TSTP Solution File: SYO304^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYO304^5 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n002.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 09:03:54 EDT 2024

% Result   : Theorem 0.17s 0.34s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   54 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :  182 (  75 equ;   5 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :  247 (  42   ~;  37   |;   4   &; 116   @)
%                                         (   4 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   64 (  64   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (   9 usr;  10 con; 0-2 aty)
%                                         (  16  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   77 (  62   ^  12   !;   2   ?;  77   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_11,type,
    sK0: ( a > a > $o ) > $o ).

thf(func_def_14,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(func_def_15,type,
    sK3: a ).

thf(func_def_16,type,
    sK4: a ).

thf(func_def_17,type,
    sK5: a > $o ).

thf(f126,plain,
    $false,
    inference(avatar_sat_refutation,[],[f36,f41,f46,f75,f121]) ).

thf(f121,plain,
    ( ~ spl1_1
    | ~ spl1_3
    | ~ spl1_4 ),
    inference(avatar_contradiction_clause,[],[f120]) ).

thf(f120,plain,
    ( $false
    | ~ spl1_1
    | ~ spl1_3
    | ~ spl1_4 ),
    inference(trivial_inequality_removal,[],[f116]) ).

thf(f116,plain,
    ( ( $true = $false )
    | ~ spl1_1
    | ~ spl1_3
    | ~ spl1_4 ),
    inference(superposition,[],[f45,f76]) ).

thf(f76,plain,
    ( ( $false
      = ( sK5 @ sK3 ) )
    | ~ spl1_1
    | ~ spl1_3 ),
    inference(superposition,[],[f40,f32]) ).

thf(f32,plain,
    ( ( sK3 = sK4 )
    | ~ spl1_1 ),
    inference(avatar_component_clause,[],[f30]) ).

thf(f30,plain,
    ( spl1_1
  <=> ( sK3 = sK4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

thf(f40,plain,
    ( ( ( sK5 @ sK4 )
      = $false )
    | ~ spl1_3 ),
    inference(avatar_component_clause,[],[f38]) ).

thf(f38,plain,
    ( spl1_3
  <=> ( ( sK5 @ sK4 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

thf(f45,plain,
    ( ( $true
      = ( sK5 @ sK3 ) )
    | ~ spl1_4 ),
    inference(avatar_component_clause,[],[f43]) ).

thf(f43,plain,
    ( spl1_4
  <=> ( $true
      = ( sK5 @ sK3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

thf(f75,plain,
    ( spl1_1
    | ~ spl1_2 ),
    inference(avatar_contradiction_clause,[],[f74]) ).

thf(f74,plain,
    ( $false
    | spl1_1
    | ~ spl1_2 ),
    inference(subsumption_resolution,[],[f48,f31]) ).

thf(f31,plain,
    ( ( sK3 != sK4 )
    | spl1_1 ),
    inference(avatar_component_clause,[],[f30]) ).

thf(f48,plain,
    ( ( sK3 = sK4 )
    | ~ spl1_2 ),
    inference(leibniz_equality_elimination,[],[f35]) ).

thf(f35,plain,
    ( ! [X1: a > $o] :
        ( ( $false
          = ( X1 @ sK3 ) )
        | ( ( X1 @ sK4 )
          = $true ) )
    | ~ spl1_2 ),
    inference(avatar_component_clause,[],[f34]) ).

thf(f34,plain,
    ( spl1_2
  <=> ! [X1: a > $o] :
        ( ( ( X1 @ sK4 )
          = $true )
        | ( $false
          = ( X1 @ sK3 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

thf(f46,plain,
    ( ~ spl1_1
    | spl1_4 ),
    inference(avatar_split_clause,[],[f24,f43,f30]) ).

thf(f24,plain,
    ( ( sK3 != sK4 )
    | ( $true
      = ( sK5 @ sK3 ) ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f22,plain,
    ( ( $false
      = ( ( sK5 @ sK3 )
       => ( sK5 @ sK4 ) ) )
    | ( sK3 != sK4 ) ),
    inference(beta_eta_normalization,[],[f21]) ).

thf(f21,plain,
    ( ( ( ^ [Y0: a > $o] :
            ( ( Y0 @ sK3 )
           => ( Y0 @ sK4 ) )
        @ sK5 )
      = $false )
    | ( sK3 != sK4 ) ),
    inference(sigma_clausification,[],[f20]) ).

thf(f20,plain,
    ( ( ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( Y0 @ sK3 )
           => ( Y0 @ sK4 ) ) )
      = $false )
    | ( sK3 != sK4 ) ),
    inference(equality_proxy_clausification,[],[f19]) ).

