TSTP Solution File: SEV087^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV087^5 : TPTP v8.1.2. 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 : n025.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 : Sun May  5 09:41:17 EDT 2024

% Result   : Theorem 0.22s 0.42s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   81 (   2 unt;   9 typ;   0 def)
%            Number of atoms       :  602 ( 249 equ;   0 cnn)
%            Maximal formula atoms :    8 (   8 avg)
%            Number of connectives :  592 (  96   ~;  82   |;  57   &; 337   @)
%                                         (   7 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  375 ( 375   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   9 con; 0-2 aty)
%            Number of variables   :  288 ( 194   ^  53   !;  40   ?; 288   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(func_def_4,type,
    sP0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $o ).

thf(func_def_5,type,
    sP1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $o ).

thf(func_def_6,type,
    sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_7,type,
    sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_8,type,
    sK4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_9,type,
    sK5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_10,type,
    sK6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_11,type,
    sK7: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).

thf(func_def_13,type,
    ph9: 
      !>[X0: $tType] : X0 ).

thf(f124,plain,
    $false,
    inference(avatar_sat_refutation,[],[f63,f81,f86,f91,f92,f96,f121,f123]) ).

thf(f123,plain,
    ( spl8_8
    | ~ spl8_3 ),
    inference(avatar_split_clause,[],[f112,f60,f118]) ).

thf(f118,plain,
    ( spl8_8
  <=> ( ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

thf(f60,plain,
    ( spl8_3
  <=> ( $true
      = ( sP1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

thf(f112,plain,
    ( ( ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl8_3 ),
    inference(equality_proxy_clausification,[],[f111]) ).

thf(f111,plain,
    ( ( $true
      = ( ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_3 ),
    inference(beta_eta_normalization,[],[f110]) ).

thf(f110,plain,
    ( ( $true
      = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_3 ),
    inference(trivial_inequality_removal,[],[f109]) ).

thf(f109,plain,
    ( ( $true != $true )
    | ( $true
      = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK2
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK3
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_3 ),
    inference(superposition,[],[f24,f62]) ).

thf(f62,plain,
    ( ( $true
      = ( sP1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl8_3 ),
    inference(avatar_component_clause,[],[f60]) ).

thf(f24,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( sP1 @ X0 ) )
      | ( $true
        = ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( ( sK2 @ X0 )
         != ( sK3 @ X0 ) )
        & ( $true
          = ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
        & ( $true
          = ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) )
      | ( $true
       != ( sP1 @ X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f14]) ).

thf(f14,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o,X2: $i > $o] :
          ( ( X1 != X2 )
          & ( ( X0 @ X1 @ X2 )
            = $true )
          & ( $true
            = ( X0 @ X2 @ X1 ) ) )
     => ( ( ( sK2 @ X0 )
         != ( sK3 @ X0 ) )
        & ( $true
          = ( X0 @ ( sK2 @ X0 ) @ ( sK3 @ X0 ) ) )
        & ( $true
          = ( X0 @ ( sK3 @ X0 ) @ ( sK2 @ X0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f13,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o,X2: $i > $o] :
          ( ( X1 != X2 )
          & ( ( X0 @ X1 @ X2 )
            = $true )
          & ( $true
            = ( X0 @ X2 @ X1 ) ) )
      | ( $true
       != ( sP1 @ X0 ) ) ),
    inference(rectify,[],[f12]) ).

thf(f12,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X2: $i > $o,X1: $i > $o] :
          ( ( X1 != X2 )
          & ( $true
            = ( X0 @ X2 @ X1 ) )
          & ( ( X0 @ X1 @ X2 )
            = $true ) )
      | ( $true
       != ( sP1 @ X0 ) ) ),
    inference(nnf_transformation,[],[f10]) ).

thf(f10,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X2: $i > $o,X1: $i > $o] :
          ( ( X1 != X2 )
          & ( $true
            = ( X0 @ X2 @ X1 ) )
          & ( ( X0 @ X1 @ X2 )
            = $true ) )
      | ( $true
       != ( sP1 @ X0 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f121,plain,
    ( ~ spl8_8
    | ~ spl8_3 ),
    inference(avatar_split_clause,[],[f116,f60,f118]) ).

