TSTP Solution File: SET587^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET587^5 : 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 : n011.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 03:12:13 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   54 (   4 unt;   8 typ;   0 def)
%            Number of atoms       :  283 (  83 equ;   0 cnn)
%            Maximal formula atoms :   12 (   6 avg)
%            Number of connectives :  319 (  85   ~;  64   |;  38   &; 115   @)
%                                         (   9 <=>;   7  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   91 (  48   ^  28   !;  13   ?;  91   :)
%                                         (   2  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

thf(func_def_9,type,
    sK0: a > $o ).

thf(func_def_10,type,
    sK1: a > $o ).

thf(func_def_11,type,
    sK2: a ).

thf(func_def_13,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(func_def_14,type,
    sK5: a ).

thf(f56,plain,
    $false,
    inference(avatar_sat_refutation,[],[f24,f28,f33,f43,f55]) ).

thf(f55,plain,
    ( ~ spl3_1
    | spl3_2
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f54]) ).

thf(f54,plain,
    ( $false
    | ~ spl3_1
    | spl3_2
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f53]) ).

thf(f53,plain,
    ( ( $false = $true )
    | ~ spl3_1
    | spl3_2
    | ~ spl3_4 ),
    inference(backward_demodulation,[],[f32,f52]) ).

thf(f52,plain,
    ( ( $false
      = ( sK0 @ sK2 ) )
    | ~ spl3_1
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f51]) ).

thf(f51,plain,
    ( ( $false
      = ( sK0 @ sK2 ) )
    | ( $true != $true )
    | ~ spl3_1
    | spl3_2 ),
    inference(superposition,[],[f23,f50]) ).

thf(f50,plain,
    ( ! [X1: a] :
        ( ( $true
          = ( sK1 @ X1 ) )
        | ( $false
          = ( sK0 @ X1 ) ) )
    | ~ spl3_1 ),
    inference(not_proxy_clausification,[],[f49]) ).

thf(f49,plain,
    ( ! [X1: a] :
        ( ( $false
          = ( ~ ( sK1 @ X1 ) ) )
        | ( $false
          = ( sK0 @ X1 ) ) )
    | ~ spl3_1 ),
    inference(binary_proxy_clausification,[],[f48]) ).

thf(f48,plain,
    ( ! [X1: a] :
        ( $false
        = ( ~ ( sK1 @ X1 )
          & ( sK0 @ X1 ) ) )
    | ~ spl3_1 ),
    inference(beta_eta_normalization,[],[f47]) ).

thf(f47,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
          @ X1 )
        = ( ^ [Y0: a] : $false
          @ X1 ) )
    | ~ spl3_1 ),
    inference(argument_congruence,[],[f18]) ).

thf(f18,plain,
    ( ( ( ^ [Y0: a] :
            ( ~ ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) ) )
      = ( ^ [Y0: a] : $false ) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f17]) ).

thf(f17,plain,
    ( spl3_1
  <=> ( ( ^ [Y0: a] :
            ( ~ ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) ) )
      = ( ^ [Y0: a] : $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f23,plain,
    ( ( ( sK1 @ sK2 )
     != $true )
    | spl3_2 ),
    inference(avatar_component_clause,[],[f21]) ).

thf(f21,plain,
    ( spl3_2
  <=> ( ( sK1 @ sK2 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f32,plain,
    ( ( $true
      = ( sK0 @ sK2 ) )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f30]) ).

thf(f30,plain,
    ( spl3_4
  <=> ( $true
      = ( sK0 @ sK2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

thf(f43,plain,
    ( spl3_1
    | ~ spl3_3 ),
    inference(avatar_contradiction_clause,[],[f42]) ).

thf(f42,plain,
    ( $false
    | spl3_1
    | ~ spl3_3 ),
    inference(trivial_inequality_removal,[],[f41]) ).

thf(f41,plain,
    ( ( $false = $true )
    | spl3_1
    | ~ spl3_3 ),
    inference(forward_demodulation,[],[f40,f38]) ).

thf(f38,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | spl3_1 ),
    inference(not_proxy_clausification,[],[f37]) ).

thf(f37,plain,
    ( ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | spl3_1 ),
    inference(binary_proxy_clausification,[],[f35]) ).

thf(f35,plain,
    ( ( $false
     != ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) ) )
    | spl3_1 ),
    inference(beta_eta_normalization,[],[f34]) ).

thf(f34,plain,
    ( ( ( ^ [Y0: a] :
            ( ~ ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) )
        @ sK5 )
     != ( ^ [Y0: a] : $false
        @ sK5 ) )
    | spl3_1 ),
    inference(negative_extensionality,[],[f19]) ).

