TSTP Solution File: SET610^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET610^5 : 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 : n015.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 03:12:24 EDT 2024

% Result   : Theorem 0.22s 0.38s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   49 (  12 unt;   6 typ;   0 def)
%            Number of atoms       :  229 (  62 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  275 (  59   ~;  56   |;  32   &; 124   @)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   33 (  20   ^   8   !;   4   ?;  33   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

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

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

thf(func_def_12,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_13,type,
    sK4: a ).

thf(f64,plain,
    $false,
    inference(avatar_sat_refutation,[],[f46,f51,f57,f63]) ).

thf(f63,plain,
    ( ~ spl2_1
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[],[f62]) ).

thf(f62,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f58]) ).

thf(f58,plain,
    ( ( $false = $true )
    | ~ spl2_1
    | ~ spl2_3 ),
    inference(superposition,[],[f41,f50]) ).

thf(f50,plain,
    ( ( $false
      = ( sK1 @ sK4 ) )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f48]) ).

thf(f48,plain,
    ( spl2_3
  <=> ( $false
      = ( sK1 @ sK4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f41,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f39]) ).

thf(f39,plain,
    ( spl2_1
  <=> ( ( sK1 @ sK4 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f57,plain,
    ~ spl2_2,
    inference(avatar_contradiction_clause,[],[f56]) ).

thf(f56,plain,
    ( $false
    | ~ spl2_2 ),
    inference(trivial_inequality_removal,[],[f52]) ).

thf(f52,plain,
    ( ( $false = $true )
    | ~ spl2_2 ),
    inference(superposition,[],[f45,f37]) ).

thf(f37,plain,
    ( ( sK0 @ sK4 )
    = $false ),
    inference(duplicate_literal_removal,[],[f36]) ).

thf(f36,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f33]) ).

thf(f33,plain,
    ( ( ( sK0 @ sK4 )
      = $false )
    | ( $true
      = ( ~ ( sK0 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f32]) ).

thf(f32,plain,
    ( ( $true
      = ( ( ( sK1 @ sK4 )
          | ( sK0 @ sK4 ) )
        & ~ ( sK0 @ sK4 ) ) )
    | ( ( sK0 @ sK4 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f25]) ).

thf(f25,plain,
    ( ( $true
      = ( ~ ( sK0 @ sK4 ) ) )
    | ( $true
      = ( ( ( sK1 @ sK4 )
          | ( sK0 @ sK4 ) )
        & ~ ( sK0 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

thf(f12,plain,
    ( ( $true
      = ( ( sK1 @ sK4 )
        & ~ ( sK0 @ sK4 ) ) )
    | ( $true
      = ( ( ( sK1 @ sK4 )
          | ( sK0 @ sK4 ) )
        & ~ ( sK0 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f11,plain,
    ( ( ( sK1 @ sK4 )
      & ~ ( sK0 @ sK4 ) )
   != ( ( ( sK1 @ sK4 )
        | ( sK0 @ sK4 ) )
      & ~ ( sK0 @ sK4 ) ) ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( ( ^ [Y0: a] :
          ( ( sK1 @ Y0 )
          & ~ ( sK0 @ Y0 ) )
      @ sK4 )
   != ( ^ [Y0: a] :
          ( ( ( sK1 @ Y0 )
            | ( sK0 @ Y0 ) )
          & ~ ( sK0 @ Y0 ) )
      @ sK4 ) ),
    inference(negative_extensionality,[],[f9]) ).

thf(f9,plain,
    ( ( ^ [Y0: a] :
          ( ( ( sK1 @ Y0 )
            | ( sK0 @ Y0 ) )
          & ~ ( sK0 @ Y0 ) ) )
   != ( ^ [Y0: a] :
          ( ( sK1 @ Y0 )
          & ~ ( sK0 @ Y0 ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( ^ [Y0: a] :
          ( ( ( sK1 @ Y0 )
            | ( sK0 @ Y0 ) )
          & ~ ( sK0 @ Y0 ) ) )
   != ( ^ [Y0: a] :
          ( ( sK1 @ Y0 )
          & ~ ( sK0 @ Y0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: a > $o,X1: a > $o] :
        ( ( ^ [Y0: a] :
              ( ( ( X1 @ Y0 )
                | ( X0 @ Y0 ) )
              & ~ ( X0 @ Y0 ) ) )
       != ( ^ [Y0: a] :
              ( ( X1 @ Y0 )
              & ~ ( X0 @ Y0 ) ) ) )
   => ( ( ^ [Y0: a] :
            ( ( ( sK1 @ Y0 )
              | ( sK0 @ Y0 ) )
            & ~ ( sK0 @ Y0 ) ) )
     != ( ^ [Y0: a] :
            ( ( sK1 @ Y0 )
            & ~ ( sK0 @ Y0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

thf(f1,conjecture,
    ! [X1: a > $o,X0: a > $o] :
      ( ( ^ [X2: a] :
            ( ~ ( X1 @ X2 )
            & ( ( X1 @ X2 )
              | ( X0 @ X2 ) ) ) )
      = ( ^ [X2: a] :
            ( ~ ( X1 @ X2 )
            & ( X0 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_83_pme) ).

thf(f45,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f43]) ).

thf(f43,plain,
    ( spl2_2
  <=> ( ( sK0 @ sK4 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f51,plain,
    ( spl2_2
    | spl2_3 ),
    inference(avatar_split_clause,[],[f21,f48,f43]) ).

thf(f21,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( $false
      = ( sK1 @ sK4 ) ) ),
    inference(duplicate_literal_removal,[],[f20]) ).

