TSTP Solution File: COM003+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : COM003+2 : TPTP v8.2.0. Bugfixed v2.2.0.
% 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 : n002.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 : Mon May 20 19:09:54 EDT 2024

% Result   : Theorem 0.56s 0.75s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  117 (   7 unt;   0 def)
%            Number of atoms       :  393 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  471 ( 195   ~; 174   |;  64   &)
%                                         (  20 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   26 (  25 usr;  13 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-1 aty)
%            Number of variables   :  167 ( 136   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f238,plain,
    $false,
    inference(avatar_sat_refutation,[],[f123,f130,f134,f139,f146,f150,f155,f170,f178,f186,f220,f230,f237]) ).

fof(f237,plain,
    ( ~ spl8_5
    | ~ spl8_13 ),
    inference(avatar_contradiction_clause,[],[f236]) ).

fof(f236,plain,
    ( $false
    | ~ spl8_5
    | ~ spl8_13 ),
    inference(subsumption_resolution,[],[f203,f189]) ).

fof(f189,plain,
    ( ! [X0] :
        ( ~ program_halts2(sK4,X0)
        | ~ program_halts2(X0,X0) )
    | ~ spl8_5 ),
    inference(resolution,[],[f133,f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( halts2(X0,X1)
      | ~ program_halts2(X0,X1) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( program_halts2(X0,X1)
        | ~ halts2(X0,X1)
        | ~ program(X0) )
      & ( ( halts2(X0,X1)
          & program(X0) )
        | ~ program_halts2(X0,X1) ) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( program_halts2(X0,X1)
        | ~ halts2(X0,X1)
        | ~ program(X0) )
      & ( ( halts2(X0,X1)
          & program(X0) )
        | ~ program_halts2(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( program_halts2(X0,X1)
    <=> ( halts2(X0,X1)
        & program(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_halts2_def) ).

fof(f133,plain,
    ( ! [X1] :
        ( ~ halts2(sK4,X1)
        | ~ program_halts2(X1,X1) )
    | ~ spl8_5 ),
    inference(avatar_component_clause,[],[f132]) ).

fof(f132,plain,
    ( spl8_5
  <=> ! [X1] :
        ( ~ halts2(sK4,X1)
        | ~ program_halts2(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).

fof(f203,plain,
    ( program_halts2(sK4,sK4)
    | ~ spl8_13 ),
    inference(avatar_component_clause,[],[f202]) ).

fof(f202,plain,
    ( spl8_13
  <=> program_halts2(sK4,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).

fof(f230,plain,
    ( ~ spl8_4
    | ~ spl8_6
    | ~ spl8_12
    | spl8_13 ),
    inference(avatar_contradiction_clause,[],[f227]) ).

fof(f227,plain,
    ( $false
    | ~ spl8_4
    | ~ spl8_6
    | ~ spl8_12
    | spl8_13 ),
    inference(resolution,[],[f225,f129]) ).

fof(f129,plain,
    ( ! [X1] : program_not_halts2_halts2_outputs(sK4,X1,good)
    | ~ spl8_4 ),
    inference(avatar_component_clause,[],[f128]) ).

fof(f128,plain,
    ( spl8_4
  <=> ! [X1] : program_not_halts2_halts2_outputs(sK4,X1,good) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

fof(f225,plain,
    ( ! [X0] : ~ program_not_halts2_halts2_outputs(sK4,sK4,X0)
    | ~ spl8_6
    | ~ spl8_12
    | spl8_13 ),
    inference(resolution,[],[f200,f214]) ).

fof(f214,plain,
    ( ! [X0] : ~ halts2_outputs(sK4,sK4,X0)
    | ~ spl8_6
    | spl8_13 ),
    inference(resolution,[],[f209,f107]) ).

