TSTP Solution File: COM003-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : COM003-1 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 Apr 30 10:46:32 EDT 2024

% Result   : Unsatisfiable 0.12s 0.37s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   71
% Syntax   : Number of formulae    :  219 (   2 unt;   0 def)
%            Number of atoms       :  847 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives : 1172 ( 544   ~; 595   |;   0   &)
%                                         (  33 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   40 (  39 usr;  34 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-1 aty)
%            Number of variables   :  142 ( 142   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f628,plain,
    $false,
    inference(avatar_sat_refutation,[],[f58,f62,f70,f78,f82,f83,f87,f94,f102,f106,f110,f117,f129,f134,f138,f142,f146,f150,f158,f166,f167,f168,f169,f171,f172,f173,f174,f179,f182,f183,f185,f187,f199,f277,f295,f296,f307,f311,f441,f498,f550,f575,f588,f594,f598,f603,f612,f618,f620,f627]) ).

fof(f627,plain,
    ( ~ spl0_1
    | ~ spl0_7
    | spl0_38
    | spl0_48 ),
    inference(avatar_contradiction_clause,[],[f626]) ).

fof(f626,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_7
    | spl0_38
    | spl0_48 ),
    inference(subsumption_resolution,[],[f625,f54]) ).

fof(f54,plain,
    ( program(c1)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f52,plain,
    ( spl0_1
  <=> program(c1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f625,plain,
    ( ~ program(c1)
    | ~ spl0_1
    | ~ spl0_7
    | spl0_38
    | spl0_48 ),
    inference(resolution,[],[f624,f77]) ).

fof(f77,plain,
    ( ! [X3] :
        ( program(f5(X3))
        | ~ program(X3) )
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f76,plain,
    ( spl0_7
  <=> ! [X3] :
        ( ~ program(X3)
        | program(f5(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f624,plain,
    ( ~ program(f5(c1))
    | ~ spl0_1
    | spl0_38
    | spl0_48 ),
    inference(subsumption_resolution,[],[f623,f54]) ).

fof(f623,plain,
    ( ~ program(f5(c1))
    | ~ program(c1)
    | spl0_38
    | spl0_48 ),
    inference(subsumption_resolution,[],[f621,f264]) ).

fof(f264,plain,
    ( ~ program(f4(c1))
    | spl0_38 ),
    inference(avatar_component_clause,[],[f262]) ).

fof(f262,plain,
    ( spl0_38
  <=> program(f4(c1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f621,plain,
    ( ~ program(f5(c1))
    | program(f4(c1))
    | ~ program(c1)
    | spl0_48 ),
    inference(resolution,[],[f413,f301]) ).

fof(f301,plain,
    ! [X2,X3,X1] :
      ( halts3(X3,X1,X2)
      | ~ program(X1)
      | program(f4(X3))
      | ~ program(X3) ),
    inference(subsumption_resolution,[],[f7,f5]) ).

fof(f5,axiom,
    ! [X2,X3,X1] :
      ( halts3(X3,X1,X2)
      | ~ program(X1)
      | ~ halts2(X1,X2)
      | program(f4(X3))
      | ~ program(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_1) ).

fof(f7,axiom,
    ! [X2,X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | program(f4(X3))
      | halts2(X1,X2)
      | halts3(X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_3) ).

fof(f413,plain,
    ( ~ halts3(c1,f5(c1),f5(c1))
    | spl0_48 ),
    inference(avatar_component_clause,[],[f411]) ).

fof(f411,plain,
    ( spl0_48
  <=> halts3(c1,f5(c1),f5(c1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f620,plain,
    ( ~ spl0_39
    | ~ spl0_48
    | ~ spl0_1
    | ~ spl0_27
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f619,f274,f156,f52,f411,f266]) ).

fof(f266,plain,
    ( spl0_39
  <=> outputs(c1,good) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f156,plain,
    ( spl0_27
  <=> ! [X3] :
        ( ~ program(X3)
        | ~ halts3(X3,f5(X3),f5(X3))
        | ~ outputs(X3,bad)
        | ~ outputs(X3,good) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f274,plain,
    ( spl0_40
  <=> outputs(c1,bad) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f619,plain,
    ( ~ halts3(c1,f5(c1),f5(c1))
    | ~ outputs(c1,good)
    | ~ spl0_1
    | ~ spl0_27
    | ~ spl0_40 ),
    inference(subsumption_resolution,[],[f616,f54]) ).

fof(f616,plain,
    ( ~ halts3(c1,f5(c1),f5(c1))
    | ~ program(c1)
    | ~ outputs(c1,good)
    | ~ spl0_27
    | ~ spl0_40 ),
    inference(resolution,[],[f276,f157]) ).

fof(f157,plain,
    ( ! [X3] :
        ( ~ outputs(X3,bad)
        | ~ halts3(X3,f5(X3),f5(X3))
        | ~ program(X3)
        | ~ outputs(X3,good) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f156]) ).

