TSTP Solution File: SET632^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET632^5 : 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 : n029.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 03:12:34 EDT 2024

% Result   : Theorem 0.15s 0.32s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   33 (  10 unt;   7 typ;   0 def)
%            Number of atoms       :  203 (  80 equ;   0 cnn)
%            Maximal formula atoms :   14 (   7 avg)
%            Number of connectives :  207 (  51   ~;  30   |;  30   &;  83   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   74 (  12   ^  45   !;  16   ?;  74   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_5,type,
    sK0: a > $o ).

thf(func_def_6,type,
    sK1: a > $o ).

thf(func_def_7,type,
    sK2: a > $o ).

thf(func_def_9,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(func_def_10,type,
    sK5: a ).

thf(f43,plain,
    $false,
    inference(subsumption_resolution,[],[f40,f35]) ).

thf(f35,plain,
    ( ( sK1 @ sK5 )
   != $true ),
    inference(trivial_inequality_removal,[],[f34]) ).

thf(f34,plain,
    ( ( $true != $true )
    | ( ( sK1 @ sK5 )
     != $true ) ),
    inference(superposition,[],[f12,f29]) ).

thf(f29,plain,
    ( ( sK2 @ sK5 )
    = $true ),
    inference(trivial_inequality_removal,[],[f25]) ).

thf(f25,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( $false != $false ) ),
    inference(superposition,[],[f16,f19]) ).

thf(f19,plain,
    ! [X5: a] :
      ( ( $false
        = ( sK0 @ X5 ) )
      | ( ( sK2 @ X5 )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f18]) ).

thf(f18,plain,
    ! [X5: a] :
      ( ( $false
        = ( sK0 @ X5 ) )
      | ( ( sK2 @ X5 )
        = $true )
      | ( $true != $true ) ),
    inference(fool_paramodulation,[],[f11]) ).

thf(f11,plain,
    ! [X5: a] :
      ( ( ( sK0 @ X5 )
       != $true )
      | ( ( sK2 @ X5 )
        = $true ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ( ( sK0
     != ( ^ [Y0: a] : $false ) )
    & ! [X3: a] :
        ( ( ( sK0 @ X3 )
         != $true )
        | ( ( sK1 @ X3 )
          = $true ) )
    & ! [X4: a] :
        ( ( ( sK2 @ X4 )
         != $true )
        | ( ( sK1 @ X4 )
         != $true ) )
    & ! [X5: a] :
        ( ( ( sK0 @ X5 )
         != $true )
        | ( ( sK2 @ X5 )
          = $true ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).

thf(f9,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ( ^ [Y0: a] : $false )
         != X0 )
        & ! [X3: a] :
            ( ( ( X0 @ X3 )
             != $true )
            | ( ( X1 @ X3 )
              = $true ) )
        & ! [X4: a] :
            ( ( ( X2 @ X4 )
             != $true )
            | ( $true
             != ( X1 @ X4 ) ) )
        & ! [X5: a] :
            ( ( ( X0 @ X5 )
             != $true )
            | ( ( X2 @ X5 )
              = $true ) ) )
   => ( ( sK0
       != ( ^ [Y0: a] : $false ) )
      & ! [X3: a] :
          ( ( ( sK0 @ X3 )
           != $true )
          | ( ( sK1 @ X3 )
            = $true ) )
      & ! [X4: a] :
          ( ( ( sK2 @ X4 )
           != $true )
          | ( ( sK1 @ X4 )
           != $true ) )
      & ! [X5: a] :
          ( ( ( sK0 @ X5 )
           != $true )
          | ( ( sK2 @ X5 )
            = $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ( ^ [Y0: a] : $false )
       != X0 )
      & ! [X3: a] :
          ( ( ( X0 @ X3 )
           != $true )
          | ( ( X1 @ X3 )
            = $true ) )
      & ! [X4: a] :
          ( ( ( X2 @ X4 )
           != $true )
          | ( $true
           != ( X1 @ X4 ) ) )
      & ! [X5: a] :
          ( ( ( X0 @ X5 )
           != $true )
          | ( ( X2 @ X5 )
            = $true ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ? [X0: a > $o,X2: a > $o,X1: a > $o] :
      ( ( ( ^ [Y0: a] : $false )
       != X0 )
      & ! [X3: a] :
          ( ( ( X0 @ X3 )
           != $true )
          | ( ( X2 @ X3 )
            = $true ) )
      & ! [X5: a] :
          ( ( ( X1 @ X5 )
           != $true )
          | ( ( X2 @ X5 )
           != $true ) )
      & ! [X4: a] :
          ( ( ( X0 @ X4 )
           != $true )
          | ( $true
            = ( X1 @ X4 ) ) ) ),
    inference(flattening,[],[f6]) ).

