TSTP Solution File: SEU890^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU890^5 : 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 : n007.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 03:52:05 EDT 2024

% Result   : Theorem 0.12s 0.35s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   59 (   1 unt;  13 typ;   0 def)
%            Number of atoms       :  271 ( 123 equ;   0 cnn)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  355 (  71   ~;  71   |;  43   &; 155   @)
%                                         (  10 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;  12 con; 0-2 aty)
%            Number of variables   :   62 (   0   ^  26   !;  36   ?;  62   :)

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

thf(type_def_6,type,
    b: $tType ).

thf(type_def_8,type,
    a: $tType ).

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

thf(func_def_1,type,
    b: $tType ).

thf(func_def_2,type,
    a: $tType ).

thf(func_def_3,type,
    cG: c > b ).

thf(func_def_4,type,
    cF: b > a ).

thf(func_def_5,type,
    cS: c > $o ).

thf(func_def_9,type,
    sK0: a ).

thf(func_def_10,type,
    sK1: c ).

thf(func_def_11,type,
    sK2: b ).

thf(func_def_12,type,
    sK3: c ).

thf(f62,plain,
    $false,
    inference(avatar_sat_refutation,[],[f30,f35,f39,f44,f49,f50,f51,f57,f61]) ).

thf(f61,plain,
    ( ~ spl4_1
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(avatar_contradiction_clause,[],[f60]) ).

thf(f60,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(subsumption_resolution,[],[f59,f25]) ).

thf(f25,plain,
    ( ( ( cS @ sK1 )
      = $true )
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f23]) ).

thf(f23,plain,
    ( spl4_1
  <=> ( ( cS @ sK1 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

thf(f59,plain,
    ( ( ( cS @ sK1 )
     != $true )
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(trivial_inequality_removal,[],[f58]) ).

thf(f58,plain,
    ( ( sK0 != sK0 )
    | ( ( cS @ sK1 )
     != $true )
    | ~ spl4_4
    | ~ spl4_5 ),
    inference(superposition,[],[f38,f43]) ).

thf(f43,plain,
    ( ( sK0
      = ( cF @ ( cG @ sK1 ) ) )
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f41]) ).

thf(f41,plain,
    ( spl4_5
  <=> ( sK0
      = ( cF @ ( cG @ sK1 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

thf(f38,plain,
    ( ! [X1: c] :
        ( ( ( cF @ ( cG @ X1 ) )
         != sK0 )
        | ( ( cS @ X1 )
         != $true ) )
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f37]) ).

thf(f37,plain,
    ( spl4_4
  <=> ! [X1: c] :
        ( ( ( cF @ ( cG @ X1 ) )
         != sK0 )
        | ( ( cS @ X1 )
         != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

thf(f57,plain,
    ( ~ spl4_2
    | ~ spl4_3
    | ~ spl4_4
    | ~ spl4_6 ),
    inference(avatar_split_clause,[],[f56,f46,f37,f32,f27]) ).

thf(f27,plain,
    ( spl4_2
  <=> ( ( cS @ sK3 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

thf(f32,plain,
    ( spl4_3
  <=> ( sK2
      = ( cG @ sK3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

thf(f46,plain,
    ( spl4_6
  <=> ( sK0
      = ( cF @ sK2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

thf(f56,plain,
    ( ( ( cS @ sK3 )
     != $true )
    | ~ spl4_3
    | ~ spl4_4
    | ~ spl4_6 ),
    inference(subsumption_resolution,[],[f52,f48]) ).

thf(f48,plain,
    ( ( sK0
      = ( cF @ sK2 ) )
    | ~ spl4_6 ),
    inference(avatar_component_clause,[],[f46]) ).

thf(f52,plain,
    ( ( sK0
     != ( cF @ sK2 ) )
    | ( ( cS @ sK3 )
     != $true )
    | ~ spl4_3
    | ~ spl4_4 ),
    inference(superposition,[],[f38,f34]) ).

thf(f34,plain,
    ( ( sK2
      = ( cG @ sK3 ) )
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f32]) ).

thf(f51,plain,
    ( spl4_6
    | spl4_1 ),
    inference(avatar_split_clause,[],[f19,f23,f46]) ).

