TSTP Solution File: NUN025^3 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUN025^3 : TPTP v8.1.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -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  : 600s
% DateTime : Mon Jul 18 16:37:46 EDT 2022

% Result   : Theorem 4.69s 4.93s
% Output   : Proof 4.77s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_zero,type,
    zero: $i ).

thf(ty_h,type,
    h: $i > $i ).

thf(ty_s,type,
    s: $i > $i ).

thf(ty_ite,type,
    ite: $o > $i > $i > $i ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( ~ ( ~ ( ! [X1: $o,X2: $i,X3: $i] :
                      ( X1
                     => ( ( ite @ X1 @ X2 @ X3 )
                        = X2 ) )
                 => ~ ! [X1: $o,X2: $i,X3: $i] :
                        ( ~ X1
                       => ( ( ite @ X1 @ X2 @ X3 )
                          = X3 ) ) )
             => ~ ! [X1: $i] :
                    ( ( s @ X1 )
                   != zero ) )
         => ~ ! [X1: $i] :
                ( ( s @ X1 )
               != X1 ) )
     => ~ ! [X1: $i] :
            ( ( h @ X1 )
            = ( ite @ ( X1 = zero ) @ ( s @ zero )
              @ ( ite
                @ ( X1
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ite
        @ ( ( s @ ( s @ zero ) )
          = zero )
        @ ( s @ zero )
        @ ( s @ zero ) )
      = ( s @ zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i,X2: $i > $o] :
        ( ( X2 @ X1 )
       => ! [X3: $i] :
            ( ( X1 = X3 )
           => ( X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $o,X2: $i,X3: $i] :
        ( X1
       => ( ( ite @ X1 @ X2 @ X3 )
          = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: $i] :
        ( ( ( s @ zero )
          = ( s @ zero ) )
       => ( ( ite
            @ ( ( s @ zero )
              = ( s @ zero ) )
            @ X1
            @ X2 )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ( ( ( s @ zero )
          = ( s @ zero ) )
       => ( ( ite
            @ ( ( s @ zero )
              = ( s @ zero ) )
            @ zero
            @ X1 )
          = zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( ( ite @ ( zero = zero ) @ ( s @ zero )
          @ ( ite
            @ ( zero
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) ) )
        = ( ite
          @ ( zero
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) )
     => ( ~ ( ( ( ite
                @ ( zero
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) )
              = ( s @ zero ) )
           => ( ( ite
                @ ( ( s @ zero )
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) )
             != zero ) )
       => ( ( h @ ( s @ ( s @ zero ) ) )
         != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( ( s @ ( s @ zero ) )
         != ( s @ zero ) )
       => ( ( ite
            @ ( ( s @ ( s @ zero ) )
              = ( s @ zero ) )
            @ zero
            @ X1 )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( zero = zero )
     => ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ ( s @ zero ) )
        = ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( ( s @ zero )
        = ( s @ ( s @ zero ) ) )
     => ( ( s @ ( s @ zero ) )
        = ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ~ ( ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ ( s @ zero ) )
            = ( s @ zero ) )
         => ( ( ite
              @ ( ( s @ zero )
                = zero )
              @ ( s @ zero )
              @ ( ite
                @ ( ( s @ zero )
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) )
           != zero ) )
     => ( ( h @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ( ( s @ zero )
          = X1 )
       => ( X1
          = ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( h @ ( s @ ( s @ zero ) ) )
      = ( ite
        @ ( ( s @ ( s @ zero ) )
          = zero )
        @ ( s @ zero )
        @ ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( ( s @ zero )
       != zero )
     => ( ( ite
          @ ( ( s @ zero )
            = zero )
          @ ( s @ zero )
          @ ( ite
            @ ( ( s @ zero )
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) ) )
        = ( ite
          @ ( ( s @ zero )
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( sP13
     => ! [X1: $i] :
          ( ( ( ite
              @ ( ( s @ ( s @ zero ) )
                = zero )
              @ ( s @ zero )
              @ ( s @ zero ) )
            = X1 )
         => ( ( h @ ( s @ ( s @ zero ) ) )
            = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP2
     => ( ( h @ ( s @ ( s @ zero ) ) )
        = ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: $i,X2: $i] :
        ( ( zero
