TSTP Solution File: SET159^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET159^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:04:26 EDT 2024

% Result   : Theorem 0.16s 0.38s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   63 (  16 unt;   7 typ;   0 def)
%            Number of atoms       :  298 (  75 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :  316 (  34   ~; 121   |;   0   &; 154   @)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   39 (  20   ^  12   !;   6   ?;  39   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    a: $tType ).

thf(func_def_0,type,
    a: $tType ).

thf(func_def_7,type,
    sK0: a > $o ).

thf(func_def_8,type,
    sK1: a > $o ).

thf(func_def_9,type,
    sK2: a > $o ).

thf(func_def_11,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(func_def_12,type,
    sK5: a ).

thf(f84,plain,
    $false,
    inference(avatar_sat_refutation,[],[f51,f66,f67,f71,f75,f79,f82]) ).

thf(f82,plain,
    ( ~ spl3_1
    | ~ spl3_6 ),
    inference(avatar_contradiction_clause,[],[f81]) ).

thf(f81,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_6 ),
    inference(trivial_inequality_removal,[],[f80]) ).

thf(f80,plain,
    ( ( $true = $false )
    | ~ spl3_1
    | ~ spl3_6 ),
    inference(forward_demodulation,[],[f42,f64]) ).

thf(f64,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f62]) ).

thf(f62,plain,
    ( spl3_6
  <=> ( $false
      = ( sK0 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

thf(f42,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f40]) ).

thf(f40,plain,
    ( spl3_1
  <=> ( $true
      = ( sK0 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f79,plain,
    ( ~ spl3_3
    | ~ spl3_5 ),
    inference(avatar_contradiction_clause,[],[f78]) ).

thf(f78,plain,
    ( $false
    | ~ spl3_3
    | ~ spl3_5 ),
    inference(trivial_inequality_removal,[],[f77]) ).

thf(f77,plain,
    ( ( $true = $false )
    | ~ spl3_3
    | ~ spl3_5 ),
    inference(forward_demodulation,[],[f50,f59]) ).

thf(f59,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f57]) ).

thf(f57,plain,
    ( spl3_5
  <=> ( ( sK2 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

thf(f50,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f48]) ).

thf(f48,plain,
    ( spl3_3
  <=> ( $true
      = ( sK2 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

thf(f75,plain,
    ( ~ spl3_2
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f74]) ).

thf(f74,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f73]) ).

thf(f73,plain,
    ( ( $true = $false )
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(backward_demodulation,[],[f46,f55]) ).

thf(f55,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f53]) ).

thf(f53,plain,
    ( spl3_4
  <=> ( ( sK1 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

thf(f46,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f44]) ).

thf(f44,plain,
    ( spl3_2
  <=> ( ( sK1 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f71,plain,
    spl3_6,
    inference(avatar_split_clause,[],[f22,f62]) ).

thf(f22,plain,
    ( $false
    = ( sK0 @ sK5 ) ),
    inference(duplicate_literal_removal,[],[f20]) ).

thf(f20,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ( $false
      = ( sK0 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f19]) ).

thf(f19,plain,
    ( ( $false
      = ( sK0 @ sK5 ) )
    | ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ( ( $false
      = ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) )
    | ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( ( $false
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( ( ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) )
      = $false )
    | ( $false
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f11,plain,
    ( ( ( sK0 @ sK5 )
      | ( sK2 @ sK5 )
      | ( sK1 @ sK5 ) )
   != ( ( sK1 @ sK5 )
      | ( sK0 @ sK5 )
      | ( sK2 @ sK5 ) ) ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( ( ^ [Y0: a] :
          ( ( sK0 @ Y0 )
          | ( sK2 @ Y0 )
          | ( sK1 @ Y0 ) )
      @ sK5 )
   != ( ^ [Y0: a] :
          ( ( sK1 @ Y0 )
          | ( sK0 @ Y0 )
          | ( sK2 @ Y0 ) )
      @ sK5 ) ),
    inference(negative_extensionality,[],[f9]) ).