thf(f116,plain,
    ( ( ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl8_3 ),
    inference(trivial_inequality_removal,[],[f107]) ).

thf(f107,plain,
    ( ( $true != $true )
    | ( ( sK3
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK2
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl8_3 ),
    inference(superposition,[],[f25,f62]) ).

thf(f25,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( sK2 @ X0 )
       != ( sK3 @ X0 ) )
      | ( $true
       != ( sP1 @ X0 ) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f96,plain,
    ~ spl8_1,
    inference(avatar_contradiction_clause,[],[f95]) ).

thf(f95,plain,
    ( $false
    | ~ spl8_1 ),
    inference(trivial_inequality_removal,[],[f94]) ).

thf(f94,plain,
    ( ( $true = $false )
    | ~ spl8_1 ),
    inference(beta_eta_normalization,[],[f93]) ).

thf(f93,plain,
    ( ! [X1: $i] :
        ( ( ^ [Y0: $i] : $true
          @ X1 )
        = ( ^ [Y0: $i] : $false
          @ X1 ) )
    | ~ spl8_1 ),
    inference(argument_congruence,[],[f54]) ).

thf(f54,plain,
    ( ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) )
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f52]) ).

thf(f52,plain,
    ( spl8_1
  <=> ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

thf(f92,plain,
    ( ( ( sK6
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK5
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( ( sK4
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK5
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( ( sK6
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK4
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(theory_tautology_sat_conflict,[]) ).

thf(f91,plain,
    ( spl8_6
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f70,f56,f88]) ).

thf(f88,plain,
    ( spl8_6
  <=> ( ( sK6
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK5
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

thf(f56,plain,
    ( spl8_2
  <=> ( $true
      = ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

thf(f70,plain,
    ( ( ( sK6
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK5
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl8_2 ),
    inference(equality_proxy_clausification,[],[f69]) ).

thf(f69,plain,
    ( ( $true
      = ( ( sK5
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK6
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_2 ),
    inference(beta_eta_normalization,[],[f68]) ).

thf(f68,plain,
    ( ( $true
      = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK6
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK5
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_2 ),
    inference(trivial_inequality_removal,[],[f66]) ).

thf(f66,plain,
    ( ( $true
      = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK6
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK5
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true != $true )
    | ~ spl8_2 ),
    inference(superposition,[],[f28,f58]) ).

thf(f58,plain,
    ( ( $true
      = ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f56]) ).

thf(f28,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( sP0 @ X0 ) )
      | ( $true
        = ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f19,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( ( $true
          = ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
        & ( $true
         != ( X0 @ ( sK6 @ X0 ) @ ( sK4 @ X0 ) ) )
        & ( $true
          = ( X0 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) ) )
      | ( $true
       != ( sP0 @ X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f17,f18]) ).

thf(f18,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
          ( ( $true
            = ( X0 @ X3 @ X2 ) )
          & ( ( X0 @ X3 @ X1 )
           != $true )
          & ( $true
            = ( X0 @ X2 @ X1 ) ) )
     => ( ( $true
          = ( X0 @ ( sK6 @ X0 ) @ ( sK5 @ X0 ) ) )
        & ( $true
         != ( X0 @ ( sK6 @ X0 ) @ ( sK4 @ X0 ) ) )
        & ( $true
          = ( X0 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f17,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
          ( ( $true
            = ( X0 @ X3 @ X2 ) )
          & ( ( X0 @ X3 @ X1 )
           != $true )
          & ( $true
            = ( X0 @ X2 @ X1 ) ) )
      | ( $true
       != ( sP0 @ X0 ) ) ),
    inference(rectify,[],[f16]) ).

thf(f16,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
          ( ( $true
            = ( X0 @ X6 @ X5 ) )
          & ( $true
           != ( X0 @ X6 @ X4 ) )
          & ( ( X0 @ X5 @ X4 )
            = $true ) )
      | ( $true
       != ( sP0 @ X0 ) ) ),
    inference(nnf_transformation,[],[f9]) ).