fof(f276,plain,
    ( outputs(c1,bad)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f618,plain,
    ( spl0_47
    | ~ spl0_48
    | ~ spl0_1
    | ~ spl0_29
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f617,f274,f164,f52,f411,f407]) ).

fof(f407,plain,
    ( spl0_47
  <=> halts2(f5(c1),f5(c1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f164,plain,
    ( spl0_29
  <=> ! [X3] :
        ( ~ program(X3)
        | ~ halts3(X3,f5(X3),f5(X3))
        | halts2(f5(X3),f5(X3))
        | ~ outputs(X3,bad) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f617,plain,
    ( ~ halts3(c1,f5(c1),f5(c1))
    | halts2(f5(c1),f5(c1))
    | ~ spl0_1
    | ~ spl0_29
    | ~ spl0_40 ),
    inference(subsumption_resolution,[],[f615,f54]) ).

fof(f615,plain,
    ( ~ halts3(c1,f5(c1),f5(c1))
    | halts2(f5(c1),f5(c1))
    | ~ program(c1)
    | ~ spl0_29
    | ~ spl0_40 ),
    inference(resolution,[],[f276,f165]) ).

fof(f165,plain,
    ( ! [X3] :
        ( ~ outputs(X3,bad)
        | ~ halts3(X3,f5(X3),f5(X3))
        | halts2(f5(X3),f5(X3))
        | ~ program(X3) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f164]) ).

fof(f612,plain,
    ( ~ spl0_1
    | ~ spl0_17
    | spl0_38
    | spl0_40 ),
    inference(avatar_contradiction_clause,[],[f611]) ).

fof(f611,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_17
    | spl0_38
    | spl0_40 ),
    inference(subsumption_resolution,[],[f610,f264]) ).

fof(f610,plain,
    ( program(f4(c1))
    | ~ spl0_1
    | ~ spl0_17
    | spl0_40 ),
    inference(subsumption_resolution,[],[f607,f54]) ).

fof(f607,plain,
    ( ~ program(c1)
    | program(f4(c1))
    | ~ spl0_17
    | spl0_40 ),
    inference(resolution,[],[f116,f275]) ).

fof(f275,plain,
    ( ~ outputs(c1,bad)
    | spl0_40 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f116,plain,
    ( ! [X3] :
        ( outputs(X3,bad)
        | ~ program(X3)
        | program(f4(X3)) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f115]) ).

fof(f115,plain,
    ( spl0_17
  <=> ! [X3] :
        ( ~ program(X3)
        | outputs(X3,bad)
        | program(f4(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f603,plain,
    ( ~ spl0_1
    | ~ spl0_10
    | ~ spl0_34 ),
    inference(avatar_contradiction_clause,[],[f602]) ).

fof(f602,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_10
    | ~ spl0_34 ),
    inference(subsumption_resolution,[],[f601,f54]) ).

fof(f601,plain,
    ( ~ program(c1)
    | ~ spl0_10
    | ~ spl0_34 ),
    inference(resolution,[],[f90,f239]) ).

fof(f239,plain,
    ( halts2(c1,c1)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f237]) ).

fof(f237,plain,
    ( spl0_34
  <=> halts2(c1,c1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f90,plain,
    ( ! [X2,X1] :
        ( ~ halts2(X1,X2)
        | ~ program(X1) )
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f89]) ).

fof(f89,plain,
    ( spl0_10
  <=> ! [X2,X1] :
        ( ~ program(X1)
        | ~ halts2(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f598,plain,
    ( ~ spl0_1
    | ~ spl0_11
    | spl0_38
    | spl0_39 ),
    inference(avatar_contradiction_clause,[],[f597]) ).

fof(f597,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_11
    | spl0_38
    | spl0_39 ),
    inference(subsumption_resolution,[],[f596,f264]) ).

fof(f596,plain,
    ( program(f4(c1))
    | ~ spl0_1
    | ~ spl0_11
    | spl0_39 ),
    inference(subsumption_resolution,[],[f595,f54]) ).

fof(f595,plain,
    ( ~ program(c1)
    | program(f4(c1))
    | ~ spl0_11
    | spl0_39 ),
    inference(resolution,[],[f267,f93]) ).

fof(f93,plain,
    ( ! [X3] :
        ( outputs(X3,good)
        | ~ program(X3)
        | program(f4(X3)) )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f92]) ).

fof(f92,plain,
    ( spl0_11
  <=> ! [X3] :
        ( ~ program(X3)
        | outputs(X3,good)
        | program(f4(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f267,plain,
    ( ~ outputs(c1,good)
    | spl0_39 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f594,plain,
    ( ~ spl0_38
    | spl0_39
    | ~ spl0_1
    | ~ spl0_8
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f593,f108,f80,f52,f266,f262]) ).