thf(f9,plain,
    ( ( ^ [Y0: a] :
          ( ( sK1 @ Y0 )
          | ( sK0 @ Y0 )
          | ( sK2 @ Y0 ) ) )
   != ( ^ [Y0: a] :
          ( ( sK0 @ Y0 )
          | ( sK2 @ Y0 )
          | ( sK1 @ Y0 ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( ^ [Y0: a] :
          ( ( sK1 @ Y0 )
          | ( sK0 @ Y0 )
          | ( sK2 @ Y0 ) ) )
   != ( ^ [Y0: a] :
          ( ( sK0 @ Y0 )
          | ( sK2 @ Y0 )
          | ( sK1 @ Y0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ^ [Y0: a] :
              ( ( X1 @ Y0 )
              | ( X0 @ Y0 )
              | ( X2 @ Y0 ) ) )
       != ( ^ [Y0: a] :
              ( ( X0 @ Y0 )
              | ( X2 @ Y0 )
              | ( X1 @ Y0 ) ) ) )
   => ( ( ^ [Y0: a] :
            ( ( sK1 @ Y0 )
            | ( sK0 @ Y0 )
            | ( sK2 @ Y0 ) ) )
     != ( ^ [Y0: a] :
            ( ( sK0 @ Y0 )
            | ( sK2 @ Y0 )
            | ( sK1 @ Y0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f6,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ^ [Y0: a] :
            ( ( X1 @ Y0 )
            | ( X0 @ Y0 )
            | ( X2 @ Y0 ) ) )
     != ( ^ [Y0: a] :
            ( ( X0 @ Y0 )
            | ( X2 @ Y0 )
            | ( X1 @ Y0 ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ^ [Y0: a] :
              ( ( X1 @ Y0 )
              | ( X0 @ Y0 )
              | ( X2 @ Y0 ) ) )
        = ( ^ [Y0: a] :
              ( ( X0 @ Y0 )
              | ( X2 @ Y0 )
              | ( X1 @ Y0 ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ^ [X3: a] :
              ( ( X1 @ X3 )
              | ( X2 @ X3 )
              | ( X0 @ X3 ) ) )
        = ( ^ [X4: a] :
              ( ( X2 @ X4 )
              | ( X0 @ X4 )
              | ( X1 @ X4 ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ^ [X3: a] :
              ( ( X1 @ X3 )
              | ( X2 @ X3 )
              | ( X0 @ X3 ) ) )
        = ( ^ [X3: a] :
              ( ( X2 @ X3 )
              | ( X0 @ X3 )
              | ( X1 @ X3 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ^ [X3: a] :
            ( ( X1 @ X3 )
            | ( X2 @ X3 )
            | ( X0 @ X3 ) ) )
      = ( ^ [X3: a] :
            ( ( X2 @ X3 )
            | ( X0 @ X3 )
            | ( X1 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.5XBuXfzt5d/Vampire---4.8_18808',cBOOL_PROP_64_pme) ).

thf(f67,plain,
    spl3_5,
    inference(avatar_split_clause,[],[f27,f57]) ).

thf(f27,plain,
    ( ( sK2 @ sK5 )
    = $false ),
    inference(duplicate_literal_removal,[],[f25]) ).

thf(f25,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f16]) ).

thf(f16,plain,
    ( ( $false
      = ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f66,plain,
    spl3_4,
    inference(avatar_split_clause,[],[f32,f53]) ).

thf(f32,plain,
    ( ( sK1 @ sK5 )
    = $false ),
    inference(duplicate_literal_removal,[],[f31]) ).

thf(f31,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f29]) ).

thf(f29,plain,
    ( ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f14,plain,
    ( ( $false
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f51,plain,
    ( spl3_1
    | spl3_2
    | spl3_3 ),
    inference(avatar_split_clause,[],[f38,f48,f44,f40]) ).

thf(f38,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( $true
      = ( sK2 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f37]) ).

thf(f37,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ( $true
      = ( sK2 @ sK5 ) )
    | ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( sK0 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f36]) ).

thf(f36,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( sK2 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( $true
      = ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) ) ),
    inference(duplicate_literal_removal,[],[f35]) ).

thf(f35,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( $true
      = ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( $true
      = ( sK0 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f34]) ).

thf(f34,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( sK2 @ sK5 ) )
    | ( ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f33]) ).

thf(f33,plain,
    ( ( $true
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) ) )
    | ( $true
      = ( sK2 @ sK5 ) )
    | ( ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

thf(f12,plain,
    ( ( $true
      = ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 )
        | ( sK2 @ sK5 ) ) )
    | ( ( ( sK0 @ sK5 )
        | ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET159^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36  % Computer : n023.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 16:29:08 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a TH0_THM_EQU_NAR problem
% 0.16/0.36  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.5XBuXfzt5d/Vampire---4.8_18808
% 0.16/0.38  % (19063)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (3000ds/18Mi)
% 0.16/0.38  % (19063)First to succeed.
% 0.16/0.38  % (19059)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (3000ds/27Mi)
% 0.16/0.38  % (19057)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (3000ds/183Mi)
% 0.16/0.38  % (19060)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.16/0.38  % (19061)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.16/0.38  % (19062)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (3000ds/275Mi)
% 0.16/0.38  % (19063)Refutation found. Thanks to Tanya!
% 0.16/0.38  % SZS status Theorem for Vampire---4
% 0.16/0.38  % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.38  % (19063)------------------------------
% 0.16/0.38  % (19063)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38  % (19063)Termination reason: Refutation
% 0.16/0.38  
% 0.16/0.38  % (19063)Memory used [KB]: 5500
% 0.16/0.38  % (19063)Time elapsed: 0.004 s
% 0.16/0.38  % (19063)Instructions burned: 3 (million)
% 0.16/0.38  % (19063)------------------------------
% 0.16/0.38  % (19063)------------------------------
% 0.16/0.38  % (19056)Success in time 0.003 s
% 0.16/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------