TSTP Solution File: SYO271^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYO271^5 : TPTP v8.2.0. 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n007.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 : Tue May 21 09:03:43 EDT 2024

% Result   : Theorem 0.12s 0.37s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   39 (   6 unt;  10 typ;   0 def)
%            Number of atoms       :  123 (  92 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  298 (  67   ~;  16   |;   8   &; 192   @)
%                                         (   2 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   77 (  39   ^  26   !;  10   ?;  77   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_7,type,
    a: $tType ).

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

thf(func_def_1,type,
    a: $tType ).

thf(func_def_2,type,
    cJ: ( b > $o ) > b ).

thf(func_def_4,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_11,type,
    sK0: b > a ).

thf(func_def_12,type,
    sK1: b > a ).

thf(func_def_14,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_15,type,
    sK4: b ).

thf(f41,plain,
    $false,
    inference(avatar_sat_refutation,[],[f36,f37,f40]) ).

thf(f40,plain,
    ~ spl2_1,
    inference(avatar_contradiction_clause,[],[f39]) ).

thf(f39,plain,
    ( $false
    | ~ spl2_1 ),
    inference(trivial_inequality_removal,[],[f38]) ).

thf(f38,plain,
    ( ( ( sK0 @ sK4 )
     != ( sK0 @ sK4 ) )
    | ~ spl2_1 ),
    inference(superposition,[],[f13,f22]) ).

thf(f22,plain,
    ( ! [X1: b] :
        ( ( sK1 @ X1 )
        = ( sK0 @ X1 ) )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f21]) ).

thf(f21,plain,
    ( spl2_1
  <=> ! [X1: b] :
        ( ( sK1 @ X1 )
        = ( sK0 @ X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f13,plain,
    ( ( sK1 @ sK4 )
   != ( sK0 @ sK4 ) ),
    inference(negative_extensionality,[],[f11]) ).

thf(f11,plain,
    sK0 != sK1,
    inference(cnf_transformation,[],[f9]) ).

thf(f9,plain,
    ( ( ( sK0
        @ ( cJ
          @ ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) ) ) )
      = ( sK1
        @ ( cJ
          @ ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) ) ) ) )
    & ( sK0 != sK1 )
    & ! [X2: b > $o] :
        ( ! [X3: b] :
            ( $true
           != ( X2 @ X3 ) )
        | ( ( X2 @ ( cJ @ X2 ) )
          = $true ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).

thf(f8,plain,
    ( ? [X0: b > a,X1: b > a] :
        ( ( ( X0
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( X0 @ Y0 )
                 != ( X1 @ Y0 ) ) ) )
          = ( X1
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( X0 @ Y0 )
                 != ( X1 @ Y0 ) ) ) ) )
        & ( X0 != X1 ) )
   => ( ( ( sK0
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) )
        = ( sK1
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) ) )
      & ( sK0 != sK1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f7,plain,
    ( ? [X0: b > a,X1: b > a] :
        ( ( ( X0
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( X0 @ Y0 )
                 != ( X1 @ Y0 ) ) ) )
          = ( X1
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( X0 @ Y0 )
                 != ( X1 @ Y0 ) ) ) ) )
        & ( X0 != X1 ) )
    & ! [X2: b > $o] :
        ( ! [X3: b] :
            ( $true
           != ( X2 @ X3 ) )
        | ( ( X2 @ ( cJ @ X2 ) )
          = $true ) ) ),
    inference(rectify,[],[f6]) ).

thf(f6,plain,
    ( ? [X2: b > a,X3: b > a] :
        ( ( ( X2
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( X2 @ Y0 )
                 != ( X3 @ Y0 ) ) ) )
          = ( X3
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( X2 @ Y0 )
                 != ( X3 @ Y0 ) ) ) ) )
        & ( X2 != X3 ) )
    & ! [X0: b > $o] :
        ( ! [X1: b] :
            ( ( X0 @ X1 )
           != $true )
        | ( ( X0 @ ( cJ @ X0 ) )
          = $true ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ! [X0: b > $o] :
          ( ? [X1: b] :
              ( ( X0 @ X1 )
              = $true )
         => ( ( X0 @ ( cJ @ X0 ) )
            = $true ) )
     => ! [X2: b > a,X3: b > a] :
          ( ( ( X2
              @ ( cJ
                @ ^ [Y0: b] :
                    ( ( X2 @ Y0 )
                   != ( X3 @ Y0 ) ) ) )
            = ( X3
              @ ( cJ
                @ ^ [Y0: b] :
                    ( ( X2 @ Y0 )
                   != ( X3 @ Y0 ) ) ) ) )
         => ( X2 = X3 ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ! [X0: b > $o] :
          ( ? [X1: b] : ( X0 @ X1 )
         => ( X0 @ ( cJ @ X0 ) ) )
     => ! [X2: b > a,X3: b > a] :
          ( ( ( X2
              @ ( cJ
                @ ^ [X4: b] :
                    ( ( X2 @ X4 )
                   != ( X3 @ X4 ) ) ) )
            = ( X3
              @ ( cJ
                @ ^ [X5: b] :
                    ( ( X2 @ X5 )
                   != ( X3 @ X5 ) ) ) ) )
         => ( X2 = X3 ) ) ),
    inference(rectify,[],[f2]) ).