fof(f80,plain,
    ( spl0_8
  <=> ! [X2,X1] :
        ( ~ program(X1)
        | decides(c1,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f108,plain,
    ( spl0_15
  <=> ! [X3] :
        ( ~ program(X3)
        | ~ decides(X3,f4(X3),f3(X3))
        | outputs(X3,good) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f593,plain,
    ( outputs(c1,good)
    | ~ program(f4(c1))
    | ~ spl0_1
    | ~ spl0_8
    | ~ spl0_15 ),
    inference(subsumption_resolution,[],[f582,f54]) ).

fof(f582,plain,
    ( ~ program(c1)
    | outputs(c1,good)
    | ~ program(f4(c1))
    | ~ spl0_8
    | ~ spl0_15 ),
    inference(resolution,[],[f109,f81]) ).

fof(f81,plain,
    ( ! [X2,X1] :
        ( decides(c1,X1,X2)
        | ~ program(X1) )
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f80]) ).

fof(f109,plain,
    ( ! [X3] :
        ( ~ decides(X3,f4(X3),f3(X3))
        | ~ program(X3)
        | outputs(X3,good) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f108]) ).

fof(f588,plain,
    ( ~ spl0_1
    | ~ spl0_5
    | ~ spl0_16
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(avatar_contradiction_clause,[],[f587]) ).

fof(f587,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_5
    | ~ spl0_16
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(subsumption_resolution,[],[f585,f54]) ).

fof(f585,plain,
    ( ~ program(c1)
    | ~ spl0_5
    | ~ spl0_16
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(resolution,[],[f578,f268]) ).

fof(f268,plain,
    ( outputs(c1,good)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f578,plain,
    ( ! [X0] :
        ( ~ outputs(X0,good)
        | ~ program(X0) )
    | ~ spl0_5
    | ~ spl0_16
    | ~ spl0_25 ),
    inference(subsumption_resolution,[],[f577,f113]) ).

fof(f113,plain,
    ( ! [X2,X1] :
        ( halts2(X1,X2)
        | ~ program(X1) )
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f112]) ).

fof(f112,plain,
    ( spl0_16
  <=> ! [X2,X1] :
        ( ~ program(X1)
        | halts2(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f577,plain,
    ( ! [X0] :
        ( ~ program(X0)
        | ~ halts2(X0,f6(X0))
        | ~ outputs(X0,good) )
    | ~ spl0_5
    | ~ spl0_16
    | ~ spl0_25 ),
    inference(subsumption_resolution,[],[f570,f69]) ).

fof(f69,plain,
    ( ! [X4] :
        ( program(f6(X4))
        | ~ program(X4) )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f68,plain,
    ( spl0_5
  <=> ! [X4] :
        ( ~ program(X4)
        | program(f6(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f570,plain,
    ( ! [X0] :
        ( ~ program(f6(X0))
        | ~ program(X0)
        | ~ halts2(X0,f6(X0))
        | ~ outputs(X0,good) )
    | ~ spl0_16
    | ~ spl0_25 ),
    inference(resolution,[],[f113,f149]) ).

fof(f149,plain,
    ( ! [X4] :
        ( ~ halts2(f6(X4),f6(X4))
        | ~ program(X4)
        | ~ halts2(X4,f6(X4))
        | ~ outputs(X4,good) )
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f148]) ).

fof(f148,plain,
    ( spl0_25
  <=> ! [X4] :
        ( ~ program(X4)
        | ~ halts2(f6(X4),f6(X4))
        | ~ halts2(X4,f6(X4))
        | ~ outputs(X4,good) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f575,plain,
    ( ~ spl0_1
    | ~ spl0_16
    | spl0_34 ),
    inference(avatar_contradiction_clause,[],[f574]) ).

fof(f574,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_16
    | spl0_34 ),
    inference(subsumption_resolution,[],[f564,f54]) ).

fof(f564,plain,
    ( ~ program(c1)
    | ~ spl0_16
    | spl0_34 ),
    inference(resolution,[],[f113,f238]) ).

fof(f238,plain,
    ( ~ halts2(c1,c1)
    | spl0_34 ),
    inference(avatar_component_clause,[],[f237]) ).

fof(f550,plain,
    ( ~ spl0_1
    | ~ spl0_7
    | ~ spl0_10
    | ~ spl0_47 ),
    inference(avatar_contradiction_clause,[],[f549]) ).

fof(f549,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_7
    | ~ spl0_10
    | ~ spl0_47 ),
    inference(subsumption_resolution,[],[f548,f54]) ).

fof(f548,plain,
    ( ~ program(c1)
    | ~ spl0_7
    | ~ spl0_10
    | ~ spl0_47 ),
    inference(resolution,[],[f546,f77]) ).

fof(f546,plain,
    ( ~ program(f5(c1))
    | ~ spl0_10
    | ~ spl0_47 ),
    inference(resolution,[],[f409,f90]) ).

fof(f409,plain,
    ( halts2(f5(c1),f5(c1))
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f407]) ).

fof(f498,plain,
    ( ~ spl0_4
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(avatar_contradiction_clause,[],[f497]) ).

fof(f497,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(subsumption_resolution,[],[f496,f464]) ).