thf(f9,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
          ( ( $true
            = ( X0 @ X6 @ X5 ) )
          & ( $true
           != ( X0 @ X6 @ X4 ) )
          & ( ( X0 @ X5 @ X4 )
            = $true ) )
      | ( $true
       != ( sP0 @ X0 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f86,plain,
    ( spl8_5
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f73,f56,f83]) ).

thf(f83,plain,
    ( spl8_5
  <=> ( ( sK4
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK5
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).

thf(f73,plain,
    ( ( ( sK4
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK5
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl8_2 ),
    inference(equality_proxy_clausification,[],[f72]) ).

thf(f72,plain,
    ( ( $true
      = ( ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK5
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_2 ),
    inference(beta_eta_normalization,[],[f71]) ).

thf(f71,plain,
    ( ( $true
      = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK5
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_2 ),
    inference(trivial_inequality_removal,[],[f65]) ).

thf(f65,plain,
    ( ( $true != $true )
    | ( $true
      = ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK5
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_2 ),
    inference(superposition,[],[f26,f58]) ).

thf(f26,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( sP0 @ X0 ) )
      | ( $true
        = ( X0 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f81,plain,
    ( ~ spl8_4
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f76,f56,f78]) ).

thf(f78,plain,
    ( spl8_4
  <=> ( ( sK6
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
      = ( sK4
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

thf(f76,plain,
    ( ( ( sK6
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
     != ( sK4
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ~ spl8_2 ),
    inference(equality_proxy_clausification,[],[f75]) ).

thf(f75,plain,
    ( ( ( ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK6
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ~ spl8_2 ),
    inference(beta_eta_normalization,[],[f74]) ).

thf(f74,plain,
    ( ( $true
     != ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK6
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ~ spl8_2 ),
    inference(trivial_inequality_removal,[],[f67]) ).

thf(f67,plain,
    ( ( $true
     != ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK6
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK4
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true != $true )
    | ~ spl8_2 ),
    inference(superposition,[],[f27,f58]) ).

thf(f27,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( X0 @ ( sK6 @ X0 ) @ ( sK4 @ X0 ) ) )
      | ( $true
       != ( sP0 @ X0 ) ) ),
    inference(cnf_transformation,[],[f19]) ).

thf(f63,plain,
    ( spl8_1
    | spl8_2
    | spl8_3 ),
    inference(avatar_split_clause,[],[f43,f60,f56,f52]) ).

thf(f43,plain,
    ( ( $true
      = ( sP1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( ( ^ [Y0: $i] : $true )
      = ( ^ [Y0: $i] : $false ) )
    | ( $true
      = ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    inference(equality_proxy_clausification,[],[f42]) ).

thf(f42,plain,
    ( ( $true
      = ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( $true
      = ( sP1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) ) ),
    inference(trivial_inequality_removal,[],[f41]) ).

thf(f41,plain,
    ( ( $true
      = ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) )
    | ( $true != $true )
    | ( $true
      = ( sP1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    inference(boolean_simplification,[],[f40]) ).

thf(f40,plain,
    ( ( $true
      = ( sP1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( $true
     != ( ( sK7
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        = ( sK7
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) )
    | ( $true
      = ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( $true
      = ( ( ^ [Y0: $i] : $false )
        = ( ^ [Y0: $i] : $true ) ) ) ),
    inference(beta_eta_normalization,[],[f31]) ).

thf(f31,plain,
    ( ( $true
      = ( sP1
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ( sK7
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
        @ ( sK7
          @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
     != $true )
    | ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
        @ ^ [Y0: $i] : $true
        @ ^ [Y0: $i] : $false )
      = $true )
    | ( $true
      = ( sP0
        @ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
    inference(primitive_instantiation,[],[f29]) ).

thf(f29,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
       != ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) ) )
      | ( $true
        = ( sP1 @ X0 ) )
      | ( $true
        = ( sP0 @ X0 ) )
      | ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) ) ),
    inference(cnf_transformation,[],[f22]) ).

thf(f22,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) )
      | ( $true
        = ( sP1 @ X0 ) )
      | ( $true
        = ( sP0 @ X0 ) )
      | ( $true
       != ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f20,f21]) ).