fof(f107,plain,
    ! [X2,X0,X1] :
      ( halts2(X0,X1)
      | ~ halts2_outputs(X0,X1,X2) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ( halts2_outputs(X0,X1,X2)
        | ~ outputs(X0,X2)
        | ~ halts2(X0,X1) )
      & ( ( outputs(X0,X2)
          & halts2(X0,X1) )
        | ~ halts2_outputs(X0,X1,X2) ) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ( halts2_outputs(X0,X1,X2)
        | ~ outputs(X0,X2)
        | ~ halts2(X0,X1) )
      & ( ( outputs(X0,X2)
          & halts2(X0,X1) )
        | ~ halts2_outputs(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( halts2_outputs(X0,X1,X2)
    <=> ( outputs(X0,X2)
        & halts2(X0,X1) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X3] :
      ( halts2_outputs(X0,X1,X3)
    <=> ( outputs(X0,X3)
        & halts2(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',halts2_outputs_def) ).

fof(f209,plain,
    ( ~ halts2(sK4,sK4)
    | ~ spl8_6
    | spl8_13 ),
    inference(subsumption_resolution,[],[f207,f138]) ).

fof(f138,plain,
    ( program(sK4)
    | ~ spl8_6 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f136,plain,
    ( spl8_6
  <=> program(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

fof(f207,plain,
    ( ~ halts2(sK4,sK4)
    | ~ program(sK4)
    | spl8_13 ),
    inference(resolution,[],[f204,f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( program_halts2(X0,X1)
      | ~ halts2(X0,X1)
      | ~ program(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f204,plain,
    ( ~ program_halts2(sK4,sK4)
    | spl8_13 ),
    inference(avatar_component_clause,[],[f202]) ).

fof(f200,plain,
    ( ! [X0,X1] :
        ( halts2_outputs(X0,sK4,X1)
        | ~ program_not_halts2_halts2_outputs(X0,sK4,X1) )
    | ~ spl8_12 ),
    inference(avatar_component_clause,[],[f199]) ).

fof(f199,plain,
    ( spl8_12
  <=> ! [X0,X1] :
        ( halts2_outputs(X0,sK4,X1)
        | ~ program_not_halts2_halts2_outputs(X0,sK4,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).

fof(f220,plain,
    ( spl8_12
    | ~ spl8_6
    | spl8_13 ),
    inference(avatar_split_clause,[],[f219,f202,f136,f199]) ).

fof(f219,plain,
    ( ! [X0,X1] :
        ( halts2_outputs(X0,sK4,X1)
        | ~ program_not_halts2_halts2_outputs(X0,sK4,X1) )
    | ~ spl8_6
    | spl8_13 ),
    inference(resolution,[],[f216,f110]) ).

fof(f110,plain,
    ! [X2,X0,X1] :
      ( ~ program_not_halts2(X1,X1)
      | halts2_outputs(X0,X1,X2)
      | ~ program_not_halts2_halts2_outputs(X0,X1,X2) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ( program_not_halts2_halts2_outputs(X0,X1,X2)
        | ( ~ halts2_outputs(X0,X1,X2)
          & program_not_halts2(X1,X1) ) )
      & ( halts2_outputs(X0,X1,X2)
        | ~ program_not_halts2(X1,X1)
        | ~ program_not_halts2_halts2_outputs(X0,X1,X2) ) ),
    inference(flattening,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( ( program_not_halts2_halts2_outputs(X0,X1,X2)
        | ( ~ halts2_outputs(X0,X1,X2)
          & program_not_halts2(X1,X1) ) )
      & ( halts2_outputs(X0,X1,X2)
        | ~ program_not_halts2(X1,X1)
        | ~ program_not_halts2_halts2_outputs(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( program_not_halts2_halts2_outputs(X0,X1,X2)
    <=> ( halts2_outputs(X0,X1,X2)
        | ~ program_not_halts2(X1,X1) ) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( program_not_halts2_halts2_outputs(X0,X1,X2)
    <=> ( program_not_halts2(X1,X1)
       => halts2_outputs(X0,X1,X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1,X3] :
      ( program_not_halts2_halts2_outputs(X0,X1,X3)
    <=> ( program_not_halts2(X1,X1)
       => halts2_outputs(X0,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs_def) ).

fof(f216,plain,
    ( program_not_halts2(sK4,sK4)
    | ~ spl8_6
    | spl8_13 ),
    inference(subsumption_resolution,[],[f213,f138]) ).