fof(f464,plain,
    ( halts2(c3,c3)
    | ~ spl0_4
    | ~ spl0_20 ),
    inference(duplicate_literal_removal,[],[f463]) ).

fof(f463,plain,
    ( halts2(c3,c3)
    | halts2(c3,c3)
    | ~ spl0_4
    | ~ spl0_20 ),
    inference(resolution,[],[f128,f66]) ).

fof(f66,plain,
    ( program(c3)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f64,plain,
    ( spl0_4
  <=> program(c3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f128,plain,
    ( ! [X1] :
        ( ~ program(X1)
        | halts2(c3,X1)
        | halts2(X1,X1) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f127,plain,
    ( spl0_20
  <=> ! [X1] :
        ( ~ program(X1)
        | halts2(c3,X1)
        | halts2(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f496,plain,
    ( ~ halts2(c3,c3)
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(subsumption_resolution,[],[f493,f66]) ).

fof(f493,plain,
    ( ~ program(c3)
    | ~ halts2(c3,c3)
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(resolution,[],[f464,f86]) ).

fof(f86,plain,
    ( ! [X1] :
        ( ~ halts2(c3,X1)
        | ~ program(X1)
        | ~ halts2(X1,X1) )
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f85,plain,
    ( spl0_9
  <=> ! [X1] :
        ( ~ program(X1)
        | ~ halts2(c3,X1)
        | ~ halts2(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f441,plain,
    ( ~ spl0_1
    | ~ spl0_7
    | ~ spl0_8
    | ~ spl0_38
    | spl0_48 ),
    inference(avatar_contradiction_clause,[],[f440]) ).

fof(f440,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_7
    | ~ spl0_8
    | ~ spl0_38
    | spl0_48 ),
    inference(subsumption_resolution,[],[f439,f54]) ).

fof(f439,plain,
    ( ~ program(c1)
    | ~ spl0_1
    | ~ spl0_7
    | ~ spl0_8
    | ~ spl0_38
    | spl0_48 ),
    inference(resolution,[],[f436,f77]) ).

fof(f436,plain,
    ( ~ program(f5(c1))
    | ~ spl0_1
    | ~ spl0_8
    | ~ spl0_38
    | spl0_48 ),
    inference(resolution,[],[f413,f421]) ).

fof(f421,plain,
    ( ! [X0,X1] :
        ( halts3(c1,X0,X1)
        | ~ program(X0) )
    | ~ spl0_1
    | ~ spl0_8
    | ~ spl0_38 ),
    inference(subsumption_resolution,[],[f420,f263]) ).

fof(f263,plain,
    ( program(f4(c1))
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f262]) ).

fof(f420,plain,
    ( ! [X0,X1] :
        ( ~ program(X0)
        | halts3(c1,X0,X1)
        | ~ program(f4(c1)) )
    | ~ spl0_1
    | ~ spl0_8 ),
    inference(subsumption_resolution,[],[f419,f54]) ).

fof(f419,plain,
    ( ! [X0,X1] :
        ( ~ program(X0)
        | halts3(c1,X0,X1)
        | ~ program(c1)
        | ~ program(f4(c1)) )
    | ~ spl0_8 ),
    inference(resolution,[],[f341,f81]) ).

fof(f341,plain,
    ! [X2,X3,X1] :
      ( ~ decides(X3,f4(X3),f3(X3))
      | ~ program(X1)
      | halts3(X3,X1,X2)
      | ~ program(X3) ),
    inference(subsumption_resolution,[],[f11,f9]) ).

fof(f9,axiom,
    ! [X2,X3,X1] :
      ( ~ halts2(X1,X2)
      | ~ program(X1)
      | ~ program(X3)
      | halts3(X3,X1,X2)
      | ~ decides(X3,f4(X3),f3(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_5) ).

fof(f11,axiom,
    ! [X2,X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | halts2(X1,X2)
      | halts3(X3,X1,X2)
      | ~ decides(X3,f4(X3),f3(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_7) ).

fof(f311,plain,
    ( ~ spl0_5
    | ~ spl0_6
    | spl0_41 ),
    inference(avatar_contradiction_clause,[],[f310]) ).

fof(f310,plain,
    ( $false
    | ~ spl0_5
    | ~ spl0_6
    | spl0_41 ),
    inference(subsumption_resolution,[],[f309,f74]) ).

fof(f74,plain,
    ( program(c2)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f72,plain,
    ( spl0_6
  <=> program(c2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f309,plain,
    ( ~ program(c2)
    | ~ spl0_5
    | spl0_41 ),
    inference(resolution,[],[f288,f69]) ).

fof(f288,plain,
    ( ~ program(f6(c2))
    | spl0_41 ),
    inference(avatar_component_clause,[],[f286]) ).

fof(f286,plain,
    ( spl0_41
  <=> program(f6(c2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f307,plain,
    ( ~ spl0_41
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_12
    | ~ spl0_14
    | ~ spl0_19
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f306,f148,f136,f123,f104,f96,f72,f68,f286]) ).