thf(f19,plain,
    ( ( sK0
      = ( cF @ sK2 ) )
    | ( ( cS @ sK1 )
      = $true ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f13,plain,
    ( ( ! [X1: c] :
          ( ( ( cS @ X1 )
           != $true )
          | ( ( cF @ ( cG @ X1 ) )
           != sK0 ) )
      | ! [X2: b] :
          ( ( sK0
           != ( cF @ X2 ) )
          | ! [X3: c] :
              ( ( ( cS @ X3 )
               != $true )
              | ( ( cG @ X3 )
               != X2 ) ) ) )
    & ( ( ( ( cS @ sK1 )
          = $true )
        & ( sK0
          = ( cF @ ( cG @ sK1 ) ) ) )
      | ( ( sK0
          = ( cF @ sK2 ) )
        & ( ( cS @ sK3 )
          = $true )
        & ( sK2
          = ( cG @ sK3 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f12,f11,f10,f9]) ).

thf(f9,plain,
    ( ? [X0: a] :
        ( ( ! [X1: c] :
              ( ( ( cS @ X1 )
               != $true )
              | ( ( cF @ ( cG @ X1 ) )
               != X0 ) )
          | ! [X2: b] :
              ( ( ( cF @ X2 )
               != X0 )
              | ! [X3: c] :
                  ( ( ( cS @ X3 )
                   != $true )
                  | ( ( cG @ X3 )
                   != X2 ) ) ) )
        & ( ? [X4: c] :
              ( ( ( cS @ X4 )
                = $true )
              & ( ( cF @ ( cG @ X4 ) )
                = X0 ) )
          | ? [X5: b] :
              ( ( ( cF @ X5 )
                = X0 )
              & ? [X6: c] :
                  ( ( ( cS @ X6 )
                    = $true )
                  & ( ( cG @ X6 )
                    = X5 ) ) ) ) )
   => ( ( ! [X1: c] :
            ( ( ( cS @ X1 )
             != $true )
            | ( ( cF @ ( cG @ X1 ) )
             != sK0 ) )
        | ! [X2: b] :
            ( ( sK0
             != ( cF @ X2 ) )
            | ! [X3: c] :
                ( ( ( cS @ X3 )
                 != $true )
                | ( ( cG @ X3 )
                 != X2 ) ) ) )
      & ( ? [X4: c] :
            ( ( ( cS @ X4 )
              = $true )
            & ( sK0
              = ( cF @ ( cG @ X4 ) ) ) )
        | ? [X5: b] :
            ( ( sK0
              = ( cF @ X5 ) )
            & ? [X6: c] :
                ( ( ( cS @ X6 )
                  = $true )
                & ( ( cG @ X6 )
                  = X5 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f10,plain,
    ( ? [X4: c] :
        ( ( ( cS @ X4 )
          = $true )
        & ( sK0
          = ( cF @ ( cG @ X4 ) ) ) )
   => ( ( ( cS @ sK1 )
        = $true )
      & ( sK0
        = ( cF @ ( cG @ sK1 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f11,plain,
    ( ? [X5: b] :
        ( ( sK0
          = ( cF @ X5 ) )
        & ? [X6: c] :
            ( ( ( cS @ X6 )
              = $true )
            & ( ( cG @ X6 )
              = X5 ) ) )
   => ( ( sK0
        = ( cF @ sK2 ) )
      & ? [X6: c] :
          ( ( ( cS @ X6 )
            = $true )
          & ( sK2
            = ( cG @ X6 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ( ? [X6: c] :
        ( ( ( cS @ X6 )
          = $true )
        & ( sK2
          = ( cG @ X6 ) ) )
   => ( ( ( cS @ sK3 )
        = $true )
      & ( sK2
        = ( cG @ sK3 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f8,plain,
    ? [X0: a] :
      ( ( ! [X1: c] :
            ( ( ( cS @ X1 )
             != $true )
            | ( ( cF @ ( cG @ X1 ) )
             != X0 ) )
        | ! [X2: b] :
            ( ( ( cF @ X2 )
             != X0 )
            | ! [X3: c] :
                ( ( ( cS @ X3 )
                 != $true )
                | ( ( cG @ X3 )
                 != X2 ) ) ) )
      & ( ? [X4: c] :
            ( ( ( cS @ X4 )
              = $true )
            & ( ( cF @ ( cG @ X4 ) )
              = X0 ) )
        | ? [X5: b] :
            ( ( ( cF @ X5 )
              = X0 )
            & ? [X6: c] :
                ( ( ( cS @ X6 )
                  = $true )
                & ( ( cG @ X6 )
                  = X5 ) ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,plain,
    ? [X0: a] :
      ( ( ! [X1: c] :
            ( ( ( cS @ X1 )
             != $true )
            | ( ( cF @ ( cG @ X1 ) )
             != X0 ) )
        | ! [X2: b] :
            ( ( ( cF @ X2 )
             != X0 )
            | ! [X3: c] :
                ( ( ( cS @ X3 )
                 != $true )
                | ( ( cG @ X3 )
                 != X2 ) ) ) )
      & ( ? [X1: c] :
            ( ( ( cS @ X1 )
              = $true )
            & ( ( cF @ ( cG @ X1 ) )
              = X0 ) )
        | ? [X2: b] :
            ( ( ( cF @ X2 )
              = X0 )
            & ? [X3: c] :
                ( ( ( cS @ X3 )
                  = $true )
                & ( ( cG @ X3 )
                  = X2 ) ) ) ) ),
    inference(nnf_transformation,[],[f6]) ).