         != ( s @ zero ) )
       => ( ( ite
            @ ( zero
              = ( s @ zero ) )
            @ X1
            @ X2 )
          = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i > $o] :
        ( ( X1 @ ( h @ zero ) )
       => ! [X2: $i] :
            ( ( ( h @ zero )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ( ite
        @ ( ( s @ ( s @ zero ) )
          = ( s @ zero ) )
        @ zero
        @ ( s @ zero ) )
      = ( s @ zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ~ ( sP4
         => ~ ! [X1: $o,X2: $i,X3: $i] :
                ( ~ X1
               => ( ( ite @ X1 @ X2 @ X3 )
                  = X3 ) ) )
     => ~ ! [X1: $i] :
            ( ( s @ X1 )
           != zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( ( h @ ( s @ zero ) )
      = ( ite
        @ ( ( s @ zero )
          = zero )
        @ ( s @ zero )
        @ ( ite
          @ ( ( s @ zero )
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ( ~ ( ( ( h @ zero )
              = ( s @ zero ) )
           => ( ( ite
                @ ( ( s @ zero )
                  = zero )
                @ ( s @ zero )
                @ ( ite
                  @ ( ( s @ zero )
                    = ( s @ zero ) )
                  @ zero
                  @ ( s @ zero ) ) )
             != zero ) )
       => ( ( h @ ( s @ ( s @ zero ) ) )
         != ( s @ zero ) ) )
     => ! [X1: $i] :
          ( ( ( ite
              @ ( ( s @ zero )
                = zero )
              @ ( s @ zero )
              @ ( ite
                @ ( ( s @ zero )
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) )
            = X1 )
         => ( ~ ( ( ( h @ zero )
                  = ( s @ zero ) )
               => ( X1 != zero ) )
           => ( ( h @ ( s @ ( s @ zero ) ) )
             != ( s @ zero ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: $i,X2: $i] :
        ( ( ( s @ zero )
         != zero )
       => ( ( ite
            @ ( ( s @ zero )
              = zero )
            @ X1
            @ X2 )
          = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ( ite
        @ ( zero
          = ( s @ zero ) )
        @ zero
        @ ( s @ zero ) )
      = ( s @ zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: $i] :
        ( ( ( ite
            @ ( ( s @ zero )
              = zero )
            @ ( s @ zero )
            @ ( ite
              @ ( ( s @ zero )
                = ( s @ zero ) )
              @ zero
              @ ( s @ zero ) ) )
          = X1 )
       => ( ~ ( ( ( h @ zero )
                = ( s @ zero ) )
             => ( X1 != zero ) )
         => ( ( h @ ( s @ ( s @ zero ) ) )
           != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( ( ( s @ ( s @ zero ) )
       != zero )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ( s @ zero )
      = ( s @ ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ! [X1: $i] :
        ( ( ( h @ ( s @ zero ) )
          = X1 )
       => ( ~ ( ( ( h @ zero )
                = ( s @ zero ) )
             => ( X1 != zero ) )
         => ( ( h @ ( s @ ( s @ zero ) ) )
           != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( ~ ( ( ( h @ zero )
            = ( s @ zero ) )
         => ( ( ite
              @ ( ( s @ zero )
                = zero )
              @ ( s @ zero )
              @ ( ite
                @ ( ( s @ zero )
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) )
           != zero ) )
     => ( ( h @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( sP19
     => sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ( h @ zero )
      = ( ite @ ( zero = zero ) @ ( s @ zero )
        @ ( ite
          @ ( zero
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ~ ( ( ( h @ zero )
            = ( s @ zero ) )
         => ( ( h @ ( s @ zero ) )
           != zero ) )
     => ( ( h @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( ( zero
       != ( s @ zero ) )
     => sP24 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: $i] :
        ( ( zero != zero )
       => ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ X1 )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( ( ite @ ( zero = zero ) @ ( s @ zero )
        @ ( ite
          @ ( zero
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) )
      = ( ite
        @ ( zero
          = ( s @ zero ) )
        @ zero
        @ ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ! [X1: $i] :
        ( ( zero = zero )
       => ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ X1 )
          = ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( sP4
     => ~ ! [X1: $o,X2: $i,X3: $i] :
            ( ~ X1
           => ( ( ite @ X1 @ X2 @ X3 )
              = X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( ( ( ite