fof(f96,plain,
    ( spl0_12
  <=> outputs(c2,good) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f104,plain,
    ( spl0_14
  <=> ! [X1] :
        ( ~ program(X1)
        | halts2(c2,X1)
        | ~ halts2(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f123,plain,
    ( spl0_19
  <=> ! [X1] :
        ( ~ program(X1)
        | halts2(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f136,plain,
    ( spl0_22
  <=> ! [X1] :
        ( ~ program(X1)
        | halts2(c2,X1)
        | halts2(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f306,plain,
    ( ~ program(f6(c2))
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_12
    | ~ spl0_14
    | ~ spl0_19
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(subsumption_resolution,[],[f305,f98]) ).

fof(f98,plain,
    ( outputs(c2,good)
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f96]) ).

fof(f305,plain,
    ( ~ outputs(c2,good)
    | ~ program(f6(c2))
    | ~ spl0_5
    | ~ spl0_6
    | ~ spl0_14
    | ~ spl0_19
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(subsumption_resolution,[],[f304,f74]) ).

fof(f304,plain,
    ( ~ program(c2)
    | ~ outputs(c2,good)
    | ~ program(f6(c2))
    | ~ spl0_5
    | ~ spl0_14
    | ~ spl0_19
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(resolution,[],[f303,f245]) ).

fof(f245,plain,
    ( ! [X1] :
        ( halts2(c2,X1)
        | ~ program(X1) )
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(subsumption_resolution,[],[f137,f105]) ).

fof(f105,plain,
    ( ! [X1] :
        ( ~ halts2(X1,X1)
        | halts2(c2,X1)
        | ~ program(X1) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f104]) ).

fof(f137,plain,
    ( ! [X1] :
        ( ~ program(X1)
        | halts2(c2,X1)
        | halts2(X1,X1) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f303,plain,
    ( ! [X0] :
        ( ~ halts2(X0,f6(X0))
        | ~ program(X0)
        | ~ outputs(X0,good) )
    | ~ spl0_5
    | ~ spl0_19
    | ~ spl0_25 ),
    inference(subsumption_resolution,[],[f302,f69]) ).

fof(f302,plain,
    ( ! [X0] :
        ( ~ program(X0)
        | ~ halts2(X0,f6(X0))
        | ~ outputs(X0,good)
        | ~ program(f6(X0)) )
    | ~ spl0_19
    | ~ spl0_25 ),
    inference(resolution,[],[f149,f124]) ).

fof(f124,plain,
    ( ! [X1] :
        ( halts2(X1,X1)
        | ~ program(X1) )
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f123]) ).

fof(f296,plain,
    ( ~ spl0_41
    | ~ spl0_12
    | ~ spl0_21
    | ~ spl0_6
    | ~ spl0_14
    | ~ spl0_22
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f279,f144,f136,f104,f72,f131,f96,f286]) ).

fof(f131,plain,
    ( spl0_21
  <=> outputs(c2,bad) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f144,plain,
    ( spl0_24
  <=> ! [X4] :
        ( ~ program(X4)
        | ~ halts2(X4,f6(X4))
        | ~ outputs(X4,bad)
        | ~ outputs(X4,good) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f279,plain,
    ( ~ outputs(c2,bad)
    | ~ outputs(c2,good)
    | ~ program(f6(c2))
    | ~ spl0_6
    | ~ spl0_14
    | ~ spl0_22
    | ~ spl0_24 ),
    inference(subsumption_resolution,[],[f278,f74]) ).

fof(f278,plain,
    ( ~ program(c2)
    | ~ outputs(c2,bad)
    | ~ outputs(c2,good)
    | ~ program(f6(c2))
    | ~ spl0_14
    | ~ spl0_22
    | ~ spl0_24 ),
    inference(resolution,[],[f145,f245]) ).

fof(f145,plain,
    ( ! [X4] :
        ( ~ halts2(X4,f6(X4))
        | ~ program(X4)
        | ~ outputs(X4,bad)
        | ~ outputs(X4,good) )
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f295,plain,
    ( ~ spl0_6
    | ~ spl0_13
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(avatar_contradiction_clause,[],[f294]) ).

fof(f294,plain,
    ( $false
    | ~ spl0_6
    | ~ spl0_13
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(subsumption_resolution,[],[f293,f74]) ).

fof(f293,plain,
    ( ~ program(c2)
    | ~ spl0_13
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(duplicate_literal_removal,[],[f292]) ).

fof(f292,plain,
    ( ~ program(c2)
    | ~ program(c2)
    | ~ spl0_13
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(resolution,[],[f101,f245]) ).

fof(f101,plain,
    ( ! [X1] :
        ( ~ halts2(X1,X1)
        | ~ program(X1) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f100]) ).

fof(f100,plain,
    ( spl0_13
  <=> ! [X1] :
        ( ~ program(X1)
        | ~ halts2(X1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f277,plain,
    ( ~ spl0_38
    | spl0_40
    | ~ spl0_1
    | ~ spl0_8
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f272,f140,f80,f52,f274,f262]) ).