thf(f6,plain,
    ? [X0: a] :
      ( ? [X2: b] :
          ( ( ( cF @ X2 )
            = X0 )
          & ? [X3: c] :
              ( ( ( cS @ X3 )
                = $true )
              & ( ( cG @ X3 )
                = X2 ) ) )
    <~> ? [X1: c] :
          ( ( ( cS @ X1 )
            = $true )
          & ( ( cF @ ( cG @ X1 ) )
            = X0 ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a] :
        ( ? [X1: c] :
            ( ( ( cS @ X1 )
              = $true )
            & ( ( cF @ ( cG @ X1 ) )
              = X0 ) )
      <=> ? [X2: b] :
            ( ( ( cF @ X2 )
              = X0 )
            & ? [X3: c] :
                ( ( ( cS @ X3 )
                  = $true )
                & ( ( cG @ X3 )
                  = X2 ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a] :
        ( ? [X1: c] :
            ( ( ( cF @ ( cG @ X1 ) )
              = X0 )
            & ( cS @ X1 ) )
      <=> ? [X2: b] :
            ( ? [X3: c] :
                ( ( ( cG @ X3 )
                  = X2 )
                & ( cS @ X3 ) )
            & ( ( cF @ X2 )
              = X0 ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a] :
        ( ? [X1: c] :
            ( ( ( cF @ ( cG @ X1 ) )
              = X0 )
            & ( cS @ X1 ) )
      <=> ? [X1: b] :
            ( ? [X2: c] :
                ( ( ( cG @ X2 )
                  = X1 )
                & ( cS @ X2 ) )
            & ( ( cF @ X1 )
              = X0 ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a] :
      ( ? [X1: c] :
          ( ( ( cF @ ( cG @ X1 ) )
            = X0 )
          & ( cS @ X1 ) )
    <=> ? [X1: b] :
          ( ? [X2: c] :
              ( ( ( cG @ X2 )
                = X1 )
              & ( cS @ X2 ) )
          & ( ( cF @ X1 )
            = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM29_pme) ).

thf(f50,plain,
    ( spl4_5
    | spl4_3 ),
    inference(avatar_split_clause,[],[f14,f32,f41]) ).

thf(f14,plain,
    ( ( sK0
      = ( cF @ ( cG @ sK1 ) ) )
    | ( sK2
      = ( cG @ sK3 ) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f49,plain,
    ( spl4_6
    | spl4_5 ),
    inference(avatar_split_clause,[],[f16,f41,f46]) ).

thf(f16,plain,
    ( ( sK0
      = ( cF @ sK2 ) )
    | ( sK0
      = ( cF @ ( cG @ sK1 ) ) ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f44,plain,
    ( spl4_5
    | spl4_2 ),
    inference(avatar_split_clause,[],[f15,f27,f41]) ).

thf(f15,plain,
    ( ( sK0
      = ( cF @ ( cG @ sK1 ) ) )
    | ( ( cS @ sK3 )
      = $true ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f39,plain,
    ( spl4_4
    | spl4_4 ),
    inference(avatar_split_clause,[],[f21,f37,f37]) ).

thf(f21,plain,
    ! [X3: c,X1: c] :
      ( ( sK0
       != ( cF @ ( cG @ X3 ) ) )
      | ( ( cS @ X3 )
       != $true )
      | ( ( cF @ ( cG @ X1 ) )
       != sK0 )
      | ( ( cS @ X1 )
       != $true ) ),
    inference(equality_resolution,[],[f20]) ).