thf(f6,plain,
    ? [X2: a > $o,X1: a > $o,X0: a > $o] :
      ( ( ( ^ [Y0: a] : $false )
       != X0 )
      & ! [X5: a] :
          ( ( ( X1 @ X5 )
           != $true )
          | ( ( X2 @ X5 )
           != $true ) )
      & ! [X3: a] :
          ( ( ( X0 @ X3 )
           != $true )
          | ( ( X2 @ X3 )
            = $true ) )
      & ! [X4: a] :
          ( ( ( X0 @ X4 )
           != $true )
          | ( $true
            = ( X1 @ X4 ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
        ( ( ~ ? [X5: a] :
                ( ( ( X2 @ X5 )
                  = $true )
                & ( ( X1 @ X5 )
                  = $true ) )
          & ! [X3: a] :
              ( ( ( X0 @ X3 )
                = $true )
             => ( ( X2 @ X3 )
                = $true ) )
          & ! [X4: a] :
              ( ( ( X0 @ X4 )
                = $true )
             => ( $true
                = ( X1 @ X4 ) ) ) )
       => ( ( ^ [Y0: a] : $false )
          = X0 ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ! [X3: a] :
              ( ( X0 @ X3 )
             => ( X2 @ X3 ) )
          & ! [X4: a] :
              ( ( X0 @ X4 )
             => ( X1 @ X4 ) )
          & ~ ? [X5: a] :
                ( ( X2 @ X5 )
                & ( X1 @ X5 ) ) )
       => ( ( ^ [X6: a] : $false )
          = X0 ) ),
    inference(rectify,[],[f2]) ).

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

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ! [X3: a] :
            ( ( X0 @ X3 )
           => ( X2 @ X3 ) )
        & ! [X3: a] :
            ( ( X0 @ X3 )
           => ( X1 @ X3 ) )
        & ~ ? [X3: a] :
              ( ( X2 @ X3 )
              & ( X1 @ X3 ) ) )
     => ( ( ^ [X3: a] : $false )
        = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_114_pme) ).

thf(f16,plain,
    ( ( sK0 @ sK5 )
   != $false ),
    inference(beta_eta_normalization,[],[f15]) ).

thf(f15,plain,
    ( ( sK0 @ sK5 )
   != ( ^ [Y0: a] : $false
      @ sK5 ) ),
    inference(negative_extensionality,[],[f14]) ).

thf(f14,plain,
    ( sK0
   != ( ^ [Y0: a] : $false ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f12,plain,
    ! [X4: a] :
      ( ( ( sK2 @ X4 )
       != $true )
      | ( ( sK1 @ X4 )
       != $true ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f40,plain,
    ( ( sK1 @ sK5 )
    = $true ),
    inference(trivial_inequality_removal,[],[f37]) ).

thf(f37,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( $false != $false ) ),
    inference(superposition,[],[f16,f23]) ).

thf(f23,plain,
    ! [X3: a] :
      ( ( $false
        = ( sK0 @ X3 ) )
      | ( ( sK1 @ X3 )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f22]) ).

thf(f22,plain,
    ! [X3: a] :
      ( ( ( sK1 @ X3 )
        = $true )
      | ( $true != $true )
      | ( $false
        = ( sK0 @ X3 ) ) ),
    inference(fool_paramodulation,[],[f13]) ).