fof(f213,plain,
    ( program_not_halts2(sK4,sK4)
    | ~ program(sK4)
    | ~ spl8_6
    | spl8_13 ),
    inference(resolution,[],[f209,f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( halts2(X0,X1)
      | program_not_halts2(X0,X1)
      | ~ program(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ( program_not_halts2(X0,X1)
        | halts2(X0,X1)
        | ~ program(X0) )
      & ( ( ~ halts2(X0,X1)
          & program(X0) )
        | ~ program_not_halts2(X0,X1) ) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ( program_not_halts2(X0,X1)
        | halts2(X0,X1)
        | ~ program(X0) )
      & ( ( ~ halts2(X0,X1)
          & program(X0) )
        | ~ program_not_halts2(X0,X1) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( program_not_halts2(X0,X1)
    <=> ( ~ halts2(X0,X1)
        & program(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_not_halts2_def) ).

fof(f186,plain,
    ~ spl8_1,
    inference(avatar_contradiction_clause,[],[f184]) ).

fof(f184,plain,
    ( $false
    | ~ spl8_1 ),
    inference(resolution,[],[f118,f73]) ).

fof(f73,plain,
    algorithm_program_decides(sK0),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    algorithm_program_decides(sK0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f35]) ).

fof(f35,plain,
    ( ? [X0] : algorithm_program_decides(X0)
   => algorithm_program_decides(sK0) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0] : algorithm_program_decides(X0),
    inference(flattening,[],[f17]) ).

fof(f17,negated_conjecture,
    ~ ~ ? [X0] : algorithm_program_decides(X0),
    inference(negated_conjecture,[],[f16]) ).

fof(f16,conjecture,
    ~ ? [X0] : algorithm_program_decides(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

fof(f118,plain,
    ( ! [X1] : ~ algorithm_program_decides(X1)
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f117,plain,
    ( spl8_1
  <=> ! [X1] : ~ algorithm_program_decides(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f178,plain,
    ( ~ spl8_10
    | ~ spl8_3
    | ~ spl8_8
    | ~ spl8_9 ),
    inference(avatar_split_clause,[],[f177,f148,f144,f125,f152]) ).

fof(f152,plain,
    ( spl8_10
  <=> program(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).

fof(f125,plain,
    ( spl8_3
  <=> ! [X2] :
        ( ~ program_not_halts2_halts2_outputs(X2,sK5(X2),bad)
        | ~ program(X2)
        | ~ program_halts2_halts2_outputs(X2,sK5(X2),good) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

fof(f144,plain,
    ( spl8_8
  <=> ! [X1] : program_not_halts2_halts2_outputs(sK6,X1,bad) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

fof(f148,plain,
    ( spl8_9
  <=> ! [X1] : program_halts2_halts2_outputs(sK6,X1,good) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).

fof(f177,plain,
    ( ~ program(sK6)
    | ~ spl8_3
    | ~ spl8_8
    | ~ spl8_9 ),
    inference(subsumption_resolution,[],[f173,f145]) ).

fof(f145,plain,
    ( ! [X1] : program_not_halts2_halts2_outputs(sK6,X1,bad)
    | ~ spl8_8 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f173,plain,
    ( ~ program(sK6)
    | ~ program_not_halts2_halts2_outputs(sK6,sK5(sK6),bad)
    | ~ spl8_3
    | ~ spl8_9 ),
    inference(resolution,[],[f149,f126]) ).

fof(f126,plain,
    ( ! [X2] :
        ( ~ program_halts2_halts2_outputs(X2,sK5(X2),good)
        | ~ program(X2)
        | ~ program_not_halts2_halts2_outputs(X2,sK5(X2),bad) )
    | ~ spl8_3 ),
    inference(avatar_component_clause,[],[f125]) ).

fof(f149,plain,
    ( ! [X1] : program_halts2_halts2_outputs(sK6,X1,good)
    | ~ spl8_9 ),
    inference(avatar_component_clause,[],[f148]) ).

fof(f170,plain,
    ( ~ spl8_2
    | ~ spl8_7 ),
    inference(avatar_contradiction_clause,[],[f168]) ).

fof(f168,plain,
    ( $false
    | ~ spl8_2
    | ~ spl8_7 ),
    inference(resolution,[],[f167,f122]) ).

fof(f122,plain,
    ( program_program_decides(sK1)
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f120]) ).