          @ ( ( s @ zero )
            = zero )
          @ ( s @ zero )
          @ ( ite
            @ ( ( s @ zero )
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) ) )
        = ( ite
          @ ( ( s @ zero )
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) )
     => ( ( ( s @ zero )
          = ( s @ zero ) )
       => ( ( ite
            @ ( ( s @ zero )
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) )
         != zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ! [X1: $i] :
        ( ( ( ite @ ( zero = zero ) @ ( s @ zero ) @ ( s @ zero ) )
          = X1 )
       => ( ~ ( ( X1
                = ( s @ zero ) )
             => ( ( ite
                  @ ( ( s @ zero )
                    = zero )
                  @ ( s @ zero )
                  @ ( ite
                    @ ( ( s @ zero )
                      = ( s @ zero ) )
                    @ zero
                    @ ( s @ zero ) ) )
               != zero ) )
         => ( ( h @ ( s @ ( s @ zero ) ) )
           != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( sP21
     => sP29 ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ! [X1: $i > $o] :
        ( ( X1
          @ ( ite
            @ ( ( s @ zero )
              = zero )
            @ ( s @ zero )
            @ ( ite
              @ ( ( s @ zero )
                = ( s @ zero ) )
              @ zero
              @ ( s @ zero ) ) ) )
       => ! [X2: $i] :
            ( ( ( ite
                @ ( ( s @ zero )
                  = zero )
                @ ( s @ zero )
                @ ( ite
                  @ ( ( s @ zero )
                    = ( s @ zero ) )
                  @ zero
                  @ ( s @ zero ) ) )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ( sP24
     => sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( zero = zero ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ! [X1: $i] :
        ( ( ( ite
            @ ( zero
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) )
          = X1 )
       => ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ X1 )
                = ( s @ zero ) )
             => ( ( ite
                  @ ( ( s @ zero )
                    = zero )
                  @ ( s @ zero )
                  @ ( ite
                    @ ( ( s @ zero )
                      = ( s @ zero ) )
                    @ zero
                    @ ( s @ zero ) ) )
               != zero ) )
         => ( ( h @ ( s @ ( s @ zero ) ) )
           != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( ~ sP44
     => sP35 ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ( zero
      = ( s @ zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( ( s @ zero )
      = zero ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ( ( ( s @ zero )
        = ( s @ zero ) )
     => ( ( ite
          @ ( ( s @ zero )
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) )
        = zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
            = ( s @ zero ) )
         => ( ( ite @ sP48 @ ( s @ zero )
              @ ( ite
                @ ( ( s @ zero )
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) ) )
           != zero ) )
     => ( ( h @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ( ( ( s @ ( s @ zero ) )
       != ( s @ zero ) )
     => sP19 ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ! [X1: $i > $o] :
        ( ( X1 @ ( h @ ( s @ zero ) ) )
       => ! [X2: $i] :
            ( ( ( h @ ( s @ zero ) )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( sP50
     => sP45 ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ( ( ( ite @ sP48 @ ( s @ zero )
          @ ( ite
            @ ( ( s @ zero )
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) ) )
        = ( ite
          @ ( ( s @ zero )
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) ) )
     => ( ~ ( ( ( h @ zero )
              = ( s @ zero ) )
           => ( ( ite
                @ ( ( s @ zero )
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) )
             != zero ) )
       => ( ( h @ ( s @ ( s @ zero ) ) )
         != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ( sP31
     => ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
              = ( s @ zero ) )
           => ( ( ite
                @ ( ( s @ zero )
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) )
             != zero ) )
       => ( ( h @ ( s @ ( s @ zero ) ) )
         != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ( ( s @ ( s @ zero ) )
      = ( s @ zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ( ( ( ite @ sP44 @ ( s @ zero ) @ ( s @ zero ) )
        = ( s @ zero ) )
     => ( ~ ( ( ( s @ zero )
              = ( s @ zero ) )