thf(f21,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X1: $i > $o] :
          ( ( X0 @ X1 @ X1 )
         != $true )
     => ( $true
       != ( X0 @ ( sK7 @ X0 ) @ ( sK7 @ X0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f20,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) )
      | ( $true
        = ( sP1 @ X0 ) )
      | ( $true
        = ( sP0 @ X0 ) )
      | ? [X1: $i > $o] :
          ( ( X0 @ X1 @ X1 )
         != $true ) ),
    inference(rectify,[],[f11]) ).

thf(f11,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) )
      | ( $true
        = ( sP1 @ X0 ) )
      | ( $true
        = ( sP0 @ X0 ) )
      | ? [X3: $i > $o] :
          ( $true
         != ( X0 @ X3 @ X3 ) ) ),
    inference(definition_folding,[],[f8,f10,f9]) ).

thf(f8,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) )
      | ? [X2: $i > $o,X1: $i > $o] :
          ( ( X1 != X2 )
          & ( $true
            = ( X0 @ X2 @ X1 ) )
          & ( ( X0 @ X1 @ X2 )
            = $true ) )
      | ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
          ( ( $true
            = ( X0 @ X6 @ X5 ) )
          & ( $true
           != ( X0 @ X6 @ X4 ) )
          & ( ( X0 @ X5 @ X4 )
            = $true ) )
      | ? [X3: $i > $o] :
          ( $true
         != ( X0 @ X3 @ X3 ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ? [X3: $i > $o] :
          ( $true
         != ( X0 @ X3 @ X3 ) )
      | ( $true
        = ( X0
          @ ^ [Y0: $i] : $true
          @ ^ [Y0: $i] : $false ) )
      | ? [X2: $i > $o,X1: $i > $o] :
          ( ( X1 != X2 )
          & ( ( X0 @ X1 @ X2 )
            = $true )
          & ( $true
            = ( X0 @ X2 @ X1 ) ) )
      | ? [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
          ( ( $true
           != ( X0 @ X6 @ X4 ) )
          & ( ( X0 @ X5 @ X4 )
            = $true )
          & ( $true
            = ( X0 @ X6 @ X5 ) ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ! [X3: $i > $o] :
            ( $true
            = ( X0 @ X3 @ X3 ) )
        & ( $true
         != ( X0
            @ ^ [Y0: $i] : $true
            @ ^ [Y0: $i] : $false ) )
        & ! [X2: $i > $o,X1: $i > $o] :
            ( ( ( ( X0 @ X1 @ X2 )
                = $true )
              & ( $true
                = ( X0 @ X2 @ X1 ) ) )
           => ( X1 = X2 ) )
        & ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
            ( ( ( ( X0 @ X5 @ X4 )
                = $true )
              & ( $true
                = ( X0 @ X6 @ X5 ) ) )
           => ( $true
              = ( X0 @ X6 @ X4 ) ) ) ),
    inference(flattening,[],[f5]) ).