thf(f19,plain,
    ( ( ( sK3 = sK4 )
      = $false )
    | ( ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( Y0 @ sK3 )
           => ( Y0 @ sK4 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ( ( !! @ ( a > $o )
      @ ^ [Y0: a > $o] :
          ( ( Y0 @ sK3 )
         => ( Y0 @ sK4 ) ) )
   != ( sK3 = sK4 ) ),
    inference(beta_eta_normalization,[],[f16]) ).

thf(f16,plain,
    ( ( sK3 = sK4 )
   != ( ^ [Y0: a] :
          ( !! @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( Y1 @ sK3 )
             => ( Y1 @ Y0 ) ) )
      @ sK4 ) ),
    inference(negative_extensionality,[],[f15]) ).

thf(f15,plain,
    ( ( (=) @ sK3 )
   != ( ^ [Y0: a] :
          ( !! @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( Y1 @ sK3 )
             => ( Y1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f14]) ).

thf(f14,plain,
    ( ( ^ [Y0: a,Y1: a] :
          ( !! @ ( a > $o )
          @ ^ [Y2: a > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) )
      @ sK3 )
   != ( (=) @ sK3 ) ),
    inference(negative_extensionality,[],[f13]) ).

thf(f13,plain,
    ( ( ^ [Y0: a,Y1: a] :
          ( !! @ ( a > $o )
          @ ^ [Y2: a > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) ) )
   != (=) ),
    inference(trivial_inequality_removal,[],[f12]) ).

thf(f12,plain,
    ( ( ( ^ [Y0: a,Y1: a] :
            ( !! @ ( a > $o )
            @ ^ [Y2: a > $o] :
                ( ( Y2 @ Y0 )
               => ( Y2 @ Y1 ) ) ) )
     != (=) )
    | ( $true != $true ) ),
    inference(constrained_superposition,[],[f11,f9]) ).

thf(f9,plain,
    ( $true
    = ( sK0
      @ ^ [Y0: a,Y1: a] :
          ( !! @ ( a > $o )
          @ ^ [Y2: a > $o] :
              ( ( Y2 @ Y0 )
             => ( Y2 @ Y1 ) ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( ( sK0
        @ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
     != $true )
    & ( $true
      = ( sK0
        @ ^ [Y0: a,Y1: a] :
            ( !! @ ( a > $o )
            @ ^ [Y2: a > $o] :
                ( ( Y2 @ Y0 )
               => ( Y2 @ Y1 ) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: ( a > a > $o ) > $o] :
        ( ( $true
         != ( X0
            @ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) )
        & ( $true
          = ( X0
            @ ^ [Y0: a,Y1: a] :
                ( !! @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( Y2 @ Y0 )
                   => ( Y2 @ Y1 ) ) ) ) ) )
   => ( ( ( sK0
          @ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
       != $true )
      & ( $true
        = ( sK0
          @ ^ [Y0: a,Y1: a] :
              ( !! @ ( a > $o )
              @ ^ [Y2: a > $o] :
                  ( ( Y2 @ Y0 )
                 => ( Y2 @ Y1 ) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f6,plain,
    ? [X0: ( a > a > $o ) > $o] :
      ( ( $true
       != ( X0
          @ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) )
      & ( $true
        = ( X0
          @ ^ [Y0: a,Y1: a] :
              ( !! @ ( a > $o )
              @ ^ [Y2: a > $o] :
                  ( ( Y2 @ Y0 )
                 => ( Y2 @ Y1 ) ) ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: ( a > a > $o ) > $o] :
        ( ( $true
          = ( X0
            @ ^ [Y0: a,Y1: a] :
                ( !! @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( Y2 @ Y0 )
                   => ( Y2 @ Y1 ) ) ) ) )
       => ( $true
          = ( X0
            @ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ! [X0: ( a > a > $o ) > $o] :
      ( ( X0
        @ ^ [X1: a,X2: a] :
          ! [X3: a > $o] :
            ( ( X3 @ X1 )
           => ( X3 @ X2 ) ) )
     => ( X0
        @ ^ [X1: a,X2: a] : ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE2_eq__pme) ).

thf(f11,plain,
    ( ( sK0 @ (=) )
   != $true ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( ( sK0
      @ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
   != $true ),
    inference(cnf_transformation,[],[f8]) ).

thf(f41,plain,
    ( spl1_3
    | ~ spl1_1 ),
    inference(avatar_split_clause,[],[f23,f30,f38]) ).

thf(f23,plain,
    ( ( sK3 != sK4 )
    | ( ( sK5 @ sK4 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f36,plain,
    ( spl1_1
    | spl1_2 ),
    inference(avatar_split_clause,[],[f28,f34,f30]) ).

thf(f28,plain,
    ! [X1: a > $o] :
      ( ( ( X1 @ sK4 )
        = $true )
      | ( $false
        = ( X1 @ sK3 ) )
      | ( sK3 = sK4 ) ),
    inference(binary_proxy_clausification,[],[f27]) ).