           => ( ( ite @ sP48 @ ( s @ zero )
                @ ( ite
                  @ ( ( s @ zero )
                    = ( s @ zero ) )
                  @ zero
                  @ ( s @ zero ) ) )
             != zero ) )
       => ( ( h @ ( s @ ( s @ zero ) ) )
         != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ! [X1: $i > $o] :
        ( ( X1 @ ( ite @ sP56 @ zero @ ( s @ zero ) ) )
       => ! [X2: $i] :
            ( ( ( ite @ sP56 @ zero @ ( s @ zero ) )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
    ( sP59
  <=> ! [X1: $i] :
        ( ( ( ite
            @ ( ( s @ ( s @ zero ) )
              = zero )
            @ ( s @ zero )
            @ ( s @ zero ) )
          = X1 )
       => ( ( h @ ( s @ ( s @ zero ) ) )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
    ( sP60
  <=> ( ~ ( sP24
         => ( ( ite
              @ ( ( s @ zero )
                = ( s @ zero ) )
              @ zero
              @ ( s @ zero ) )
           != zero ) )
     => ( ( h @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
    ( sP61
  <=> ! [X1: $i > $i] :
        ( ~ ( ( ( X1 @ zero )
              = ( s @ zero ) )
           => ( ( X1 @ ( s @ zero ) )
             != zero ) )
       => ( ( X1 @ ( s @ ( s @ zero ) ) )
         != ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
    ( sP62
  <=> ! [X1: $o,X2: $i,X3: $i] :
        ( ~ X1
       => ( ( ite @ X1 @ X2 @ X3 )
          = X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
    ( sP63
  <=> ! [X1: $i > $o] :
        ( ( X1 @ ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) ) )
       => ! [X2: $i] :
            ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
    ( sP64
  <=> ( ~ sP1
     => ~ sP61 ) ),
    introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
    ( sP65
  <=> ( sP24
     => ( ( ite
          @ ( ( s @ zero )
            = ( s @ zero ) )
          @ zero
          @ ( s @ zero ) )
       != zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
    ( sP66
  <=> ( ( ( s @ zero )
        = ( s @ zero ) )
     => ( ( ite @ sP48 @ ( s @ zero )
          @ ( ite
            @ ( ( s @ zero )
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) ) )
       != zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
    ( sP67
  <=> ( ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
              = ( s @ zero ) )
           => ( ( ite
                @ ( ( s @ zero )
                  = ( s @ zero ) )
                @ zero
                @ ( s @ zero ) )
             != zero ) )
       => ( ( h @ ( s @ ( s @ zero ) ) )
         != ( s @ zero ) ) )
     => ! [X1: $i] :
          ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
            = X1 )
         => ( ~ ( ( X1
                  = ( s @ zero ) )
               => ( ( ite
                    @ ( ( s @ zero )
                      = ( s @ zero ) )
                    @ zero
                    @ ( s @ zero ) )
                 != zero ) )
           => ( ( h @ ( s @ ( s @ zero ) ) )
             != ( s @ zero ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
    ( sP68
  <=> ( sP31
     => sP50 ) ),
    introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
    ( sP69
  <=> ! [X1: $i,X2: $i] :
        ( ~ sP44
       => ( ( ite @ sP44 @ X1 @ X2 )
          = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
    ( sP70
  <=> ! [X1: $i] :
        ( ( ( h @ zero )
          = X1 )
       => ( ~ ( ( X1
                = ( s @ zero ) )
             => ( ( ite @ sP48 @ ( s @ zero )
                  @ ( ite
                    @ ( ( s @ zero )
                      = ( s @ zero ) )
                    @ zero
                    @ ( s @ zero ) ) )
               != zero ) )
         => ( ( h @ ( s @ ( s @ zero ) ) )
           != ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
    ( sP71
  <=> ( ( s @ zero )
      = ( s @ zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
    ( sP72
  <=> ( sP29
     => sP70 ) ),
    introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
    ( sP73
  <=> ( ( h @ ( s @ ( s @ zero ) ) )
      = ( s @ zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
    ( sP74
  <=> ( ~ ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
            = ( s @ zero ) )
         => ( ( ite @ sP71 @ zero @ ( s @ zero ) )
           != zero ) )
     => ~ sP73 ) ),
    introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
    ( sP75
  <=> ( sP11
     => sP39 ) ),
    introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(sP76,plain,
    ( sP76
  <=> ( ( h @ ( s @ ( s @ zero ) ) )
      = ( ite
        @ ( ( s @ ( s @ zero ) )
          = zero )
        @ ( s @ zero )
        @ ( ite @ sP56 @ zero @ ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP76])]) ).

