TSTP Solution File: LCL727^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL727^5 : 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 : n018.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 00:22:23 EDT 2024

% Result   : Theorem 0.21s 0.39s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   24 (   4 unt;   7 typ;   0 def)
%            Number of atoms       :  121 (  49 equ;   0 cnn)
%            Maximal formula atoms :    8 (   7 avg)
%            Number of connectives :  197 (  25   ~;  12   |;  15   &; 121   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  119 ( 119   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   82 (   0   ^  49   !;  32   ?;  82   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_4,type,
    sK0: ( a > $o ) > $o ).

thf(func_def_5,type,
    sK1: ( ( a > $o ) > a ) > a > $o ).

thf(func_def_6,type,
    sK2: ( a > $o ) > a ).

thf(func_def_7,type,
    sK3: ( ( a > $o ) > a > $o ) > ( a > $o ) > a ).

thf(func_def_9,type,
    ph5: 
      !>[X0: $tType] : X0 ).

thf(f27,plain,
    $false,
    inference(subsumption_resolution,[],[f26,f15]) ).

thf(f15,plain,
    ! [X1: ( a > $o ) > a] :
      ( ( sK0 @ ( sK1 @ X1 ) )
      = $true ),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ! [X1: ( a > $o ) > a] :
        ( ( ( sK1 @ X1 @ ( X1 @ ( sK1 @ X1 ) ) )
         != $true )
        & ( ( sK0 @ ( sK1 @ X1 ) )
          = $true ) )
    & ! [X3: a > $o] :
        ( ( ( sK0 @ X3 )
         != $true )
        | ( $true
          = ( X3 @ ( sK2 @ X3 ) ) ) )
    & ! [X5: ( a > $o ) > a > $o,X7: a > $o] :
        ( ! [X8: a] :
            ( ( X5 @ X7 @ X8 )
           != $true )
        | ( ( X5 @ X7 @ ( sK3 @ X5 @ X7 ) )
          = $true ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f11,f10,f9,f8]) ).

thf(f8,plain,
    ( ? [X0: ( a > $o ) > $o] :
        ( ! [X1: ( a > $o ) > a] :
          ? [X2: a > $o] :
            ( ( ( X2 @ ( X1 @ X2 ) )
             != $true )
            & ( $true
              = ( X0 @ X2 ) ) )
        & ! [X3: a > $o] :
            ( ( ( X0 @ X3 )
             != $true )
            | ? [X4: a] :
                ( ( X3 @ X4 )
                = $true ) ) )
   => ( ! [X1: ( a > $o ) > a] :
        ? [X2: a > $o] :
          ( ( ( X2 @ ( X1 @ X2 ) )
           != $true )
          & ( $true
            = ( sK0 @ X2 ) ) )
      & ! [X3: a > $o] :
          ( ( ( sK0 @ X3 )
           != $true )
          | ? [X4: a] :
              ( ( X3 @ X4 )
              = $true ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ! [X1: ( a > $o ) > a] :
      ( ? [X2: a > $o] :
          ( ( ( X2 @ ( X1 @ X2 ) )
           != $true )
          & ( $true
            = ( sK0 @ X2 ) ) )
     => ( ( ( sK1 @ X1 @ ( X1 @ ( sK1 @ X1 ) ) )
         != $true )
        & ( ( sK0 @ ( sK1 @ X1 ) )
          = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ! [X3: a > $o] :
      ( ? [X4: a] :
          ( ( X3 @ X4 )
          = $true )
     => ( $true
        = ( X3 @ ( sK2 @ X3 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ! [X5: ( a > $o ) > a > $o] :
      ( ? [X6: ( a > $o ) > a] :
        ! [X7: a > $o] :
          ( ! [X8: a] :
              ( ( X5 @ X7 @ X8 )
             != $true )
          | ( ( X5 @ X7 @ ( X6 @ X7 ) )
            = $true ) )
     => ! [X7: a > $o] :
          ( ! [X8: a] :
              ( ( X5 @ X7 @ X8 )
             != $true )
          | ( ( X5 @ X7 @ ( sK3 @ X5 @ X7 ) )
            = $true ) ) ),
    introduced(choice_axiom,[]) ).

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

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

thf(f5,plain,
    ~ ( ! [X0: ( a > $o ) > a > $o] :
        ? [X1: ( a > $o ) > a] :
        ! [X2: a > $o] :
          ( ? [X3: a] :
              ( ( X0 @ X2 @ X3 )
              = $true )
         => ( ( X0 @ X2 @ ( X1 @ X2 ) )
            = $true ) )
     => ! [X4: ( a > $o ) > $o] :
          ( ! [X5: a > $o] :
              ( ( ( X4 @ X5 )
                = $true )
             => ? [X6: a] :
                  ( ( X5 @ X6 )
                  = $true ) )
         => ? [X7: ( a > $o ) > a] :
            ! [X8: a > $o] :
              ( ( ( X4 @ X8 )
                = $true )
             => ( ( X8 @ ( X7 @ X8 ) )
                = $true ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ! [X0: ( a > $o ) > a > $o] :
        ? [X1: ( a > $o ) > a] :
        ! [X2: a > $o] :
          ( ? [X3: a] : ( X0 @ X2 @ X3 )
         => ( X0 @ X2 @ ( X1 @ X2 ) ) )
     => ! [X4: ( a > $o ) > $o] :
          ( ! [X5: a > $o] :
              ( ( X4 @ X5 )
             => ? [X6: a] : ( X5 @ X6 ) )
         => ? [X7: ( a > $o ) > a] :
            ! [X8: a > $o] :
              ( ( X4 @ X8 )
             => ( X8 @ ( X7 @ X8 ) ) ) ) ),
    inference(rectify,[],[f2]) ).