fof(f120,plain,
    ( spl8_2
  <=> program_program_decides(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f167,plain,
    ( ! [X0] : ~ program_program_decides(X0)
    | ~ spl8_7 ),
    inference(subsumption_resolution,[],[f166,f79]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
      | ~ program_program_decides(X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
          & program_halts2_halts3_outputs(X0,X1,X2,good) )
      | ~ program_program_decides(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( program_program_decides(X0)
     => ! [X1,X2] :
          ( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
          & program_halts2_halts3_outputs(X0,X1,X2,good) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3] :
      ( program_program_decides(X3)
     => ! [X1,X2] :
          ( program_not_halts2_halts3_outputs(X3,X1,X2,bad)
          & program_halts2_halts3_outputs(X3,X1,X2,good) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

fof(f166,plain,
    ( ! [X0] :
        ( ~ program_not_halts2_halts3_outputs(X0,sK7(X0),sK7(X0),bad)
        | ~ program_program_decides(X0) )
    | ~ spl8_7 ),
    inference(subsumption_resolution,[],[f164,f80]) ).

fof(f80,plain,
    ! [X0] :
      ( program(X0)
      | ~ program_program_decides(X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ( program_program_decides(X0)
        | ~ program_decides(X0)
        | ~ program(X0) )
      & ( ( program_decides(X0)
          & program(X0) )
        | ~ program_program_decides(X0) ) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ( program_program_decides(X0)
        | ~ program_decides(X0)
        | ~ program(X0) )
      & ( ( program_decides(X0)
          & program(X0) )
        | ~ program_program_decides(X0) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( program_program_decides(X0)
    <=> ( program_decides(X0)
        & program(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_program_decides_def) ).

fof(f164,plain,
    ( ! [X0] :
        ( ~ program(X0)
        | ~ program_not_halts2_halts3_outputs(X0,sK7(X0),sK7(X0),bad)
        | ~ program_program_decides(X0) )
    | ~ spl8_7 ),
    inference(resolution,[],[f142,f78]) ).

fof(f78,plain,
    ! [X2,X0,X1] :
      ( program_halts2_halts3_outputs(X0,X1,X2,good)
      | ~ program_program_decides(X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f142,plain,
    ( ! [X2] :
        ( ~ program_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),good)
        | ~ program(X2)
        | ~ program_not_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),bad) )
    | ~ spl8_7 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f141,plain,
    ( spl8_7
  <=> ! [X2] :
        ( ~ program_not_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),bad)
        | ~ program(X2)
        | ~ program_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),good) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

fof(f155,plain,
    ( spl8_7
    | spl8_10 ),
    inference(avatar_split_clause,[],[f89,f152,f141]) ).

fof(f89,plain,
    ! [X2] :
      ( program(sK6)
      | ~ program_not_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),bad)
      | ~ program_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),good)
      | ~ program(X2) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ( ( ! [X1] :
          ( program_not_halts2_halts2_outputs(sK6,X1,bad)
          & program_halts2_halts2_outputs(sK6,X1,good) )
      & program(sK6) )
    | ! [X2] :
        ( ~ program_not_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),bad)
        | ~ program_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),good)
        | ~ program(X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f53,f55,f54]) ).