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

thf(f1,conjecture,
    ( ! [X0: b > $o] :
        ( ? [X1: b] : ( X0 @ X1 )
       => ( X0 @ ( cJ @ X0 ) ) )
   => ! [X3: b > a,X2: b > a] :
        ( ( ( X3
            @ ( cJ
              @ ^ [X1: b] :
                  ( ( X2 @ X1 )
                 != ( X3 @ X1 ) ) ) )
          = ( X2
            @ ( cJ
              @ ^ [X1: b] :
                  ( ( X2 @ X1 )
                 != ( X3 @ X1 ) ) ) ) )
       => ( X2 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5500) ).

thf(f37,plain,
    ( ~ spl2_2
    | spl2_1 ),
    inference(avatar_split_clause,[],[f34,f21,f24]) ).

thf(f24,plain,
    ( spl2_2
  <=> ( ( sK0
        @ ( cJ
          @ ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) ) ) )
      = ( sK1
        @ ( cJ
          @ ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f34,plain,
    ! [X1: b] :
      ( ( ( sK0
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) )
       != ( sK1
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) ) )
      | ( ( sK1 @ X1 )
        = ( sK0 @ X1 ) ) ),
    inference(equality_proxy_clausification,[],[f33]) ).

thf(f33,plain,
    ! [X1: b] :
      ( ( ( sK0
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) )
       != ( sK1
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) ) )
      | ( ( ( sK0 @ X1 )
          = ( sK1 @ X1 ) )
        = $true ) ),
    inference(not_proxy_clausification,[],[f32]) ).

thf(f32,plain,
    ! [X1: b] :
      ( ( ( sK0
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) )
       != ( sK1
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) ) )
      | ( $false
        = ( ( sK0 @ X1 )
         != ( sK1 @ X1 ) ) ) ),
    inference(equality_proxy_clausification,[],[f31]) ).

thf(f31,plain,
    ! [X1: b] :
      ( ( ( ( sK0
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( sK0 @ Y0 )
                 != ( sK1 @ Y0 ) ) ) )
          = ( sK1
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( sK0 @ Y0 )
                 != ( sK1 @ Y0 ) ) ) ) )
        = $false )
      | ( $false
        = ( ( sK0 @ X1 )
         != ( sK1 @ X1 ) ) ) ),
    inference(not_proxy_clausification,[],[f30]) ).

thf(f30,plain,
    ! [X1: b] :
      ( ( ( ( sK0
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( sK0 @ Y0 )
                 != ( sK1 @ Y0 ) ) ) )
         != ( sK1
            @ ( cJ
              @ ^ [Y0: b] :
                  ( ( sK0 @ Y0 )
                 != ( sK1 @ Y0 ) ) ) ) )
        = $true )
      | ( $false
        = ( ( sK0 @ X1 )
         != ( sK1 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f28]) ).

thf(f28,plain,
    ! [X1: b] :
      ( ( ( ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) )
          @ X1 )
        = $false )
      | ( ( ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) )
          @ ( cJ
            @ ^ [Y0: b] :
                ( ( sK0 @ Y0 )
               != ( sK1 @ Y0 ) ) ) )
        = $true ) ),
    introduced(choice_axiom,[]) ).

thf(f36,plain,
    spl2_2,
    inference(avatar_contradiction_clause,[],[f35]) ).

thf(f35,plain,
    ( $false
    | spl2_2 ),
    inference(trivial_inequality_removal,[],[f29]) ).

thf(f29,plain,
    ( ( ( sK0
        @ ( cJ
          @ ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) ) ) )
     != ( sK0
        @ ( cJ
          @ ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) ) ) ) )
    | spl2_2 ),
    inference(superposition,[],[f26,f12]) ).