thf(f5,plain,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ! [X2: $i > $o,X1: $i > $o] :
            ( ( ( ( X0 @ X1 @ X2 )
                = $true )
              & ( $true
                = ( X0 @ X2 @ X1 ) ) )
           => ( X1 = X2 ) )
        & ! [X3: $i > $o] :
            ( $true
            = ( X0 @ X3 @ X3 ) )
        & ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
            ( ( ( ( X0 @ X5 @ X4 )
                = $true )
              & ( $true
                = ( X0 @ X6 @ X5 ) ) )
           => ( $true
              = ( X0 @ X6 @ X4 ) ) )
        & ( $true
         != ( X0
            @ ^ [Y0: $i] : $true
            @ ^ [Y0: $i] : $false ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ! [X1: $i > $o,X2: $i > $o] :
            ( ( ( X0 @ X2 @ X1 )
              & ( X0 @ X1 @ X2 ) )
           => ( X1 = X2 ) )
        & ! [X3: $i > $o] : ( X0 @ X3 @ X3 )
        & ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
            ( ( ( X0 @ X5 @ X4 )
              & ( X0 @ X6 @ X5 ) )
           => ( X0 @ X6 @ X4 ) )
        & ~ ( X0
            @ ^ [X7: $i] : $true
            @ ^ [X8: $i] : $false ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
        ( ! [X5: $i > $o,X4: $i > $o] :
            ( ( ( X0 @ X4 @ X5 )
              & ( X0 @ X5 @ X4 ) )
           => ( X4 = X5 ) )
        & ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
        & ! [X3: $i > $o,X2: $i > $o,X1: $i > $o] :
            ( ( ( X0 @ X2 @ X3 )
              & ( X0 @ X1 @ X2 ) )
           => ( X0 @ X1 @ X3 ) )
        & ~ ( X0
            @ ^ [X1: $i] : $true
            @ ^ [X1: $i] : $false ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
      ( ! [X5: $i > $o,X4: $i > $o] :
          ( ( ( X0 @ X4 @ X5 )
            & ( X0 @ X5 @ X4 ) )
         => ( X4 = X5 ) )
      & ! [X1: $i > $o] : ( X0 @ X1 @ X1 )
      & ! [X3: $i > $o,X2: $i > $o,X1: $i > $o] :
          ( ( ( X0 @ X2 @ X3 )
            & ( X0 @ X1 @ X2 ) )
         => ( X0 @ X1 @ X3 ) )
      & ~ ( X0
          @ ^ [X1: $i] : $true
          @ ^ [X1: $i] : $false ) ),
    file('/export/starexec/sandbox2/tmp/tmp.MRPBNrCvvy/Vampire---4.8_15918',cTHM120H_pme) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEV087^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 12:17:29 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TH0_THM_EQU_NAR problem
% 0.15/0.36  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.MRPBNrCvvy/Vampire---4.8_15918
% 0.15/0.39  % (16111)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39  % (16113)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.39  % (16110)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39  % (16107)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.39  % (16109)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 Vampire---4 for (2999ds/27Mi)
% 0.15/0.39  % (16108)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 Vampire---4 for (2999ds/4Mi)
% 0.15/0.39  % (16112)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.39  % (16111)Instruction limit reached!
% 0.15/0.39  % (16111)------------------------------
% 0.15/0.39  % (16111)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (16111)Termination reason: Unknown
% 0.15/0.39  % (16111)Termination phase: Property scanning
% 0.15/0.39  
% 0.15/0.39  % (16111)Memory used [KB]: 895
% 0.15/0.39  % (16111)Time elapsed: 0.004 s
% 0.15/0.39  % (16111)Instructions burned: 2 (million)
% 0.15/0.39  % (16111)------------------------------
% 0.15/0.39  % (16111)------------------------------
% 0.15/0.39  % (16114)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.39  % (16110)Instruction limit reached!
% 0.15/0.39  % (16110)------------------------------
% 0.15/0.39  % (16110)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (16110)Termination reason: Unknown
% 0.15/0.39  % (16110)Termination phase: Saturation
% 0.15/0.39  
% 0.15/0.39  % (16110)Memory used [KB]: 5500
% 0.15/0.39  % (16110)Time elapsed: 0.004 s
% 0.15/0.39  % (16110)Instructions burned: 2 (million)
% 0.15/0.39  % (16110)------------------------------
% 0.15/0.39  % (16110)------------------------------
% 0.15/0.40  % (16108)Instruction limit reached!
% 0.15/0.40  % (16108)------------------------------
% 0.15/0.40  % (16108)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40  % (16108)Termination reason: Unknown
% 0.15/0.40  % (16108)Termination phase: Saturation
% 0.15/0.40  
% 0.15/0.40  % (16108)Memory used [KB]: 5500
% 0.15/0.40  % (16108)Time elapsed: 0.006 s