fof(f54,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( program_not_halts2_halts2_outputs(X0,X1,bad)
            & program_halts2_halts2_outputs(X0,X1,good) )
        & program(X0) )
   => ( ! [X1] :
          ( program_not_halts2_halts2_outputs(sK6,X1,bad)
          & program_halts2_halts2_outputs(sK6,X1,good) )
      & program(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ! [X2] :
      ( ? [X3] :
          ( ~ program_not_halts2_halts3_outputs(X2,X3,X3,bad)
          | ~ program_halts2_halts3_outputs(X2,X3,X3,good) )
     => ( ~ program_not_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),bad)
        | ~ program_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),good) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( program_not_halts2_halts2_outputs(X0,X1,bad)
            & program_halts2_halts2_outputs(X0,X1,good) )
        & program(X0) )
    | ! [X2] :
        ( ? [X3] :
            ( ~ program_not_halts2_halts3_outputs(X2,X3,X3,bad)
            | ~ program_halts2_halts3_outputs(X2,X3,X3,good) )
        | ~ program(X2) ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ( ? [X2] :
        ( ! [X3] :
            ( program_not_halts2_halts2_outputs(X2,X3,bad)
            & program_halts2_halts2_outputs(X2,X3,good) )
        & program(X2) )
    | ! [X0] :
        ( ? [X1] :
            ( ~ program_not_halts2_halts3_outputs(X0,X1,X1,bad)
            | ~ program_halts2_halts3_outputs(X0,X1,X1,good) )
        | ~ program(X0) ) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( program_not_halts2_halts3_outputs(X0,X1,X1,bad)
            & program_halts2_halts3_outputs(X0,X1,X1,good) )
        & program(X0) )
   => ? [X2] :
        ( ! [X3] :
            ( program_not_halts2_halts2_outputs(X2,X3,bad)
            & program_halts2_halts2_outputs(X2,X3,good) )
        & program(X2) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ( ? [X3] :
        ( ! [X1] :
            ( program_not_halts2_halts3_outputs(X3,X1,X1,bad)
            & program_halts2_halts3_outputs(X3,X1,X1,good) )
        & program(X3) )
   => ? [X4] :
        ( ! [X1] :
            ( program_not_halts2_halts2_outputs(X4,X1,bad)
            & program_halts2_halts2_outputs(X4,X1,good) )
        & program(X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

fof(f150,plain,
    ( spl8_7
    | spl8_9 ),
    inference(avatar_split_clause,[],[f90,f148,f141]) ).

fof(f90,plain,
    ! [X2,X1] :
      ( program_halts2_halts2_outputs(sK6,X1,good)
      | ~ program_not_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),bad)
      | ~ program_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),good)
      | ~ program(X2) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f146,plain,
    ( spl8_7
    | spl8_8 ),
    inference(avatar_split_clause,[],[f91,f144,f141]) ).

fof(f91,plain,
    ! [X2,X1] :
      ( program_not_halts2_halts2_outputs(sK6,X1,bad)
      | ~ program_not_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),bad)
      | ~ program_halts2_halts3_outputs(X2,sK7(X2),sK7(X2),good)
      | ~ program(X2) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f139,plain,
    ( spl8_3
    | spl8_6 ),
    inference(avatar_split_clause,[],[f86,f136,f125]) ).

fof(f86,plain,
    ! [X2] :
      ( program(sK4)
      | ~ program_not_halts2_halts2_outputs(X2,sK5(X2),bad)
      | ~ program_halts2_halts2_outputs(X2,sK5(X2),good)
      | ~ program(X2) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ( ( ! [X1] :
          ( program_not_halts2_halts2_outputs(sK4,X1,good)
          & ( ~ halts2(sK4,X1)
            | ~ program_halts2(X1,X1) ) )
      & program(sK4) )
    | ! [X2] :
        ( ~ program_not_halts2_halts2_outputs(X2,sK5(X2),bad)
        | ~ program_halts2_halts2_outputs(X2,sK5(X2),good)
        | ~ program(X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f49,f51,f50]) ).