fof(f140,plain,
    ( spl0_23
  <=> ! [X3] :
        ( ~ program(X3)
        | ~ decides(X3,f4(X3),f3(X3))
        | outputs(X3,bad) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f272,plain,
    ( outputs(c1,bad)
    | ~ program(f4(c1))
    | ~ spl0_1
    | ~ spl0_8
    | ~ spl0_23 ),
    inference(subsumption_resolution,[],[f271,f54]) ).

fof(f271,plain,
    ( ~ program(c1)
    | outputs(c1,bad)
    | ~ program(f4(c1))
    | ~ spl0_8
    | ~ spl0_23 ),
    inference(resolution,[],[f141,f81]) ).

fof(f141,plain,
    ( ! [X3] :
        ( ~ decides(X3,f4(X3),f3(X3))
        | ~ program(X3)
        | outputs(X3,bad) )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f140]) ).

fof(f199,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f198]) ).

fof(f198,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f197,f49]) ).

fof(f49,axiom,
    algorithm(c4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_deciding_algorithm) ).

fof(f197,plain,
    ( ~ algorithm(c4)
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(resolution,[],[f195,f57]) ).

fof(f57,plain,
    ( ! [X0] :
        ( program(f2(X0))
        | ~ algorithm(X0) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f56,plain,
    ( spl0_2
  <=> ! [X0] :
        ( ~ algorithm(X0)
        | program(f2(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f195,plain,
    ( ~ program(f2(c4))
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f194,f49]) ).

fof(f194,plain,
    ( ~ algorithm(c4)
    | ~ program(f2(c4))
    | ~ spl0_3 ),
    inference(resolution,[],[f61,f50]) ).

fof(f50,axiom,
    ! [X6,X5] :
      ( decides(c4,X5,X6)
      | ~ program(X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_the_algorithm_doesnt_exist) ).

fof(f61,plain,
    ( ! [X0] :
        ( ~ decides(X0,f2(X0),f1(X0))
        | ~ algorithm(X0) )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl0_3
  <=> ! [X0] :
        ( ~ algorithm(X0)
        | ~ decides(X0,f2(X0),f1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f187,plain,
    ( spl0_22
    | spl0_29 ),
    inference(avatar_split_clause,[],[f21,f164,f136]) ).

fof(f21,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ outputs(X3,bad)
      | halts2(X1,X1)
      | halts2(c2,X1)
      | halts2(f5(X3),f5(X3))
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_9) ).

fof(f185,plain,
    ( spl0_21
    | spl0_19
    | spl0_29 ),
    inference(avatar_split_clause,[],[f22,f164,f123,f131]) ).

fof(f22,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ outputs(X3,bad)
      | outputs(c2,bad)
      | halts2(X1,X1)
      | halts2(f5(X3),f5(X3))
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_10) ).

fof(f183,plain,
    ( spl0_14
    | spl0_29 ),
    inference(avatar_split_clause,[],[f19,f164,f104]) ).

fof(f19,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ outputs(X3,bad)
      | ~ halts2(X1,X1)
      | halts2(c2,X1)
      | halts2(f5(X3),f5(X3))
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_7) ).

fof(f182,plain,
    ( spl0_12
    | spl0_13
    | spl0_29 ),
    inference(avatar_split_clause,[],[f20,f164,f100,f96]) ).

fof(f20,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ outputs(X3,bad)
      | ~ halts2(X1,X1)
      | outputs(c2,good)
      | halts2(f5(X3),f5(X3))
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_8) ).

fof(f179,plain,
    ( spl0_20
    | spl0_25 ),
    inference(avatar_split_clause,[],[f43,f148,f127]) ).

fof(f43,axiom,
    ! [X1,X4] :
      ( ~ program(X4)
      | ~ program(X1)
      | ~ outputs(X4,good)
      | halts2(X1,X1)
      | halts2(c3,X1)
      | ~ halts2(X4,f6(X4))
      | ~ halts2(f6(X4),f6(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_11) ).

fof(f174,plain,
    ( spl0_9
    | spl0_25 ),
    inference(avatar_split_clause,[],[f42,f148,f85]) ).

fof(f42,axiom,
    ! [X1,X4] :
      ( ~ program(X4)
      | ~ program(X1)
      | ~ outputs(X4,good)
      | ~ halts2(X1,X1)
      | ~ halts2(c3,X1)
      | ~ halts2(X4,f6(X4))
      | ~ halts2(f6(X4),f6(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_10) ).

fof(f173,plain,
    ( spl0_22
    | spl0_27 ),
    inference(avatar_split_clause,[],[f31,f156,f136]) ).

fof(f31,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ outputs(X3,good)
      | ~ outputs(X3,bad)
      | halts2(X1,X1)
      | halts2(c2,X1)
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_19) ).

fof(f172,plain,
    ( spl0_20
    | spl0_24 ),
    inference(avatar_split_clause,[],[f47,f144,f127]) ).