% 0.15/0.40  % (16108)Instructions burned: 4 (million)
% 0.15/0.40  % (16108)------------------------------
% 0.15/0.40  % (16108)------------------------------
% 0.22/0.40  % (16114)Instruction limit reached!
% 0.22/0.40  % (16114)------------------------------
% 0.22/0.40  % (16114)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (16114)Termination reason: Unknown
% 0.22/0.40  % (16114)Termination phase: Saturation
% 0.22/0.40  
% 0.22/0.40  % (16114)Memory used [KB]: 5500
% 0.22/0.40  % (16114)Time elapsed: 0.006 s
% 0.22/0.40  % (16114)Instructions burned: 3 (million)
% 0.22/0.40  % (16114)------------------------------
% 0.22/0.40  % (16114)------------------------------
% 0.22/0.40  % (16109)Refutation not found, incomplete strategy
% 0.22/0.40  % (16109)------------------------------
% 0.22/0.40  % (16109)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (16109)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.40  
% 0.22/0.40  
% 0.22/0.40  % (16109)Memory used [KB]: 5500
% 0.22/0.40  % (16109)Time elapsed: 0.007 s
% 0.22/0.40  % (16109)Instructions burned: 5 (million)
% 0.22/0.40  % (16109)------------------------------
% 0.22/0.40  % (16109)------------------------------
% 0.22/0.40  % (16113)Instruction limit reached!
% 0.22/0.40  % (16113)------------------------------
% 0.22/0.40  % (16113)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (16113)Termination reason: Unknown
% 0.22/0.40  % (16113)Termination phase: Saturation
% 0.22/0.40  
% 0.22/0.40  % (16113)Memory used [KB]: 5628
% 0.22/0.40  % (16113)Time elapsed: 0.013 s
% 0.22/0.40  % (16113)Instructions burned: 18 (million)
% 0.22/0.40  % (16113)------------------------------
% 0.22/0.40  % (16113)------------------------------
% 0.22/0.41  % (16117)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.22/0.41  % (16112)Refutation not found, incomplete strategy
% 0.22/0.41  % (16112)------------------------------
% 0.22/0.41  % (16112)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41  % (16112)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.41  
% 0.22/0.41  
% 0.22/0.41  % (16112)Memory used [KB]: 5628
% 0.22/0.41  % (16112)Time elapsed: 0.020 s
% 0.22/0.41  % (16112)Instructions burned: 26 (million)
% 0.22/0.41  % (16112)------------------------------
% 0.22/0.41  % (16112)------------------------------
% 0.22/0.41  % (16120)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.41  % (16118)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.22/0.41  % (16122)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.42  % (16120)Instruction limit reached!
% 0.22/0.42  % (16120)------------------------------
% 0.22/0.42  % (16120)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42  % (16120)Termination reason: Unknown
% 0.22/0.42  % (16120)Termination phase: Saturation
% 0.22/0.42  
% 0.22/0.42  % (16120)Memory used [KB]: 5500
% 0.22/0.42  % (16120)Time elapsed: 0.004 s
% 0.22/0.42  % (16120)Instructions burned: 4 (million)
% 0.22/0.42  % (16120)------------------------------
% 0.22/0.42  % (16120)------------------------------
% 0.22/0.42  % (16121)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.22/0.42  % (16123)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.22/0.42  % (16122)Instruction limit reached!
% 0.22/0.42  % (16122)------------------------------
% 0.22/0.42  % (16122)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42  % (16122)Termination reason: Unknown
% 0.22/0.42  % (16122)Termination phase: Saturation
% 0.22/0.42  
% 0.22/0.42  % (16122)Memory used [KB]: 1023
% 0.22/0.42  % (16122)Time elapsed: 0.006 s
% 0.22/0.42  % (16122)Instructions burned: 7 (million)
% 0.22/0.42  % (16122)------------------------------
% 0.22/0.42  % (16122)------------------------------
% 0.22/0.42  % (16118)First to succeed.
% 0.22/0.42  % (16118)Refutation found. Thanks to Tanya!
% 0.22/0.42  % SZS status Theorem for Vampire---4
% 0.22/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.42  % (16118)------------------------------
% 0.22/0.42  % (16118)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42  % (16118)Termination reason: Refutation
% 0.22/0.42  
% 0.22/0.42  % (16118)Memory used [KB]: 5628
% 0.22/0.42  % (16118)Time elapsed: 0.010 s
% 0.22/0.42  % (16118)Instructions burned: 8 (million)
% 0.22/0.42  % (16118)------------------------------
% 0.22/0.42  % (16118)------------------------------
% 0.22/0.42  % (16104)Success in time 0.049 s
% 0.22/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------