fof(f50,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( program_not_halts2_halts2_outputs(X0,X1,good)
            & ( ~ halts2(X0,X1)
              | ~ program_halts2(X1,X1) ) )
        & program(X0) )
   => ( ! [X1] :
          ( program_not_halts2_halts2_outputs(sK4,X1,good)
          & ( ~ halts2(sK4,X1)
            | ~ program_halts2(X1,X1) ) )
      & program(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ! [X2] :
      ( ? [X3] :
          ( ~ program_not_halts2_halts2_outputs(X2,X3,bad)
          | ~ program_halts2_halts2_outputs(X2,X3,good) )
     => ( ~ program_not_halts2_halts2_outputs(X2,sK5(X2),bad)
        | ~ program_halts2_halts2_outputs(X2,sK5(X2),good) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( program_not_halts2_halts2_outputs(X0,X1,good)
            & ( ~ halts2(X0,X1)
              | ~ program_halts2(X1,X1) ) )
        & program(X0) )
    | ! [X2] :
        ( ? [X3] :
            ( ~ program_not_halts2_halts2_outputs(X2,X3,bad)
            | ~ program_halts2_halts2_outputs(X2,X3,good) )
        | ~ program(X2) ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ( ? [X2] :
        ( ! [X3] :
            ( program_not_halts2_halts2_outputs(X2,X3,good)
            & ( ~ halts2(X2,X3)
              | ~ program_halts2(X3,X3) ) )
        & program(X2) )
    | ! [X0] :
        ( ? [X1] :
            ( ~ program_not_halts2_halts2_outputs(X0,X1,bad)
            | ~ program_halts2_halts2_outputs(X0,X1,good) )
        | ~ program(X0) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( program_not_halts2_halts2_outputs(X0,X1,bad)
            & program_halts2_halts2_outputs(X0,X1,good) )
        & program(X0) )
   => ? [X2] :
        ( ! [X3] :
            ( program_not_halts2_halts2_outputs(X2,X3,good)
            & ( program_halts2(X3,X3)
             => ~ halts2(X2,X3) ) )
        & program(X2) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ( ? [X4] :
        ( ! [X1] :
            ( program_not_halts2_halts2_outputs(X4,X1,bad)
            & program_halts2_halts2_outputs(X4,X1,good) )
        & program(X4) )
   => ? [X5] :
        ( ! [X1] :
            ( program_not_halts2_halts2_outputs(X5,X1,good)
            & ( program_halts2(X1,X1)
             => ~ halts2(X5,X1) ) )
        & program(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).

fof(f134,plain,
    ( spl8_3
    | spl8_5 ),
    inference(avatar_split_clause,[],[f87,f132,f125]) ).

fof(f87,plain,
    ! [X2,X1] :
      ( ~ halts2(sK4,X1)
      | ~ program_halts2(X1,X1)
      | ~ program_not_halts2_halts2_outputs(X2,sK5(X2),bad)
      | ~ program_halts2_halts2_outputs(X2,sK5(X2),good)
      | ~ program(X2) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f130,plain,
    ( spl8_3
    | spl8_4 ),
    inference(avatar_split_clause,[],[f88,f128,f125]) ).

fof(f88,plain,
    ! [X2,X1] :
      ( program_not_halts2_halts2_outputs(sK4,X1,good)
      | ~ program_not_halts2_halts2_outputs(X2,sK5(X2),bad)
      | ~ program_halts2_halts2_outputs(X2,sK5(X2),good)
      | ~ program(X2) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f123,plain,
    ( spl8_1
    | spl8_2 ),
    inference(avatar_split_clause,[],[f74,f120,f117]) ).

fof(f74,plain,
    ! [X1] :
      ( program_program_decides(sK1)
      | ~ algorithm_program_decides(X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ( program_program_decides(sK1)
    | ! [X1] : ~ algorithm_program_decides(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f37,f38]) ).