fof(f47,axiom,
    ! [X1,X4] :
      ( ~ program(X4)
      | ~ program(X1)
      | ~ outputs(X4,good)
      | ~ outputs(X4,bad)
      | halts2(X1,X1)
      | halts2(c3,X1)
      | ~ halts2(X4,f6(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_15) ).

fof(f171,plain,
    ( spl0_21
    | spl0_19
    | spl0_27 ),
    inference(avatar_split_clause,[],[f32,f156,f123,f131]) ).

fof(f32,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ outputs(X3,good)
      | ~ outputs(X3,bad)
      | outputs(c2,bad)
      | halts2(X1,X1)
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_20) ).

fof(f169,plain,
    ( spl0_14
    | spl0_27 ),
    inference(avatar_split_clause,[],[f29,f156,f104]) ).

fof(f29,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ outputs(X3,good)
      | ~ outputs(X3,bad)
      | ~ halts2(X1,X1)
      | halts2(c2,X1)
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_17) ).

fof(f168,plain,
    ( spl0_12
    | spl0_13
    | spl0_27 ),
    inference(avatar_split_clause,[],[f30,f156,f100,f96]) ).

fof(f30,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ outputs(X3,good)
      | ~ outputs(X3,bad)
      | ~ halts2(X1,X1)
      | outputs(c2,good)
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_18) ).

fof(f167,plain,
    ( spl0_9
    | spl0_24 ),
    inference(avatar_split_clause,[],[f46,f144,f85]) ).

fof(f46,axiom,
    ! [X1,X4] :
      ( ~ program(X4)
      | ~ program(X1)
      | ~ outputs(X4,good)
      | ~ outputs(X4,bad)
      | ~ halts2(X1,X1)
      | ~ halts2(c3,X1)
      | ~ halts2(X4,f6(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_14) ).

fof(f166,plain,
    ( spl0_6
    | spl0_29 ),
    inference(avatar_split_clause,[],[f18,f164,f72]) ).

fof(f18,axiom,
    ! [X3] :
      ( ~ program(X3)
      | program(c2)
      | ~ outputs(X3,bad)
      | halts2(f5(X3),f5(X3))
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_6) ).

fof(f158,plain,
    ( spl0_6
    | spl0_27 ),
    inference(avatar_split_clause,[],[f28,f156,f72]) ).

fof(f28,axiom,
    ! [X3] :
      ( ~ program(X3)
      | program(c2)
      | ~ outputs(X3,good)
      | ~ outputs(X3,bad)
      | ~ halts3(X3,f5(X3),f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_16) ).

fof(f150,plain,
    ( spl0_4
    | spl0_25 ),
    inference(avatar_split_clause,[],[f41,f148,f64]) ).

fof(f41,axiom,
    ! [X4] :
      ( ~ program(X4)
      | program(c3)
      | ~ outputs(X4,good)
      | ~ halts2(X4,f6(X4))
      | ~ halts2(f6(X4),f6(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_9) ).

fof(f146,plain,
    ( spl0_4
    | spl0_24 ),
    inference(avatar_split_clause,[],[f45,f144,f64]) ).

fof(f45,axiom,
    ! [X4] :
      ( ~ program(X4)
      | program(c3)
      | ~ outputs(X4,good)
      | ~ outputs(X4,bad)
      | ~ halts2(X4,f6(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_13) ).

fof(f142,plain,
    ( spl0_16
    | spl0_23 ),
    inference(avatar_split_clause,[],[f12,f140,f112]) ).

fof(f12,axiom,
    ! [X2,X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | outputs(X3,bad)
      | halts2(X1,X2)
      | ~ decides(X3,f4(X3),f3(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_8) ).

fof(f138,plain,
    ( spl0_22
    | spl0_7 ),
    inference(avatar_split_clause,[],[f16,f76,f136]) ).

fof(f16,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | program(f5(X3))
      | halts2(X1,X1)
      | halts2(c2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_4) ).

fof(f134,plain,
    ( spl0_21
    | spl0_19
    | spl0_7 ),
    inference(avatar_split_clause,[],[f17,f76,f123,f131]) ).

fof(f17,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | program(f5(X3))
      | outputs(c2,bad)
      | halts2(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_5) ).

fof(f129,plain,
    ( spl0_20
    | spl0_5 ),
    inference(avatar_split_clause,[],[f35,f68,f127]) ).

fof(f35,axiom,
    ! [X1,X4] :
      ( ~ program(X4)
      | ~ program(X1)
      | program(f6(X4))
      | halts2(X1,X1)
      | halts2(c3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_3) ).

fof(f117,plain,
    ( spl0_16
    | spl0_17 ),
    inference(avatar_split_clause,[],[f8,f115,f112]) ).

fof(f8,axiom,
    ! [X2,X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | program(f4(X3))
      | outputs(X3,bad)
      | halts2(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_4) ).

fof(f110,plain,
    ( spl0_10
    | spl0_15 ),
    inference(avatar_split_clause,[],[f10,f108,f89]) ).