thf(f20,plain,
    ! [X2: b,X3: c,X1: c] :
      ( ( ( cS @ X1 )
       != $true )
      | ( ( cF @ ( cG @ X1 ) )
       != sK0 )
      | ( sK0
       != ( cF @ X2 ) )
      | ( ( cS @ X3 )
       != $true )
      | ( ( cG @ X3 )
       != X2 ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f35,plain,
    ( spl4_3
    | spl4_1 ),
    inference(avatar_split_clause,[],[f17,f23,f32]) ).

thf(f17,plain,
    ( ( sK2
      = ( cG @ sK3 ) )
    | ( ( cS @ sK1 )
      = $true ) ),
    inference(cnf_transformation,[],[f13]) ).

thf(f30,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f18,f27,f23]) ).

thf(f18,plain,
    ( ( ( cS @ sK1 )
      = $true )
    | ( ( cS @ sK3 )
      = $true ) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem    : SEU890^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.12  % 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
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun May 19 15:22:38 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  This is a TH0_THM_EQU_NAR problem
% 0.12/0.33  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
% 0.12/0.35  % (19009)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.12/0.35  % (19012)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.12/0.35  % (19010)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)
% 0.12/0.35  % (19011)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)
% 0.12/0.35  % (19015)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.12/0.35  % (19013)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)
% 0.12/0.35  % (19014)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)
% 0.12/0.35  % (19016)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)
% 0.12/0.35  % (19012)Instruction limit reached!
% 0.12/0.35  % (19012)------------------------------
% 0.12/0.35  % (19012)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35  % (19012)Termination reason: Unknown
% 0.12/0.35  % (19012)Termination phase: Saturation
% 0.12/0.35  % (19013)Instruction limit reached!
% 0.12/0.35  % (19013)------------------------------
% 0.12/0.35  % (19013)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35  % (19013)Termination reason: Unknown
% 0.12/0.35  % (19013)Termination phase: Saturation
% 0.12/0.35  
% 0.12/0.35  % (19013)Memory used [KB]: 5500
% 0.12/0.35  % (19013)Time elapsed: 0.003 s
% 0.12/0.35  % (19013)Instructions burned: 2 (million)
% 0.12/0.35  % (19013)------------------------------
% 0.12/0.35  % (19013)------------------------------
% 0.12/0.35  
% 0.12/0.35  % (19012)Memory used [KB]: 5500
% 0.12/0.35  % (19012)Time elapsed: 0.003 s
% 0.12/0.35  % (19012)Instructions burned: 2 (million)
% 0.12/0.35  % (19012)------------------------------
% 0.12/0.35  % (19012)------------------------------
% 0.12/0.35  % (19014)First to succeed.
% 0.12/0.35  % (19016)Instruction limit reached!
% 0.12/0.35  % (19016)------------------------------
% 0.12/0.35  % (19016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35  % (19016)Termination reason: Unknown
% 0.12/0.35  % (19016)Termination phase: Saturation
% 0.12/0.35  
% 0.12/0.35  % (19016)Memory used [KB]: 5500
% 0.12/0.35  % (19016)Time elapsed: 0.004 s
% 0.12/0.35  % (19016)Instructions burned: 3 (million)
% 0.12/0.35  % (19016)------------------------------
% 0.12/0.35  % (19016)------------------------------
% 0.12/0.35  % (19009)Also succeeded, but the first one will report.
% 0.12/0.35  % (19015)Also succeeded, but the first one will report.
% 0.12/0.35  % (19014)Refutation found. Thanks to Tanya!
% 0.12/0.35  % SZS status Theorem for theBenchmark
% 0.12/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.35  % (19014)------------------------------
% 0.12/0.35  % (19014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35  % (19014)Termination reason: Refutation
% 0.12/0.35  
% 0.12/0.35  % (19014)Memory used [KB]: 5500
% 0.12/0.35  % (19014)Time elapsed: 0.005 s
% 0.12/0.35  % (19014)Instructions burned: 2 (million)
% 0.12/0.35  % (19014)------------------------------
% 0.12/0.35  % (19014)------------------------------
% 0.12/0.35  % (19007)Success in time 0.016 s
% 0.12/0.35  % Vampire---4.8 exiting
%------------------------------------------------------------------------------