TSTP Solution File: SEV256^5 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV256^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n019.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 : Mon Jun 24 16:02:30 EDT 2024

% Result   : Theorem 0.12s 0.39s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   20 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :  142 (  39 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :  177 (  15   ~;  13   |;  19   &; 109   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   60 (  60   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   5 usr;   3 con; 0-2 aty)
%                                         (   0  !!;   8  ??;   0 @@+;   0 @@-)
%            Number of variables   :   57 (  33   ^  19   !;   5   ?;  57   :)

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

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

thf(func_def_1,type,
    cOPEN: ( a > $o ) > $o ).

thf(func_def_10,type,
    sK0: ( ( a > $o ) > $o ) > a > $o ).

thf(func_def_13,type,
    ph2: 
      !>[X0: $tType] : X0 ).

thf(func_def_14,type,
    sK3: ( ( a > $o ) > $o ) > a ).

thf(func_def_15,type,
    sK4: ( ( a > $o ) > $o ) > a > $o ).

thf(f34,plain,
    $false,
    inference(trivial_inequality_removal,[],[f33]) ).

thf(f33,plain,
    $true = $false,
    inference(duplicate_literal_removal,[],[f32]) ).

thf(f32,plain,
    ( ( $true = $false )
    | ( $true = $false ) ),
    inference(beta_eta_normalization,[],[f26]) ).

thf(f26,plain,
    ( ( $true
      = ( ^ [Y0: a > $o] : $false
        @ ( sK4
          @ ^ [Y0: a > $o] : $false ) ) )
    | ( ( ^ [Y0: a > $o] : $false
        @ ( sK0
          @ ^ [Y0: a > $o] : $false ) )
      = $true ) ),
    inference(primitive_instantiation,[],[f23]) ).

thf(f23,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ( $true
        = ( X0 @ ( sK4 @ X0 ) ) )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f22,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ( $true
        = ( X0 @ ( sK0 @ X0 ) ) )
      | ( ( ( sK4 @ X0 @ ( sK3 @ X0 ) )
          & ( X0 @ ( sK4 @ X0 ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[],[f21]) ).

thf(f21,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ( $true
        = ( ^ [Y0: a > $o] :
              ( ( Y0 @ ( sK3 @ X0 ) )
              & ( X0 @ Y0 ) )
          @ ( sK4 @ X0 ) ) )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(sigma_clausification,[],[f20]) ).

thf(f20,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ( ( ?? @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( Y0 @ ( sK3 @ X0 ) )
              & ( X0 @ Y0 ) ) )
       != $false )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(beta_eta_normalization,[],[f19]) ).

thf(f19,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ( ( ^ [Y0: a] :
              ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ Y0 )
                  & ( X0 @ Y1 ) ) )
          @ ( sK3 @ X0 ) )
       != ( ^ [Y0: a] : $false
          @ ( sK3 @ X0 ) ) )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(negative_extensionality,[],[f18]) ).

thf(f18,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ( ( ^ [Y0: a] : $false )
       != ( ^ [Y0: a] :
              ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ Y0 )
                  & ( X0 @ Y1 ) ) ) ) )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(trivial_inequality_removal,[],[f13]) ).

thf(f13,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ( ( ^ [Y0: a] : $false )
       != ( ^ [Y0: a] :
              ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ Y0 )
                  & ( X0 @ Y1 ) ) ) ) )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) )
      | ( $true != $true ) ),
    inference(constrained_superposition,[],[f9,f11]) ).

thf(f11,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ( $true
        = ( cOPEN
          @ ^ [Y0: a] :
              ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ Y0 )
                  & ( X0 @ Y1 ) ) ) ) )
      | ( $true
        = ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ! [X0: ( a > $o ) > $o] :
        ( ( $true
          = ( cOPEN
            @ ^ [Y0: a] :
                ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ Y0 )
                    & ( X0 @ Y1 ) ) ) ) )
        | ( ( $true
            = ( X0 @ ( sK0 @ X0 ) ) )
          & ( $true
           != ( cOPEN @ ( sK0 @ X0 ) ) ) ) )
    & ( $true
     != ( cOPEN
        @ ^ [Y0: a] : $false ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).

thf(f7,plain,
    ! [X0: ( a > $o ) > $o] :
      ( ? [X1: a > $o] :
          ( ( ( X0 @ X1 )
            = $true )
          & ( ( cOPEN @ X1 )
           != $true ) )
     => ( ( $true
          = ( X0 @ ( sK0 @ X0 ) ) )
        & ( $true
         != ( cOPEN @ ( sK0 @ X0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f6,plain,
    ( ! [X0: ( a > $o ) > $o] :
        ( ( $true
          = ( cOPEN
            @ ^ [Y0: a] :
                ( ?? @ ( a > $o )
                @ ^ [Y1: a > $o] :
                    ( ( Y1 @ Y0 )
                    & ( X0 @ Y1 ) ) ) ) )
        | ? [X1: a > $o] :
            ( ( ( X0 @ X1 )
              = $true )
            & ( ( cOPEN @ X1 )
             != $true ) ) )
    & ( $true
     != ( cOPEN
        @ ^ [Y0: a] : $false ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ( ! [X0: ( a > $o ) > $o] :
          ( ! [X1: a > $o] :
              ( ( ( X0 @ X1 )
                = $true )
             => ( ( cOPEN @ X1 )
                = $true ) )
         => ( $true
            = ( cOPEN
              @ ^ [Y0: a] :
                  ( ?? @ ( a > $o )
                  @ ^ [Y1: a > $o] :
                      ( ( Y1 @ Y0 )
                      & ( X0 @ Y1 ) ) ) ) ) )
     => ( $true
        = ( cOPEN
          @ ^ [Y0: a] : $false ) ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ( ! [X0: ( a > $o ) > $o] :
        ( ! [X1: a > $o] :
            ( ( X0 @ X1 )
           => ( cOPEN @ X1 ) )
       => ( cOPEN
          @ ^ [X1: a] :
            ? [X2: a > $o] :
              ( ( X0 @ X2 )
              & ( X2 @ X1 ) ) ) )
   => ( cOPEN
      @ ^ [X1: a] : $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM625A_pme) ).