thf(f19,plain,
    ( ( ( ^ [Y0: a] :
            ( ~ ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) ) )
     != ( ^ [Y0: a] : $false ) )
    | spl3_1 ),
    inference(avatar_component_clause,[],[f17]) ).

thf(f40,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | spl3_1
    | ~ spl3_3 ),
    inference(trivial_inequality_removal,[],[f39]) ).

thf(f39,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( $true != $true )
    | spl3_1
    | ~ spl3_3 ),
    inference(superposition,[],[f27,f36]) ).

thf(f36,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | spl3_1 ),
    inference(binary_proxy_clausification,[],[f35]) ).

thf(f27,plain,
    ( ! [X3: a] :
        ( ( $true
         != ( sK0 @ X3 ) )
        | ( $true
          = ( sK1 @ X3 ) ) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f26]) ).

thf(f26,plain,
    ( spl3_3
  <=> ! [X3: a] :
        ( ( $true
          = ( sK1 @ X3 ) )
        | ( $true
         != ( sK0 @ X3 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

thf(f33,plain,
    ( spl3_4
    | ~ spl3_1 ),
    inference(avatar_split_clause,[],[f15,f17,f30]) ).

thf(f15,plain,
    ( ( $true
      = ( sK0 @ sK2 ) )
    | ( ( ^ [Y0: a] :
            ( ~ ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) ) )
     != ( ^ [Y0: a] : $false ) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f12,plain,
    ( ( ( ( ^ [Y0: a] :
              ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) ) )
       != ( ^ [Y0: a] : $false ) )
      | ( ( $true
          = ( sK0 @ sK2 ) )
        & ( ( sK1 @ sK2 )
         != $true ) ) )
    & ( ( ( ^ [Y0: a] :
              ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) ) )
        = ( ^ [Y0: a] : $false ) )
      | ! [X3: a] :
          ( ( $true
           != ( sK0 @ X3 ) )
          | ( $true
            = ( sK1 @ X3 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11,f10]) ).

thf(f10,plain,
    ( ? [X0: a > $o,X1: a > $o] :
        ( ( ( ( ^ [Y0: a] : $false )
           != ( ^ [Y0: a] :
                  ( ~ ( X1 @ Y0 )
                  & ( X0 @ Y0 ) ) ) )
          | ? [X2: a] :
              ( ( ( X0 @ X2 )
                = $true )
              & ( ( X1 @ X2 )
               != $true ) ) )
        & ( ( ( ^ [Y0: a] : $false )
            = ( ^ [Y0: a] :
                  ( ~ ( X1 @ Y0 )
                  & ( X0 @ Y0 ) ) ) )
          | ! [X3: a] :
              ( ( $true
               != ( X0 @ X3 ) )
              | ( ( X1 @ X3 )
                = $true ) ) ) )
   => ( ( ( ( ^ [Y0: a] :
                ( ~ ( sK1 @ Y0 )
                & ( sK0 @ Y0 ) ) )
         != ( ^ [Y0: a] : $false ) )
        | ? [X2: a] :
            ( ( $true
              = ( sK0 @ X2 ) )
            & ( ( sK1 @ X2 )
             != $true ) ) )
      & ( ( ( ^ [Y0: a] :
                ( ~ ( sK1 @ Y0 )
                & ( sK0 @ Y0 ) ) )
          = ( ^ [Y0: a] : $false ) )
        | ! [X3: a] :
            ( ( $true
             != ( sK0 @ X3 ) )
            | ( $true
              = ( sK1 @ X3 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X2: a] :
        ( ( $true
          = ( sK0 @ X2 ) )
        & ( ( sK1 @ X2 )
         != $true ) )
   => ( ( $true
        = ( sK0 @ sK2 ) )
      & ( ( sK1 @ sK2 )
       != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f9,plain,
    ? [X0: a > $o,X1: a > $o] :
      ( ( ( ( ^ [Y0: a] : $false )
         != ( ^ [Y0: a] :
                ( ~ ( X1 @ Y0 )
                & ( X0 @ Y0 ) ) ) )
        | ? [X2: a] :
            ( ( ( X0 @ X2 )
              = $true )
            & ( ( X1 @ X2 )
             != $true ) ) )
      & ( ( ( ^ [Y0: a] : $false )
          = ( ^ [Y0: a] :
                ( ~ ( X1 @ Y0 )
                & ( X0 @ Y0 ) ) ) )
        | ! [X3: a] :
            ( ( $true
             != ( X0 @ X3 ) )
            | ( ( X1 @ X3 )
              = $true ) ) ) ),
    inference(rectify,[],[f8]) ).