thf(sP77,plain,
    ( sP77
  <=> ( ~ ( ( ( h @ zero )
            = ( s @ zero ) )
         => ( ( ite @ sP71 @ zero @ ( s @ zero ) )
           != zero ) )
     => ~ sP73 ) ),
    introduced(definition,[new_symbols(definition,[sP77])]) ).

thf(sP78,plain,
    ( sP78
  <=> ! [X1: $i > $o] :
        ( ( X1
          @ ( ite
            @ ( ( s @ ( s @ zero ) )
              = zero )
            @ ( s @ zero )
            @ ( s @ zero ) ) )
       => ! [X2: $i] :
            ( ( ( ite
                @ ( ( s @ ( s @ zero ) )
                  = zero )
                @ ( s @ zero )
                @ ( s @ zero ) )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP78])]) ).

thf(sP79,plain,
    ( sP79
  <=> ( ( ite @ sP44 @ ( s @ zero ) @ ( s @ zero ) )
      = ( s @ zero ) ) ),
    introduced(definition,[new_symbols(definition,[sP79])]) ).

thf(sP80,plain,
    ( sP80
  <=> ! [X1: $i] :
        ( ( s @ X1 )
       != zero ) ),
    introduced(definition,[new_symbols(definition,[sP80])]) ).

thf(sP81,plain,
    ( sP81
  <=> ! [X1: $i,X2: $i] :
        ( ( ( s @ ( s @ zero ) )
         != zero )
       => ( ( ite
            @ ( ( s @ ( s @ zero ) )
              = zero )
            @ X1
            @ X2 )
          = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP81])]) ).

thf(sP82,plain,
    ( sP82
  <=> ! [X1: $i] :
        ( ( h @ X1 )
        = ( ite @ ( X1 = zero ) @ ( s @ zero )
          @ ( ite
            @ ( X1
              = ( s @ zero ) )
            @ zero
            @ ( s @ zero ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP82])]) ).

thf(sP83,plain,
    ( sP83
  <=> ! [X1: $i,X2: $i] :
        ( ~ sP56
       => ( ( ite @ sP56 @ X1 @ X2 )
          = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP83])]) ).

thf(sP84,plain,
    ( sP84
  <=> ! [X1: $i] :
        ( ( ( ite @ sP44 @ ( s @ zero ) @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
          = X1 )
       => ( ~ ( ( X1
                = ( s @ zero ) )
             => ( ( ite @ sP71 @ zero @ ( s @ zero ) )
               != zero ) )
         => ~ sP73 ) ) ),
    introduced(definition,[new_symbols(definition,[sP84])]) ).

thf(sP85,plain,
    ( sP85
  <=> ! [X1: $i] :
        ( ( ( s @ ( s @ zero ) )
         != zero )
       => ( ( ite
            @ ( ( s @ ( s @ zero ) )
              = zero )
            @ ( s @ zero )
            @ X1 )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP85])]) ).

thf(sP86,plain,
    ( sP86
  <=> ( ~ sP20
     => ~ ! [X1: $i] :
            ( ( s @ X1 )
           != X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP86])]) ).

thf(sP87,plain,
    ( sP87
  <=> ( sP32
     => sP28 ) ),
    introduced(definition,[new_symbols(definition,[sP87])]) ).