thf(f12,plain,
    ( ( sK0
      @ ( cJ
        @ ^ [Y0: b] :
            ( ( sK0 @ Y0 )
           != ( sK1 @ Y0 ) ) ) )
    = ( sK1
      @ ( cJ
        @ ^ [Y0: b] :
            ( ( sK0 @ Y0 )
           != ( sK1 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f9]) ).

thf(f26,plain,
    ( ( ( sK0
        @ ( cJ
          @ ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) ) ) )
     != ( sK1
        @ ( cJ
          @ ^ [Y0: b] :
              ( ( sK0 @ Y0 )
             != ( sK1 @ Y0 ) ) ) ) )
    | spl2_2 ),
    inference(avatar_component_clause,[],[f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SYO271^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon May 20 10:02:38 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  This is a TH0_THM_EQU_NAR problem
% 0.12/0.34  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/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36  % (1738)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 theBenchmark for (3000ds/27Mi)
% 0.12/0.36  % (1739)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.12/0.36  % (1740)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.12/0.36  % (1741)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.12/0.36  % (1742)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.12/0.36  % (1743)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.12/0.36  % (1739)Instruction limit reached!
% 0.12/0.36  % (1739)------------------------------
% 0.12/0.36  % (1739)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36  % (1739)Termination reason: Unknown
% 0.12/0.36  % (1739)Termination phase: Saturation
% 0.12/0.36  % (1740)Instruction limit reached!
% 0.12/0.36  % (1740)------------------------------
% 0.12/0.36  % (1740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36  % (1740)Termination reason: Unknown
% 0.12/0.36  % (1740)Termination phase: Saturation
% 0.12/0.36  
% 0.12/0.36  % (1740)Memory used [KB]: 5500
% 0.12/0.36  % (1740)Time elapsed: 0.003 s
% 0.12/0.36  % (1740)Instructions burned: 2 (million)
% 0.12/0.36  % (1740)------------------------------
% 0.12/0.36  % (1740)------------------------------
% 0.12/0.36  
% 0.12/0.36  % (1739)Memory used [KB]: 5500
% 0.12/0.36  % (1739)Time elapsed: 0.003 s
% 0.12/0.36  % (1739)Instructions burned: 2 (million)
% 0.12/0.36  % (1736)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.12/0.36  % (1739)------------------------------
% 0.12/0.36  % (1739)------------------------------
% 0.12/0.36  % (1737)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.12/0.36  % (1743)Instruction limit reached!
% 0.12/0.36  % (1743)------------------------------
% 0.12/0.36  % (1743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36  % (1743)Termination reason: Unknown
% 0.12/0.36  % (1743)Termination phase: Saturation
% 0.12/0.36  
% 0.12/0.36  % (1743)Memory used [KB]: 5500
% 0.12/0.36  % (1743)Time elapsed: 0.004 s
% 0.12/0.36  % (1743)Instructions burned: 4 (million)
% 0.12/0.36  % (1743)------------------------------
% 0.12/0.36  % (1743)------------------------------
% 0.12/0.36  % (1738)First to succeed.
% 0.12/0.36  % (1741)Refutation not found, incomplete strategy
% 0.12/0.36  % (1741)------------------------------
% 0.12/0.36  % (1741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36  % (1741)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.36  
% 0.12/0.36  
% 0.12/0.36  % (1741)Memory used [KB]: 5500
% 0.12/0.36  % (1741)Time elapsed: 0.004 s
% 0.12/0.36  % (1741)Instructions burned: 4 (million)
% 0.12/0.36  % (1741)------------------------------
% 0.12/0.36  % (1741)------------------------------
% 0.12/0.37  % (1738)Refutation found. Thanks to Tanya!
% 0.12/0.37  % SZS status Theorem for theBenchmark
% 0.12/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.37  % (1738)------------------------------
% 0.12/0.37  % (1738)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (1738)Termination reason: Refutation
% 0.12/0.37  
% 0.12/0.37  % (1738)Memory used [KB]: 5500
% 0.12/0.37  % (1738)Time elapsed: 0.005 s
% 0.12/0.37  % (1738)Instructions burned: 3 (million)
% 0.12/0.37  % (1738)------------------------------
% 0.12/0.37  % (1738)------------------------------
% 0.12/0.37  % (1735)Success in time 0.015 s
% 0.12/0.37  % Vampire---4.8 exiting
%------------------------------------------------------------------------------