thf(f9,plain,
    ( $true
   != ( cOPEN
      @ ^ [Y0: a] : $false ) ),
    inference(cnf_transformation,[],[f8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEV256^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.34  % Computer : n019.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   : Fri Jun 21 18:46:54 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.36  This is a TH0_THM_NEQ_NAR problem
% 0.12/0.36  Running higher-order theorem proving
% 0.12/0.36  Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.38  % (830)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 (2999ds/27Mi)
% 0.12/0.38  % (828)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.38  % (831)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.38  % (829)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 (2999ds/4Mi)
% 0.12/0.38  % (832)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 (2999ds/2Mi)
% 0.12/0.38  % (833)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 (2999ds/275Mi)
% 0.12/0.38  % (834)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.38  % (831)Instruction limit reached!
% 0.12/0.38  % (831)------------------------------
% 0.12/0.38  % (831)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (832)Instruction limit reached!
% 0.12/0.38  % (832)------------------------------
% 0.12/0.38  % (832)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (832)Termination reason: Unknown
% 0.12/0.38  % (832)Termination phase: Saturation
% 0.12/0.38  
% 0.12/0.38  % (832)Memory used [KB]: 5500
% 0.12/0.38  % (832)Time elapsed: 0.004 s
% 0.12/0.38  % (832)Instructions burned: 2 (million)
% 0.12/0.38  % (832)------------------------------
% 0.12/0.38  % (832)------------------------------
% 0.12/0.38  % (831)Termination reason: Unknown
% 0.12/0.38  % (831)Termination phase: Saturation
% 0.12/0.38  
% 0.12/0.38  % (831)Memory used [KB]: 5500
% 0.12/0.38  % (831)Time elapsed: 0.004 s
% 0.12/0.38  % (830)Refutation not found, incomplete strategy
% 0.12/0.38  % (830)------------------------------
% 0.12/0.38  % (830)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (830)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38  
% 0.12/0.38  
% 0.12/0.38  % (830)Memory used [KB]: 5500
% 0.12/0.38  % (830)Time elapsed: 0.004 s
% 0.12/0.38  % (830)Instructions burned: 2 (million)
% 0.12/0.38  % (830)------------------------------
% 0.12/0.38  % (830)------------------------------
% 0.12/0.38  % (831)Instructions burned: 2 (million)
% 0.12/0.38  % (831)------------------------------
% 0.12/0.38  % (831)------------------------------
% 0.12/0.38  % (833)Refutation not found, incomplete strategy
% 0.12/0.38  % (833)------------------------------
% 0.12/0.38  % (833)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38  % (833)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38  
% 0.12/0.38  
% 0.12/0.38  % (833)Memory used [KB]: 5500
% 0.12/0.39  % (833)Time elapsed: 0.004 s
% 0.12/0.39  % (833)Instructions burned: 2 (million)
% 0.12/0.39  % (833)------------------------------
% 0.12/0.39  % (833)------------------------------
% 0.12/0.39  % (829)Instruction limit reached!
% 0.12/0.39  % (829)------------------------------
% 0.12/0.39  % (829)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (829)Termination reason: Unknown
% 0.12/0.39  % (829)Termination phase: Saturation
% 0.12/0.39  
% 0.12/0.39  % (829)Memory used [KB]: 5500
% 0.12/0.39  % (829)Time elapsed: 0.006 s
% 0.12/0.39  % (829)Instructions burned: 5 (million)
% 0.12/0.39  % (829)------------------------------
% 0.12/0.39  % (829)------------------------------
% 0.12/0.39  % (834)First to succeed.
% 0.12/0.39  % (834)Refutation found. Thanks to Tanya!
% 0.12/0.39  % SZS status Theorem for theBenchmark
% 0.12/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.39  % (834)------------------------------
% 0.12/0.39  % (834)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39  % (834)Termination reason: Refutation
% 0.12/0.39  
% 0.12/0.39  % (834)Memory used [KB]: 5500
% 0.12/0.39  % (834)Time elapsed: 0.008 s
% 0.12/0.39  % (834)Instructions burned: 5 (million)
% 0.12/0.39  % (834)------------------------------
% 0.12/0.39  % (834)------------------------------
% 0.12/0.39  % (827)Success in time 0.033 s
%------------------------------------------------------------------------------