thf(sP88,plain,
    ( sP88
  <=> ( ( ite @ sP71 @ zero @ ( s @ zero ) )
      = zero ) ),
    introduced(definition,[new_symbols(definition,[sP88])]) ).

thf(sP89,plain,
    ( sP89
  <=> ! [X1: $i] :
        ( ( ( h @ zero )
          = X1 )
       => ( ~ ( ( X1
                = ( s @ zero ) )
             => ~ sP88 )
         => ~ sP73 ) ) ),
    introduced(definition,[new_symbols(definition,[sP89])]) ).

thf(sP90,plain,
    ( sP90
  <=> ! [X1: $i] :
        ( ( ( ite @ sP48 @ ( s @ zero ) @ ( ite @ sP71 @ zero @ ( s @ zero ) ) )
          = X1 )
       => ( sP71
         => ( X1 != zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP90])]) ).

thf(sP91,plain,
    ( sP91
  <=> ( ( ite @ sP48 @ ( s @ zero ) @ ( ite @ sP71 @ zero @ ( s @ zero ) ) )
      = ( ite @ sP71 @ zero @ ( s @ zero ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP91])]) ).

thf(sP92,plain,
    ( sP92
  <=> ! [X1: $i] :
        ( ~ sP48
       => ( ( ite @ sP48 @ ( s @ zero ) @ X1 )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP92])]) ).

thf(sP93,plain,
    ( sP93
  <=> ( sP77
     => sP89 ) ),
    introduced(definition,[new_symbols(definition,[sP93])]) ).

thf(sP94,plain,
    ( sP94
  <=> ! [X1: $i,X2: $i] :
        ( sP44
       => ( ( ite @ sP44 @ X1 @ X2 )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP94])]) ).

thf(sP95,plain,
    ( sP95
  <=> ! [X1: $i] :
        ( ( s @ X1 )
       != X1 ) ),
    introduced(definition,[new_symbols(definition,[sP95])]) ).

thf(sP96,plain,
    ( sP96
  <=> ( ( s @ ( s @ zero ) )
      = zero ) ),
    introduced(definition,[new_symbols(definition,[sP96])]) ).

thf(sP97,plain,
    ( sP97
  <=> ( sP71
     => ~ sP88 ) ),
    introduced(definition,[new_symbols(definition,[sP97])]) ).

thf(sP98,plain,
    ( sP98
  <=> ! [X1: $i] :
        ( ~ sP47
       => ( ( ite @ sP47 @ zero @ X1 )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP98])]) ).

thf(sP99,plain,
    ( sP99
  <=> ( sP66
     => sP90 ) ),
    introduced(definition,[new_symbols(definition,[sP99])]) ).

thf(sP100,plain,
    ( sP100
  <=> ! [X1: $i > $o] :
        ( ( X1 @ ( ite @ sP44 @ ( s @ zero ) @ ( s @ zero ) ) )
       => ! [X2: $i] :
            ( ( ( ite @ sP44 @ ( s @ zero ) @ ( s @ zero ) )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP100])]) ).

thf(sP101,plain,
    ( sP101
  <=> ! [X1: $i] :
        ( ( ( ite @ sP56 @ zero @ ( s @ zero ) )
          = X1 )
       => ( ( h @ ( s @ ( s @ zero ) ) )
          = ( ite @ sP96 @ ( s @ zero ) @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP101])]) ).

thf(sP102,plain,
    ( sP102
  <=> ( sP76
     => sP101 ) ),
    introduced(definition,[new_symbols(definition,[sP102])]) ).

thf(sP103,plain,
    ( sP103
  <=> ! [X1: $i > $o] :
        ( ( X1 @ ( ite @ sP47 @ zero @ ( s @ zero ) ) )
       => ! [X2: $i] :
            ( ( ( ite @ sP47 @ zero @ ( s @ zero ) )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP103])]) ).

thf(sP104,plain,
    ( sP104
  <=> ( ~ sP66
     => ~ sP73 ) ),
    introduced(definition,[new_symbols(definition,[sP104])]) ).

