TSTP Solution File: LCL733^5 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL733^5 : 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 : n024.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 00:22:25 EDT 2024

% Result   : Theorem 0.20s 0.38s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   29 (   5 unt;   9 typ;   0 def)
%            Number of atoms       :  136 (  54 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives :  191 (  21   ~;  10   |;  13   &; 114   @)
%                                         (   0 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   86 (  86   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   7 usr;   4 con; 0-2 aty)
%                                         (   0  !!;   0  ??;   3 @@+;   0 @@-)
%            Number of variables   :   94 (   0   ^  43   !;  49   ?;  94   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_2,type,
    vEPSILON: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

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

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

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

thf(func_def_8,type,
    sK3: b ).

thf(func_def_9,type,
    sK4: ( b > $o ) > b ).

thf(func_def_11,type,
    ph6: 
      !>[X0: $tType] : X0 ).

thf(f47,plain,
    $false,
    inference(trivial_inequality_removal,[],[f40]) ).

thf(f40,plain,
    $false = $true,
    inference(superposition,[],[f38,f17]) ).

thf(f17,plain,
    ! [X0: ( b > $o ) > b] :
      ( $true
      = ( sK0 @ X0 @ ( sK1 @ X0 ) ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f14,plain,
    ( ! [X0: ( b > $o ) > b] :
        ( ( $true
         != ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) )
        & ( $true
          = ( sK0 @ X0 @ ( sK1 @ X0 ) ) ) )
    & ( ! [X4: b] :
          ( ( $true
            = ( sK2 @ sK3 ) )
          & ( $true
           != ( sK2 @ X4 ) ) )
      | ! [X7: b > $o] :
          ( ( ( X7 @ ( sK4 @ X7 ) )
            = $true )
          | ! [X8: b] :
              ( ( X7 @ X8 )
             != $true ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f13,f12,f11,f10,f9]) ).

thf(f9,plain,
    ! [X0: ( b > $o ) > b] :
      ( ? [X1: b > $o] :
          ( ( ( X1 @ ( X0 @ X1 ) )
           != $true )
          & ? [X2: b] :
              ( ( X1 @ X2 )
              = $true ) )
     => ( ( $true
         != ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) )
        & ? [X2: b] :
            ( ( sK0 @ X0 @ X2 )
            = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ! [X0: ( b > $o ) > b] :
      ( ? [X2: b] :
          ( ( sK0 @ X0 @ X2 )
          = $true )
     => ( $true
        = ( sK0 @ X0 @ ( sK1 @ X0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X3: b > $o] :
      ! [X4: b] :
        ( ? [X5: b] :
            ( $true
            = ( X3 @ X5 ) )
        & ( ( X3 @ X4 )
         != $true ) )
   => ! [X4: b] :
        ( ? [X5: b] :
            ( $true
            = ( sK2 @ X5 ) )
        & ( $true
         != ( sK2 @ X4 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X5: b] :
        ( $true
        = ( sK2 @ X5 ) )
   => ( $true
      = ( sK2 @ sK3 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ( ? [X6: ( b > $o ) > b] :
      ! [X7: b > $o] :
        ( ( ( X7 @ ( X6 @ X7 ) )
          = $true )
        | ! [X8: b] :
            ( ( X7 @ X8 )
           != $true ) )
   => ! [X7: b > $o] :
        ( ( ( X7 @ ( sK4 @ X7 ) )
          = $true )
        | ! [X8: b] :
            ( ( X7 @ X8 )
           != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ( ! [X0: ( b > $o ) > b] :
      ? [X1: b > $o] :
        ( ( ( X1 @ ( X0 @ X1 ) )
         != $true )
        & ? [X2: b] :
            ( ( X1 @ X2 )
            = $true ) )
    & ( ? [X3: b > $o] :
        ! [X4: b] :
          ( ? [X5: b] :
              ( $true
              = ( X3 @ X5 ) )
          & ( ( X3 @ X4 )
           != $true ) )
      | ? [X6: ( b > $o ) > b] :
        ! [X7: b > $o] :
          ( ( ( X7 @ ( X6 @ X7 ) )
            = $true )
          | ! [X8: b] :
              ( ( X7 @ X8 )
             != $true ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ( ! [X6: ( b > $o ) > b] :
      ? [X7: b > $o] :
        ( ( ( X7 @ ( X6 @ X7 ) )
         != $true )
        & ? [X8: b] :
            ( ( X7 @ X8 )
            = $true ) )
    & ( ? [X0: b > $o] :
        ! [X1: b] :
          ( ? [X2: b] :
              ( $true
              = ( X0 @ X2 ) )
          & ( ( X0 @ X1 )
           != $true ) )
      | ? [X3: ( b > $o ) > b] :
        ! [X4: b > $o] :
          ( ( ( X4 @ ( X3 @ X4 ) )
            = $true )
          | ! [X5: b] :
              ( ( X4 @ X5 )
             != $true ) ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ( ( ! [X0: b > $o] :
          ? [X1: b] :
            ( ? [X2: b] :
                ( $true
                = ( X0 @ X2 ) )
           => ( ( X0 @ X1 )
              = $true ) )
       => ? [X3: ( b > $o ) > b] :
          ! [X4: b > $o] :
            ( ? [X5: b] :
                ( ( X4 @ X5 )
                = $true )
           => ( ( X4 @ ( X3 @ X4 ) )
              = $true ) ) )
     => ? [X6: ( b > $o ) > b] :
        ! [X7: b > $o] :
          ( ? [X8: b] :
              ( ( X7 @ X8 )
              = $true )
         => ( ( X7 @ ( X6 @ X7 ) )
            = $true ) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,plain,
    ~ ( ( ! [X1: b > $o] :
          ? [X2: b] :
            ( ? [X3: b] :
                ( ( X1 @ X3 )
                = $true )
           => ( ( X1 @ X2 )
              = $true ) )
       => ? [X4: ( b > $o ) > b] :
          ! [X5: b > $o] :
            ( ? [X6: b] :
                ( ( X5 @ X6 )
                = $true )
           => ( ( X5 @ ( X4 @ X5 ) )
              = $true ) ) )
     => ? [X7: ( b > $o ) > b] :
        ! [X8: b > $o] :
          ( ? [X9: b] :
              ( $true
              = ( X8 @ X9 ) )
         => ( ( X8 @ ( X7 @ X8 ) )
            = $true ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ( ! [X1: b > $o] :
          ? [X2: b] :
            ( ? [X3: b] : ( X1 @ X3 )
           => ( X1 @ X2 ) )
       => ? [X4: ( b > $o ) > b] :
          ! [X5: b > $o] :
            ( ? [X6: b] : ( X5 @ X6 )
           => ( X5 @ ( X4 @ X5 ) ) ) )
     => ? [X7: ( b > $o ) > b] :
        ! [X8: b > $o] :
          ( ? [X9: b] : ( X8 @ X9 )
         => ( X8 @ ( X7 @ X8 ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ! [X0: ( b > $o ) > b > $o] :
          ( ! [X1: b > $o] :
            ? [X2: b] :
              ( ? [X3: b] : ( X1 @ X3 )
             => ( X1 @ X2 ) )
         => ? [X4: ( b > $o ) > b] :
            ! [X1: b > $o] :
              ( ? [X3: b] : ( X1 @ X3 )
             => ( X1 @ ( X4 @ X1 ) ) ) )
     => ? [X5: ( b > $o ) > b] :
        ! [X6: b > $o] :
          ( ? [X7: b] : ( X6 @ X7 )
         => ( X6 @ ( X5 @ X6 ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ! [X0: ( b > $o ) > b > $o] :
        ( ! [X1: b > $o] :
          ? [X2: b] :
            ( ? [X3: b] : ( X1 @ X3 )
           => ( X1 @ X2 ) )
       => ? [X4: ( b > $o ) > b] :
          ! [X1: b > $o] :
            ( ? [X3: b] : ( X1 @ X3 )
           => ( X1 @ ( X4 @ X1 ) ) ) )
   => ? [X5: ( b > $o ) > b] :
      ! [X6: b > $o] :
        ( ? [X7: b] : ( X6 @ X7 )
       => ( X6 @ ( X5 @ X6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5310_SUB4) ).

