CaDiCaL version: 2.1.3
% 5.68/1.43  % (642225)Termination reason: Instruction limit
% 5.68/1.43  % (642225)Termination phase: Saturation
% 5.68/1.43  % (642225)Time elapsed: 0.106 s
% 5.68/1.43  % (642225)Peak memory usage: 88 MB
% 5.68/1.43  % (642225)Instructions burned: 114 (million)
% 5.68/1.43  % (642226)Instruction limit reached! 
% 5.68/1.43  % (642226)------------------------------
% 5.68/1.43  % (642226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43  % (642226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43  % (642226)CaDiCaL version: 2.1.3
% 5.68/1.43  % (642226)Termination reason: Instruction limit
% 5.68/1.43  % (642226)Termination phase: Saturation
% 5.68/1.43  % (642226)Time elapsed: 0.180 s
% 5.68/1.43  % (642226)Peak memory usage: 90 MB
% 5.68/1.43  % (642226)Instructions burned: 180 (million)
% 5.68/1.43  % (642237)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3441018202:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 5.68/1.43  % (642223)First to succeed.
% 5.68/1.43  % (642223)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-642210"
% 5.68/1.43  % (642238)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1413506224:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 5.68/1.43  % (642239)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3088457154:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 5.68/1.43  % (642244)lrs+10_64_to=lpo:sil=8000:random_seed=48789336:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.21/1.67  % (642237)Instruction limit reached! 
% 6.21/1.67  % (642237)------------------------------
% 6.21/1.67  % (642237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.21/1.67  % (642237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.21/1.67  % (642237)CaDiCaL version: 2.1.3
% 6.21/1.67  % (642237)Termination reason: Instruction limit
% 6.21/1.67  % (642237)Termination phase: Saturation
% 6.21/1.67  % (642237)Time elapsed: 0.139 s
% 6.21/1.67  % (642237)Peak memory usage: 89 MB
% 6.21/1.67  % (642237)Instructions burned: 143 (million)
% 6.21/1.67  % (642238)Instruction limit reached! 
% 6.21/1.67  % (642238)------------------------------
% 6.21/1.67  % (642238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.21/1.67  % (642238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.21/1.67  % (642238)CaDiCaL version: 2.1.3
% 6.21/1.67  % (642238)Termination reason: Instruction limit
% 6.21/1.67  % (642238)Termination phase: Saturation
% 6.21/1.67  % (642238)Time elapsed: 0.177 s
% 6.21/1.67  % (642238)Peak memory usage: 91 MB
% 6.21/1.67  % (642238)Instructions burned: 189 (million)
% 6.21/1.67  % (642244)Instruction limit reached! 
% 6.21/1.67  % (642244)------------------------------
% 6.21/1.67  % (642244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.21/1.67  % (642244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.21/1.67  % (642244)CaDiCaL version: 2.1.3
% 6.21/1.67  % (642244)Termination reason: Instruction limit
% 6.21/1.67  % (642244)Termination phase: Saturation
% 6.21/1.67  % (642244)Time elapsed: 0.116 s
% 6.21/1.67  % (642244)Peak memory usage: 90 MB
% 6.21/1.67  % (642244)Instructions burned: 126 (million)
% 6.21/1.67  % (642239)Instruction limit reached! 
% 6.21/1.67  % (642239)------------------------------
% 6.21/1.67  % (642239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.21/1.67  % (642239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.21/1.67  % (642239)CaDiCaL version: 2.1.3
% 6.21/1.67  % (642239)Termination reason: Instruction limit
% 6.21/1.67  % (642239)Termination phase: Saturation
% 6.21/1.67  % (642239)Time elapsed: 0.195 s
% 6.21/1.67  % (642239)Peak memory usage: 89 MB
% 6.21/1.67  % (642239)Instructions burned: 220 (million)
% 6.21/1.67  % (642223)Refutation found. Thanks to Tanya!
% 6.21/1.67  % SZS status Unsatisfiable for theBenchmark
% 6.21/1.67  % SZS output start Proof for theBenchmark
% See solution above
% 6.21/1.67  % (642223)------------------------------
% 6.21/1.67  % (642223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.21/1.67  % (642223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.21/1.67  % (642223)CaDiCaL version: 2.1.3
% 6.21/1.67  % (642223)Termination reason: Refutation
% 6.21/1.67  % (642223)Time elapsed: 0.448 s
% 6.21/1.67  % (642223)Peak memory usage: 132 MB
% 6.21/1.67  % (642223)Instructions burned: 982 (million)
% 6.21/1.67  % (642223)------------------------------
% 6.21/1.67  % (642223)------------------------------
% 6.21/1.67  % (642210)Success in time 0.795 s
% 6.21/1.67  % Vampire exiting
%------------------------------------------------------------------------------