fof(f10,axiom,
    ! [X2,X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ halts2(X1,X2)
      | outputs(X3,good)
      | ~ decides(X3,f4(X3),f3(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_6) ).

fof(f106,plain,
    ( spl0_14
    | spl0_7 ),
    inference(avatar_split_clause,[],[f14,f76,f104]) ).

fof(f14,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ halts2(X1,X1)
      | program(f5(X3))
      | halts2(c2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_2) ).

fof(f102,plain,
    ( spl0_12
    | spl0_13
    | spl0_7 ),
    inference(avatar_split_clause,[],[f15,f76,f100,f96]) ).

fof(f15,axiom,
    ! [X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ halts2(X1,X1)
      | program(f5(X3))
      | outputs(c2,good) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_3) ).

fof(f94,plain,
    ( spl0_10
    | spl0_11 ),
    inference(avatar_split_clause,[],[f6,f92,f89]) ).

fof(f6,axiom,
    ! [X2,X3,X1] :
      ( ~ program(X3)
      | ~ program(X1)
      | ~ halts2(X1,X2)
      | program(f4(X3))
      | outputs(X3,good) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_2) ).

fof(f87,plain,
    ( spl0_9
    | spl0_5 ),
    inference(avatar_split_clause,[],[f34,f68,f85]) ).

fof(f34,axiom,
    ! [X1,X4] :
      ( ~ program(X4)
      | ~ program(X1)
      | ~ halts2(X1,X1)
      | ~ halts2(c3,X1)
      | program(f6(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_2) ).

fof(f83,plain,
    ( spl0_8
    | spl0_3 ),
    inference(avatar_split_clause,[],[f4,f60,f80]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( ~ algorithm(X0)
      | ~ program(X1)
      | decides(c1,X1,X2)
      | ~ decides(X0,f2(X0),f1(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_1_4) ).

fof(f82,plain,
    ( spl0_8
    | spl0_2 ),
    inference(avatar_split_clause,[],[f2,f56,f80]) ).

fof(f2,axiom,
    ! [X2,X0,X1] :
      ( ~ algorithm(X0)
      | ~ program(X1)
      | program(f2(X0))
      | decides(c1,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_1_2) ).

fof(f78,plain,
    ( spl0_6
    | spl0_7 ),
    inference(avatar_split_clause,[],[f13,f76,f72]) ).

fof(f13,axiom,
    ! [X3] :
      ( ~ program(X3)
      | program(c2)
      | program(f5(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_1) ).

fof(f70,plain,
    ( spl0_4
    | spl0_5 ),
    inference(avatar_split_clause,[],[f33,f68,f64]) ).

fof(f33,axiom,
    ! [X4] :
      ( ~ program(X4)
      | program(c3)
      | program(f6(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_1) ).

fof(f62,plain,
    ( spl0_1
    | spl0_3 ),
    inference(avatar_split_clause,[],[f3,f60,f52]) ).

fof(f3,axiom,
    ! [X0] :
      ( ~ algorithm(X0)
      | program(c1)
      | ~ decides(X0,f2(X0),f1(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_1_3) ).

fof(f58,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f1,f56,f52]) ).

fof(f1,axiom,
    ! [X0] :
      ( ~ algorithm(X0)
      | program(c1)
      | program(f2(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_1_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : COM003-1 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.11/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Apr 30 05:26:33 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  % (7124)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36  % (7128)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.36  % (7126)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.36  % (7129)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.36  % (7130)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.36  % (7127)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.12/0.36  % (7131)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.36  % (7125)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.37  Detected minimum model sizes of [1,1,1]
% 0.12/0.37  Detected maximum model sizes of [max,max,2]
% 0.12/0.37  TRYING [1,1,1]
% 0.12/0.37  TRYING [1]
% 0.12/0.37  TRYING [2,1,1]
% 0.12/0.37  Detected minimum model sizes of [1,1,1]
% 0.12/0.37  Detected maximum model sizes of [max,max,2]
% 0.12/0.37  TRYING [1,1,1]
% 0.12/0.37  TRYING [2]
% 0.12/0.37  TRYING [2,1,1]
% 0.12/0.37  % (7130)First to succeed.
% 0.12/0.37  TRYING [1]
% 0.12/0.37  TRYING [2]
% 0.12/0.37  TRYING [3,1,1]
% 0.12/0.37  % (7130)Refutation found. Thanks to Tanya!
% 0.12/0.37  % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.37  % (7130)------------------------------
% 0.12/0.37  % (7130)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.37  % (7130)Termination reason: Refutation
% 0.12/0.37  
% 0.12/0.37  % (7130)Memory used [KB]: 1028
% 0.12/0.37  % (7130)Time elapsed: 0.011 s
% 0.12/0.37  % (7130)Instructions burned: 19 (million)
% 0.12/0.37  % (7130)------------------------------
% 0.12/0.37  % (7130)------------------------------
% 0.12/0.37  % (7124)Success in time 0.029 s
%------------------------------------------------------------------------------