fof(f38,plain,
    ( ? [X0] : program_program_decides(X0)
   => program_program_decides(sK1) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ( ? [X0] : program_program_decides(X0)
    | ! [X1] : ~ algorithm_program_decides(X1) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ( ? [X1] : program_program_decides(X1)
    | ! [X0] : ~ algorithm_program_decides(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ( ? [X0] : algorithm_program_decides(X0)
   => ? [X1] : program_program_decides(X1) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ( ? [X0] : algorithm_program_decides(X0)
   => ? [X3] : program_program_decides(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : COM003+2 : TPTP v8.2.0. Bugfixed v2.2.0.
% 0.09/0.12  % 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
% 0.11/0.33  % Computer : n002.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Sun May 19 10:38:37 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  This is a FOF_THM_RFO_NEQ problem
% 0.11/0.33  Running 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 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.75  % (4914)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2995ds/78Mi)
% 0.56/0.75  % (4915)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2995ds/33Mi)
% 0.56/0.75  % (4916)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2995ds/34Mi)
% 0.56/0.75  % (4913)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2995ds/51Mi)
% 0.56/0.75  % (4917)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2995ds/45Mi)
% 0.56/0.75  % (4918)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2995ds/83Mi)
% 0.56/0.75  % (4919)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2995ds/56Mi)
% 0.56/0.75  % (4912)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2995ds/34Mi)
% 0.56/0.75  % (4915)Refutation not found, incomplete strategy% (4915)------------------------------
% 0.56/0.75  % (4915)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (4915)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (4915)Memory used [KB]: 947
% 0.56/0.75  % (4915)Time elapsed: 0.002 s
% 0.56/0.75  % (4915)Instructions burned: 2 (million)
% 0.56/0.75  % (4919)Refutation not found, incomplete strategy% (4919)------------------------------
% 0.56/0.75  % (4919)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (4919)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (4912)Refutation not found, incomplete strategy% (4912)------------------------------
% 0.56/0.75  % (4912)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (4912)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (4912)Memory used [KB]: 948
% 0.56/0.75  % (4912)Time elapsed: 0.002 s
% 0.56/0.75  % (4912)Instructions burned: 2 (million)
% 0.56/0.75  % (4919)Memory used [KB]: 948
% 0.56/0.75  % (4919)Time elapsed: 0.002 s
% 0.56/0.75  % (4919)Instructions burned: 2 (million)
% 0.56/0.75  % (4915)------------------------------
% 0.56/0.75  % (4915)------------------------------
% 0.56/0.75  % (4912)------------------------------
% 0.56/0.75  % (4912)------------------------------
% 0.56/0.75  % (4919)------------------------------
% 0.56/0.75  % (4919)------------------------------
% 0.56/0.75  % (4917)Refutation not found, incomplete strategy% (4917)------------------------------
% 0.56/0.75  % (4917)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (4917)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (4917)Memory used [KB]: 1030
% 0.56/0.75  % (4917)Time elapsed: 0.003 s
% 0.56/0.75  % (4917)Instructions burned: 3 (million)
% 0.56/0.75  % (4916)Refutation not found, incomplete strategy% (4916)------------------------------
% 0.56/0.75  % (4916)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (4916)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (4916)Memory used [KB]: 1034
% 0.56/0.75  % (4916)Time elapsed: 0.003 s
% 0.56/0.75  % (4916)Instructions burned: 3 (million)
% 0.56/0.75  % (4917)------------------------------
% 0.56/0.75  % (4917)------------------------------
% 0.56/0.75  % (4916)------------------------------
% 0.56/0.75  % (4916)------------------------------
% 0.56/0.75  % (4914)First to succeed.
% 0.56/0.75  % (4918)Also succeeded, but the first one will report.
% 0.56/0.75  % (4920)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on theBenchmark for (2995ds/55Mi)
% 0.56/0.75  % (4922)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on theBenchmark for (2995ds/208Mi)
% 0.56/0.75  % (4921)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on theBenchmark for (2995ds/50Mi)
% 0.56/0.75  % (4922)Refutation not found, incomplete strategy% (4922)------------------------------
% 0.56/0.75  % (4922)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (4922)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (4922)Memory used [KB]: 947
% 0.56/0.75  % (4922)Time elapsed: 0.002 s
% 0.56/0.75  % (4922)Instructions burned: 2 (million)
% 0.56/0.75  % (4924)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on theBenchmark for (2995ds/518Mi)
% 0.56/0.75  % (4922)------------------------------
% 0.56/0.75  % (4922)------------------------------
% 0.56/0.75  % (4914)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4911"
% 0.56/0.75  % (4924)Refutation not found, incomplete strategy% (4924)------------------------------
% 0.56/0.75  % (4924)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (4924)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (4924)Memory used [KB]: 958
% 0.56/0.75  % (4924)Time elapsed: 0.002 s
% 0.56/0.75  % (4924)Instructions burned: 2 (million)
% 0.56/0.75  % (4914)Refutation found. Thanks to Tanya!
% 0.56/0.75  % SZS status Theorem for theBenchmark
% 0.56/0.75  % SZS output start Proof for theBenchmark
% See solution above
% 0.56/0.75  % (4914)------------------------------
% 0.56/0.75  % (4914)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (4914)Termination reason: Refutation
% 0.56/0.75  
% 0.56/0.75  % (4914)Memory used [KB]: 1109
% 0.56/0.75  % (4914)Time elapsed: 0.007 s
% 0.56/0.75  % (4914)Instructions burned: 9 (million)
% 0.56/0.75  % (4911)Success in time 0.415 s
% 0.56/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------