thf(f20,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( $false
      = ( sK1 @ sK4 ) )
    | ( ( sK0 @ sK4 )
      = $true ) ),
    inference(not_proxy_clausification,[],[f19]) ).

thf(f19,plain,
    ( ( $false
      = ( sK1 @ sK4 ) )
    | ( $false
      = ( ~ ( sK0 @ sK4 ) ) )
    | ( ( sK0 @ sK4 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f18]) ).

thf(f18,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( $false
      = ( ~ ( sK0 @ sK4 ) ) )
    | ( $false
      = ( sK1 @ sK4 ) )
    | ( $false
      = ( sK1 @ sK4 ) ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ( ( $false
      = ( ( sK1 @ sK4 )
        & ~ ( sK0 @ sK4 ) ) )
    | ( ( sK0 @ sK4 )
      = $true )
    | ( $false
      = ( sK1 @ sK4 ) ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( ( ( sK0 @ sK4 )
      = $true )
    | ( $false
      = ( ( sK1 @ sK4 )
        | ( sK0 @ sK4 ) ) )
    | ( $false
      = ( ( sK1 @ sK4 )
        & ~ ( sK0 @ sK4 ) ) ) ),
    inference(not_proxy_clausification,[],[f14]) ).

thf(f14,plain,
    ( ( $false
      = ( ~ ( sK0 @ sK4 ) ) )
    | ( $false
      = ( ( sK1 @ sK4 )
        & ~ ( sK0 @ sK4 ) ) )
    | ( $false
      = ( ( sK1 @ sK4 )
        | ( sK0 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( ( $false
      = ( ( ( sK1 @ sK4 )
          | ( sK0 @ sK4 ) )
        & ~ ( sK0 @ sK4 ) ) )
    | ( $false
      = ( ( sK1 @ sK4 )
        & ~ ( sK0 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f46,plain,
    ( spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f30,f43,f39]) ).

thf(f30,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f29]) ).

thf(f29,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( ( sK0 @ sK4 )
      = $true )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f28]) ).

thf(f28,plain,
    ( ( ( sK1 @ sK4 )
      = $true )
    | ( $true
      = ( ( sK1 @ sK4 )
        | ( sK0 @ sK4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f26]) ).

thf(f26,plain,
    ( ( $true
      = ( ( ( sK1 @ sK4 )
          | ( sK0 @ sK4 ) )
        & ~ ( sK0 @ sK4 ) ) )
    | ( ( sK1 @ sK4 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET610^5 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.14  % 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
% 0.15/0.35  % Computer : n015.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
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon May 20 11:59:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TH0_THM_EQU_NAR problem
% 0.22/0.36  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/sandbox/benchmark/theBenchmark.p
% 0.22/0.37  % (6014)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)
% 0.22/0.37  % (6014)Refutation not found, incomplete strategy
% 0.22/0.37  % (6014)------------------------------
% 0.22/0.37  % (6014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.37  % (6014)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.37  
% 0.22/0.37  
% 0.22/0.37  % (6014)Memory used [KB]: 5500
% 0.22/0.37  % (6014)Time elapsed: 0.002 s
% 0.22/0.37  % (6014)Instructions burned: 2 (million)
% 0.22/0.37  % (6014)------------------------------
% 0.22/0.37  % (6014)------------------------------
% 0.22/0.37  % (6007)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.22/0.37  % (6009)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)
% 0.22/0.37  % (6008)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)
% 0.22/0.37  % (6010)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.22/0.37  % (6011)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)
% 0.22/0.37  % (6012)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)
% 0.22/0.37  % (6013)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.22/0.38  % (6010)Instruction limit reached!
% 0.22/0.38  % (6010)------------------------------
% 0.22/0.38  % (6010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38  % (6011)Instruction limit reached!
% 0.22/0.38  % (6011)------------------------------
% 0.22/0.38  % (6011)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38  % (6011)Termination reason: Unknown
% 0.22/0.38  % (6011)Termination phase: Saturation
% 0.22/0.38  
% 0.22/0.38  % (6011)Memory used [KB]: 5373
% 0.22/0.38  % (6011)Time elapsed: 0.003 s
% 0.22/0.38  % (6011)Instructions burned: 2 (million)
% 0.22/0.38  % (6011)------------------------------
% 0.22/0.38  % (6011)------------------------------
% 0.22/0.38  % (6010)Termination reason: Unknown
% 0.22/0.38  % (6010)Termination phase: Saturation
% 0.22/0.38  
% 0.22/0.38  % (6010)Memory used [KB]: 5373
% 0.22/0.38  % (6010)Time elapsed: 0.003 s
% 0.22/0.38  % (6010)Instructions burned: 2 (million)
% 0.22/0.38  % (6010)------------------------------
% 0.22/0.38  % (6010)------------------------------
% 0.22/0.38  % (6007)First to succeed.
% 0.22/0.38  % (6008)Also succeeded, but the first one will report.
% 0.22/0.38  % (6007)Refutation found. Thanks to Tanya!
% 0.22/0.38  % SZS status Theorem for theBenchmark
% 0.22/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38  % (6007)------------------------------
% 0.22/0.38  % (6007)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38  % (6007)Termination reason: Refutation
% 0.22/0.38  
% 0.22/0.38  % (6007)Memory used [KB]: 5500
% 0.22/0.38  % (6007)Time elapsed: 0.005 s
% 0.22/0.38  % (6007)Instructions burned: 3 (million)
% 0.22/0.38  % (6007)------------------------------
% 0.22/0.38  % (6007)------------------------------
% 0.22/0.38  % (6006)Success in time 0.008 s
% 0.22/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------