thf(n10,conjecture,
    sP64 ).

thf(h0,negated_conjecture,
    ~ sP64,
    inference(assume_negation,[status(cth)],[n10]) ).

thf(1,plain,
    ( ~ sP4
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | sP49 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP49
    | ~ sP71
    | sP88 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP94 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP94
    | sP36 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP36
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP9
    | ~ sP44
    | sP79 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP38
    | ~ sP91
    | sP97 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP90
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP99
    | ~ sP66
    | sP90 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP42
    | sP99 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP65
    | ~ sP24
    | ~ sP88 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP97
    | ~ sP71
    | ~ sP88 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( sP27
    | ~ sP47 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP104
    | sP66
    | ~ sP73 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP60
    | sP65
    | ~ sP73 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP57
    | ~ sP79
    | sP104 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP39
    | sP57 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP75
    | ~ sP11
    | sP39 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP100
    | sP75 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP7
    | ~ sP35
    | sP60 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP84
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP67
    | ~ sP74
    | sP84 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP63
    | sP67 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP55
    | ~ sP31
    | sP74 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP89
    | sP55 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP93
    | ~ sP77
    | sP89 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP18
    | sP93 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP85
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP26
    | sP96
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP16
    | ~ sP2
    | sP73 ),
    inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP59
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP15
    | ~ sP13
    | sP59 ),
    inference(prop_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP78
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP3
    | sP78 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP3
    | sP100 ),
    inference(all_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP30
    | ~ sP19
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP101
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP102
    | ~ sP76
    | sP101 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP58
    | sP102 ),
    inference(all_rule,[status(thm)],]) ).

thf(42,plain,
    ( ~ sP54
    | ~ sP91
    | sP77 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( ~ sP25
    | sP54 ),
    inference(all_rule,[status(thm)],]) ).

thf(44,plain,
    ( ~ sP22
    | ~ sP29
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( ~ sP42
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(46,plain,
    ( ~ sP43
    | ~ sP24
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( ~ sP45
    | sP43 ),
    inference(all_rule,[status(thm)],]) ).

thf(48,plain,
    ( ~ sP53
    | ~ sP50
    | sP45 ),
    inference(prop_rule,[status(thm)],]) ).

thf(49,plain,
    ( ~ sP103
    | sP53 ),
    inference(all_rule,[status(thm)],]) ).

thf(50,plain,
    ( ~ sP62
    | sP83 ),
    inference(all_rule,[status(thm)],]) ).

thf(51,plain,
    ( ~ sP83
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(52,plain,
    ( ~ sP8
    | sP51 ),
    inference(all_rule,[status(thm)],]) ).

thf(53,plain,
    ( ~ sP51
    | sP56
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
    ( ~ sP3
    | sP58 ),
    inference(all_rule,[status(thm)],]) ).

thf(55,plain,
    ( ~ sP62
    | sP81 ),
    inference(all_rule,[status(thm)],]) ).

thf(56,plain,
    ( ~ sP81
    | sP85 ),
    inference(all_rule,[status(thm)],]) ).

thf(57,plain,
    ( ~ sP62
    | sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(58,plain,
    ( ~ sP23
    | sP92 ),
    inference(all_rule,[status(thm)],]) ).

thf(59,plain,
    ( ~ sP92
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(60,plain,
    ( ~ sP14
    | sP48
    | sP91 ),
    inference(prop_rule,[status(thm)],]) ).

thf(61,plain,
    ( ~ sP3
    | sP42 ),
    inference(all_rule,[status(thm)],]) ).

thf(62,plain,
    ( ~ sP62
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(63,plain,
    ( ~ sP17
    | sP98 ),
    inference(all_rule,[status(thm)],]) ).

thf(64,plain,
    ( ~ sP98
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(65,plain,
    ( ~ sP33
    | sP47
    | sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(66,plain,
    ( ~ sP3
    | sP103 ),
    inference(all_rule,[status(thm)],]) ).

thf(67,plain,
    ( ~ sP62
    | sP69 ),
    inference(all_rule,[status(thm)],]) ).