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

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

thf(f6,plain,
    ~ ! [X0: a > $o,X1: a > $o] :
        ( ! [X2: a] :
            ( ( ( X0 @ X2 )
              = $true )
           => ( ( X1 @ X2 )
              = $true ) )
      <=> ( ( ^ [Y0: a] : $false )
          = ( ^ [Y0: a] :
                ( ~ ( X1 @ Y0 )
                & ( X0 @ Y0 ) ) ) ) ),
    inference(rectify,[],[f5]) ).

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

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

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

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o] :
      ( ( ( ^ [X2: a] :
              ( ( X0 @ X2 )
              & ~ ( X1 @ X2 ) ) )
        = ( ^ [X2: a] : $false ) )
    <=> ! [X2: a] :
          ( ( X0 @ X2 )
         => ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_45_pme) ).

thf(f28,plain,
    ( spl3_3
    | spl3_1 ),
    inference(avatar_split_clause,[],[f13,f17,f26]) ).

thf(f13,plain,
    ! [X3: a] :
      ( ( ( ^ [Y0: a] :
              ( ~ ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) ) )
        = ( ^ [Y0: a] : $false ) )
      | ( $true
        = ( sK1 @ X3 ) )
      | ( $true
       != ( sK0 @ X3 ) ) ),
    inference(cnf_transformation,[],[f12]) ).

thf(f24,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f14,f21,f17]) ).

thf(f14,plain,
    ( ( ( sK1 @ sK2 )
     != $true )
    | ( ( ^ [Y0: a] :
            ( ~ ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) ) )
     != ( ^ [Y0: a] : $false ) ) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET587^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14  % 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
% 0.15/0.35  % Computer : n011.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 20 13:02:53 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  This is a TH0_THM_EQU_NAR problem
% 0.15/0.36  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
% 0.15/0.37  % (19753)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.15/0.37  % (19751)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)
% 0.15/0.37  % (19754)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)
% 0.15/0.37  % (19752)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)
% 0.15/0.37  % (19756)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.15/0.38  % (19755)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)
% 0.15/0.38  % (19753)Instruction limit reached!
% 0.15/0.38  % (19753)------------------------------
% 0.15/0.38  % (19753)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (19753)Termination reason: Unknown
% 0.15/0.38  % (19754)Instruction limit reached!
% 0.15/0.38  % (19754)------------------------------
% 0.15/0.38  % (19754)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (19754)Termination reason: Unknown
% 0.15/0.38  % (19754)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (19754)Memory used [KB]: 5500
% 0.15/0.38  % (19754)Time elapsed: 0.004 s
% 0.15/0.38  % (19754)Instructions burned: 2 (million)
% 0.15/0.38  % (19754)------------------------------
% 0.15/0.38  % (19754)------------------------------
% 0.15/0.38  % (19753)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (19753)Memory used [KB]: 5500
% 0.15/0.38  % (19753)Time elapsed: 0.004 s
% 0.15/0.38  % (19753)Instructions burned: 2 (million)
% 0.15/0.38  % (19753)------------------------------
% 0.15/0.38  % (19753)------------------------------
% 0.15/0.38  % (19752)First to succeed.
% 0.15/0.38  % (19751)Instruction limit reached!
% 0.15/0.38  % (19751)------------------------------
% 0.15/0.38  % (19751)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (19751)Termination reason: Unknown
% 0.15/0.38  % (19751)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (19751)Memory used [KB]: 5500
% 0.15/0.38  % (19751)Time elapsed: 0.005 s
% 0.15/0.38  % (19751)Instructions burned: 4 (million)
% 0.15/0.38  % (19751)------------------------------
% 0.15/0.38  % (19751)------------------------------
% 0.15/0.38  % (19757)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)
% 0.15/0.38  % (19756)Also succeeded, but the first one will report.
% 0.15/0.38  % (19755)Also succeeded, but the first one will report.
% 0.15/0.38  % (19752)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (19752)------------------------------
% 0.15/0.38  % (19752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (19752)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (19752)Memory used [KB]: 5500
% 0.15/0.38  % (19752)Time elapsed: 0.007 s
% 0.15/0.38  % (19752)Instructions burned: 3 (million)
% 0.15/0.38  % (19752)------------------------------
% 0.15/0.38  % (19752)------------------------------
% 0.15/0.38  % (19749)Success in time 0.008 s
% 0.15/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------