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

thf(f1,conjecture,
    ( ! [X0: ( a > $o ) > a > $o] :
      ? [X1: ( a > $o ) > a] :
      ! [X2: a > $o] :
        ( ? [X3: a] : ( X0 @ X2 @ X3 )
       => ( X0 @ X2 @ ( X1 @ X2 ) ) )
   => ! [X4: ( a > $o ) > $o] :
        ( ! [X5: a > $o] :
            ( ( X4 @ X5 )
           => ? [X6: a] : ( X5 @ X6 ) )
       => ? [X7: ( a > $o ) > a] :
          ! [X5: a > $o] :
            ( ( X4 @ X5 )
           => ( X5 @ ( X7 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM533) ).

thf(f26,plain,
    ( ( sK0 @ ( sK1 @ sK2 ) )
   != $true ),
    inference(trivial_inequality_removal,[],[f25]) ).

thf(f25,plain,
    ( ( $true != $true )
    | ( ( sK0 @ ( sK1 @ sK2 ) )
     != $true ) ),
    inference(superposition,[],[f16,f14]) ).

thf(f14,plain,
    ! [X3: a > $o] :
      ( ( $true
        = ( X3 @ ( sK2 @ X3 ) ) )
      | ( ( sK0 @ X3 )
       != $true ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f16,plain,
    ! [X1: ( a > $o ) > a] :
      ( ( sK1 @ X1 @ ( X1 @ ( sK1 @ X1 ) ) )
     != $true ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : LCL727^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.16  % 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
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon May 20 01:56:08 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TH0_THM_NEQ_NAR problem
% 0.15/0.37  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
% 0.21/0.38  % (28440)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)
% 0.21/0.38  % (28443)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)
% 0.21/0.38  % (28444)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)
% 0.21/0.38  % (28442)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.21/0.38  % (28439)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.21/0.38  % (28445)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.21/0.38  % (28442)Instruction limit reached!
% 0.21/0.38  % (28442)------------------------------
% 0.21/0.38  % (28442)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38  % (28442)Termination reason: Unknown
% 0.21/0.38  % (28442)Termination phase: Saturation
% 0.21/0.38  
% 0.21/0.38  % (28443)Instruction limit reached!
% 0.21/0.38  % (28443)------------------------------
% 0.21/0.38  % (28443)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38  % (28443)Termination reason: Unknown
% 0.21/0.38  % (28443)Termination phase: Saturation
% 0.21/0.38  
% 0.21/0.38  % (28443)Memory used [KB]: 5373
% 0.21/0.38  % (28443)Time elapsed: 0.003 s
% 0.21/0.38  % (28443)Instructions burned: 2 (million)
% 0.21/0.38  % (28443)------------------------------
% 0.21/0.38  % (28443)------------------------------
% 0.21/0.38  % (28442)Memory used [KB]: 895
% 0.21/0.38  % (28442)Time elapsed: 0.002 s
% 0.21/0.38  % (28442)Instructions burned: 2 (million)
% 0.21/0.38  % (28442)------------------------------
% 0.21/0.38  % (28442)------------------------------
% 0.21/0.39  % (28446)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)
% 0.21/0.39  % (28441)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)
% 0.21/0.39  % (28444)First to succeed.
% 0.21/0.39  % (28440)Instruction limit reached!
% 0.21/0.39  % (28440)------------------------------
% 0.21/0.39  % (28440)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39  % (28440)Termination reason: Unknown
% 0.21/0.39  % (28440)Termination phase: Saturation
% 0.21/0.39  
% 0.21/0.39  % (28440)Memory used [KB]: 5500
% 0.21/0.39  % (28440)Time elapsed: 0.005 s
% 0.21/0.39  % (28440)Instructions burned: 4 (million)
% 0.21/0.39  % (28440)------------------------------
% 0.21/0.39  % (28440)------------------------------
% 0.21/0.39  % (28444)Refutation found. Thanks to Tanya!
% 0.21/0.39  % SZS status Theorem for theBenchmark
% 0.21/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39  % (28444)------------------------------
% 0.21/0.39  % (28444)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39  % (28444)Termination reason: Refutation
% 0.21/0.39  
% 0.21/0.39  % (28444)Memory used [KB]: 5500
% 0.21/0.39  % (28444)Time elapsed: 0.004 s
% 0.21/0.39  % (28444)Instructions burned: 2 (million)
% 0.21/0.39  % (28444)------------------------------
% 0.21/0.39  % (28444)------------------------------
% 0.21/0.39  % (28438)Success in time 0.015 s
% 0.21/0.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------