thf(68,plain,
    ( ~ sP69
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(69,plain,
    ( ~ sP34
    | sP46 ),
    inference(all_rule,[status(thm)],]) ).

thf(70,plain,
    ( ~ sP46
    | sP44
    | sP35 ),
    inference(prop_rule,[status(thm)],]) ).

thf(71,plain,
    ( ~ sP3
    | sP63 ),
    inference(all_rule,[status(thm)],]) ).

thf(72,plain,
    ( sP37
    | sP62 ),
    inference(prop_rule,[status(thm)],]) ).

thf(73,plain,
    ( sP37
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
    ( ~ sP68
    | ~ sP31
    | sP50 ),
    inference(prop_rule,[status(thm)],]) ).

thf(75,plain,
    ( ~ sP70
    | sP68 ),
    inference(all_rule,[status(thm)],]) ).

thf(76,plain,
    ( ~ sP72
    | ~ sP29
    | sP70 ),
    inference(prop_rule,[status(thm)],]) ).

thf(77,plain,
    ( ~ sP18
    | sP72 ),
    inference(all_rule,[status(thm)],]) ).

thf(78,plain,
    ( ~ sP41
    | ~ sP21
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(79,plain,
    ( ~ sP28
    | sP41 ),
    inference(all_rule,[status(thm)],]) ).

thf(80,plain,
    ( ~ sP87
    | ~ sP32
    | sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(81,plain,
    ( ~ sP52
    | sP87 ),
    inference(all_rule,[status(thm)],]) ).

thf(82,plain,
    ( ~ sP80
    | ~ sP96 ),
    inference(all_rule,[status(thm)],]) ).

thf(83,plain,
    ( sP20
    | sP80 ),
    inference(prop_rule,[status(thm)],]) ).

thf(84,plain,
    ( sP20
    | ~ sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(85,plain,
    ( ~ sP82
    | sP76 ),
    inference(all_rule,[status(thm)],]) ).

thf(86,plain,
    ( ~ sP10
    | ~ sP27
    | sP56 ),
    inference(prop_rule,[status(thm)],]) ).

thf(87,plain,
    ( ~ sP12
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(88,plain,
    ( ~ sP3
    | sP52 ),
    inference(all_rule,[status(thm)],]) ).

thf(89,plain,
    ( ~ sP3
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(90,plain,
    ( ~ sP61
    | sP32 ),
    inference(all_rule,[status(thm)],]) ).

thf(91,plain,
    sP71,
    inference(prop_rule,[status(thm)],]) ).

thf(92,plain,
    ( ~ sP82
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(93,plain,
    ( ~ sP95
    | ~ sP48 ),
    inference(all_rule,[status(thm)],]) ).

thf(94,plain,
    ( ~ sP82
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(95,plain,
    ( ~ sP95
    | ~ sP56 ),
    inference(all_rule,[status(thm)],]) ).

thf(96,plain,
    ( ~ sP40
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(97,plain,
    ( sP86
    | sP95 ),
    inference(prop_rule,[status(thm)],]) ).

thf(98,plain,
    ( sP86
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(99,plain,
    sP3,
    inference(eq_ind,[status(thm)],]) ).

thf(100,plain,
    sP40,
    inference(eq_sym,[status(thm)],]) ).

thf(101,plain,
    ( sP1
    | sP82 ),
    inference(prop_rule,[status(thm)],]) ).

thf(102,plain,
    ( sP1
    | ~ sP86 ),
    inference(prop_rule,[status(thm)],]) ).

thf(103,plain,
    ( sP64
    | sP61 ),
    inference(prop_rule,[status(thm)],]) ).

thf(104,plain,
    ( sP64
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(105,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,h0]) ).

thf(0,theorem,
    sP64,
    inference(contra,[status(thm),contra(discharge,[h0])],[105,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUN025^3 : TPTP v8.1.0. Released v6.4.0.
% 0.06/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jun  2 08:15:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 4.69/4.93  % SZS status Theorem
% 4.69/4.93  % Mode: mode506
% 4.69/4.93  % Inferences: 89811
% 4.69/4.93  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------