thf(f27,plain,
    ! [X1: a > $o] :
      ( ( $true
        = ( ( X1 @ sK3 )
         => ( X1 @ sK4 ) ) )
      | ( sK3 = sK4 ) ),
    inference(beta_eta_normalization,[],[f26]) ).

thf(f26,plain,
    ! [X1: a > $o] :
      ( ( ( ^ [Y0: a > $o] :
              ( ( Y0 @ sK3 )
             => ( Y0 @ sK4 ) )
          @ X1 )
        = $true )
      | ( sK3 = sK4 ) ),
    inference(pi_clausification,[],[f25]) ).

thf(f25,plain,
    ( ( ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( Y0 @ sK3 )
           => ( Y0 @ sK4 ) ) )
      = $true )
    | ( sK3 = sK4 ) ),
    inference(equality_proxy_clausification,[],[f18]) ).

thf(f18,plain,
    ( ( ( sK3 = sK4 )
      = $true )
    | ( ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( Y0 @ sK3 )
           => ( Y0 @ sK4 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SYO304^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.12  % 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
% 0.11/0.32  % Computer : n002.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon May 20 09:20:52 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  This is a TH0_THM_EQU_NAR problem
% 0.11/0.32  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/benchmark/theBenchmark.p
% 0.17/0.33  % (10784)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.17/0.34  % (10785)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)
% 0.17/0.34  % (10786)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)
% 0.17/0.34  % (10786)Refutation not found, incomplete strategy
% 0.17/0.34  % (10786)------------------------------
% 0.17/0.34  % (10786)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34  % (10786)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.34  
% 0.17/0.34  
% 0.17/0.34  % (10786)Memory used [KB]: 5500
% 0.17/0.34  % (10786)Time elapsed: 0.002 s
% 0.17/0.34  % (10786)Instructions burned: 1 (million)
% 0.17/0.34  % (10786)------------------------------
% 0.17/0.34  % (10786)------------------------------
% 0.17/0.34  % (10785)Refutation not found, incomplete strategy
% 0.17/0.34  % (10785)------------------------------
% 0.17/0.34  % (10785)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34  % (10785)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.34  
% 0.17/0.34  
% 0.17/0.34  % (10785)Memory used [KB]: 5500
% 0.17/0.34  % (10785)Time elapsed: 0.002 s
% 0.17/0.34  % (10785)Instructions burned: 1 (million)
% 0.17/0.34  % (10785)------------------------------
% 0.17/0.34  % (10785)------------------------------
% 0.17/0.34  % (10788)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)
% 0.17/0.34  % (10787)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.17/0.34  % (10788)Instruction limit reached!
% 0.17/0.34  % (10788)------------------------------
% 0.17/0.34  % (10788)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34  % (10791)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)
% 0.17/0.34  % (10788)Termination reason: Unknown
% 0.17/0.34  % (10788)Termination phase: Saturation
% 0.17/0.34  
% 0.17/0.34  % (10788)Memory used [KB]: 5500
% 0.17/0.34  % (10788)Time elapsed: 0.003 s
% 0.17/0.34  % (10788)Instructions burned: 2 (million)
% 0.17/0.34  % (10788)------------------------------
% 0.17/0.34  % (10788)------------------------------
% 0.17/0.34  % (10784)First to succeed.
% 0.17/0.34  % (10787)Refutation not found, incomplete strategy
% 0.17/0.34  % (10787)------------------------------
% 0.17/0.34  % (10787)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34  % (10787)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.34  
% 0.17/0.34  
% 0.17/0.34  % (10787)Memory used [KB]: 5500
% 0.17/0.34  % (10787)Time elapsed: 0.002 s
% 0.17/0.34  % (10787)Instructions burned: 1 (million)
% 0.17/0.34  % (10787)------------------------------
% 0.17/0.34  % (10787)------------------------------
% 0.17/0.34  % (10789)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)
% 0.17/0.34  % (10791)Refutation not found, incomplete strategy
% 0.17/0.34  % (10791)------------------------------
% 0.17/0.34  % (10791)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34  % (10784)Refutation found. Thanks to Tanya!
% 0.17/0.34  % SZS status Theorem for theBenchmark
% 0.17/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.34  % (10784)------------------------------
% 0.17/0.34  % (10784)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34  % (10784)Termination reason: Refutation
% 0.17/0.34  
% 0.17/0.34  % (10784)Memory used [KB]: 5628
% 0.17/0.34  % (10784)Time elapsed: 0.007 s
% 0.17/0.34  % (10784)Instructions burned: 13 (million)
% 0.17/0.34  % (10784)------------------------------
% 0.17/0.34  % (10784)------------------------------
% 0.17/0.34  % (10783)Success in time 0.002 s
% 0.17/0.34  % Vampire---4.8 exiting
%------------------------------------------------------------------------------