thf(f38,plain,
    ! [X0: b] :
      ( $false
      = ( sK0 @ @@+ @ b @ X0 ) ),
    inference(trivial_inequality_removal,[],[f35]) ).

thf(f35,plain,
    ! [X0: b] :
      ( ( $false
        = ( sK0 @ @@+ @ b @ X0 ) )
      | ( $true != $true ) ),
    inference(superposition,[],[f18,f33]) ).

thf(f33,plain,
    ! [X0: ( b > $o ) > b,X1: b] :
      ( ( $true
        = ( sK0 @ X0 @ ( @@+ @ b @ ( sK0 @ X0 ) ) ) )
      | ( $false
        = ( sK0 @ X0 @ X1 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f18,plain,
    ! [X0: ( b > $o ) > b] :
      ( $true
     != ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : LCL733^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14  % 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
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 02:19:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TH0_THM_NEQ_NAR problem
% 0.14/0.36  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/sandbox2/benchmark/theBenchmark.p
% 0.20/0.37  % (20546)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.20/0.37  % (20548)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)
% 0.20/0.37  % (20550)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)
% 0.20/0.38  % (20550)Instruction limit reached!
% 0.20/0.38  % (20550)------------------------------
% 0.20/0.38  % (20550)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38  % (20550)Termination reason: Unknown
% 0.20/0.38  % (20550)Termination phase: Saturation
% 0.20/0.38  
% 0.20/0.38  % (20550)Memory used [KB]: 895
% 0.20/0.38  % (20550)Time elapsed: 0.003 s
% 0.20/0.38  % (20550)Instructions burned: 2 (million)
% 0.20/0.38  % (20550)------------------------------
% 0.20/0.38  % (20550)------------------------------
% 0.20/0.38  % (20548)First to succeed.
% 0.20/0.38  % (20547)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)
% 0.20/0.38  % (20548)Refutation found. Thanks to Tanya!
% 0.20/0.38  % SZS status Theorem for theBenchmark
% 0.20/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38  % (20548)------------------------------
% 0.20/0.38  % (20548)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38  % (20548)Termination reason: Refutation
% 0.20/0.38  
% 0.20/0.38  % (20548)Memory used [KB]: 5500
% 0.20/0.38  % (20548)Time elapsed: 0.006 s
% 0.20/0.38  % (20548)Instructions burned: 3 (million)
% 0.20/0.38  % (20548)------------------------------
% 0.20/0.38  % (20548)------------------------------
% 0.20/0.38  % (20545)Success in time 0.011 s
% 0.20/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------