thf(f13,plain,
    ! [X3: a] :
      ( ( ( sK0 @ X3 )
       != $true )
      | ( ( sK1 @ X3 )
        = $true ) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : SET632^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09  % 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
% 0.09/0.29  % Computer : n029.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Mon May 20 12:07:53 EDT 2024
% 0.14/0.29  % CPUTime    : 
% 0.14/0.29  This is a TH0_THM_EQU_NAR problem
% 0.14/0.30  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
% 0.15/0.31  % (16350)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.15/0.31  % (16347)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.15/0.31  % (16353)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.15/0.31  % (16352)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)
% 0.15/0.31  % (16350)Refutation not found, incomplete strategy
% 0.15/0.31  % (16350)------------------------------
% 0.15/0.31  % (16350)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31  % (16353)Refutation not found, incomplete strategy
% 0.15/0.31  % (16353)------------------------------
% 0.15/0.31  % (16353)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31  % (16353)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.31  
% 0.15/0.31  
% 0.15/0.31  % (16353)Memory used [KB]: 5500
% 0.15/0.31  % (16353)Time elapsed: 0.003 s
% 0.15/0.31  % (16353)Instructions burned: 2 (million)
% 0.15/0.31  % (16353)------------------------------
% 0.15/0.31  % (16353)------------------------------
% 0.15/0.31  % (16350)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.31  
% 0.15/0.31  
% 0.15/0.31  % (16350)Memory used [KB]: 5500
% 0.15/0.31  % (16350)Time elapsed: 0.003 s
% 0.15/0.31  % (16350)Instructions burned: 1 (million)
% 0.15/0.31  % (16350)------------------------------
% 0.15/0.31  % (16350)------------------------------
% 0.15/0.31  % (16352)Refutation not found, incomplete strategy
% 0.15/0.31  % (16352)------------------------------
% 0.15/0.31  % (16352)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31  % (16347)Refutation not found, incomplete strategy
% 0.15/0.31  % (16347)------------------------------
% 0.15/0.31  % (16347)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.31  % (16352)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.31  
% 0.15/0.31  
% 0.15/0.31  % (16352)Memory used [KB]: 5500
% 0.15/0.31  % (16352)Time elapsed: 0.003 s
% 0.15/0.31  % (16352)Instructions burned: 2 (million)
% 0.15/0.31  % (16352)------------------------------
% 0.15/0.31  % (16352)------------------------------
% 0.15/0.31  % (16347)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.31  
% 0.15/0.31  
% 0.15/0.31  % (16347)Memory used [KB]: 5500
% 0.15/0.31  % (16347)Time elapsed: 0.003 s
% 0.15/0.31  % (16347)Instructions burned: 2 (million)
% 0.15/0.31  % (16347)------------------------------
% 0.15/0.31  % (16347)------------------------------
% 0.15/0.31  % (16349)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)
% 0.15/0.31  % (16348)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)
% 0.15/0.32  % (16349)Refutation not found, incomplete strategy
% 0.15/0.32  % (16349)------------------------------
% 0.15/0.32  % (16349)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32  % (16349)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.32  
% 0.15/0.32  
% 0.15/0.32  % (16349)Memory used [KB]: 5500
% 0.15/0.32  % (16349)Time elapsed: 0.004 s
% 0.15/0.32  % (16349)Instructions burned: 2 (million)
% 0.15/0.32  % (16349)------------------------------
% 0.15/0.32  % (16349)------------------------------
% 0.15/0.32  % (16348)First to succeed.
% 0.15/0.32  % (16348)Refutation found. Thanks to Tanya!
% 0.15/0.32  % SZS status Theorem for theBenchmark
% 0.15/0.32  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.32  % (16348)------------------------------
% 0.15/0.32  % (16348)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32  % (16348)Termination reason: Refutation
% 0.15/0.32  
% 0.15/0.32  % (16348)Memory used [KB]: 5500
% 0.15/0.32  % (16348)Time elapsed: 0.006 s
% 0.15/0.32  % (16348)Instructions burned: 3 (million)
% 0.15/0.32  % (16348)------------------------------
% 0.15/0.32  % (16348)------------------------------
% 0.15/0.32  % (16346)Success in time 0.018 s
% 0.15/0.32  % Vampire---4.8 exiting
%------------------------------------------------------------------------------