%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM653^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -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  : 600s
% DateTime : Mon Jul 18 13:54:40 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_nat,type,
    nat: $tType ).

thf(ty_y,type,
    y: nat ).

thf(ty_less,type,
    less: nat > nat > $o ).

thf(ty_more,type,
    more: nat > nat > $o ).

thf(ty_x,type,
    x: nat ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: nat,X2: nat] :
        ~ ( ( ( X1 = X2 )
           => ~ ( more @ X1 @ X2 ) )
         => ( ( ( more @ X1 @ X2 )
             => ~ ( less @ X1 @ X2 ) )
           => ~ ( ( less @ X1 @ X2 )
               => ( X1 != X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( y = y )
     => ~ ( more @ y @ y ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( more @ x @ y )
     => ~ ( less @ x @ y ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( y = y ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( x = y ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( more @ y @ y ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( more @ x @ y ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: nat] :
        ~ ( ( ( y = X1 )
           => ~ ( more @ y @ X1 ) )
         => ( ( ( more @ y @ X1 )
             => ~ ( less @ y @ X1 ) )
           => ~ ( ( less @ y @ X1 )
               => ( y != X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP3
     => ~ ( ( less @ x @ y )
         => ~ sP5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP2
     => ( ( sP6
         => ~ ( less @ y @ y ) )
       => ~ ( ( less @ y @ y )
           => ~ sP4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( less @ x @ y ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( sP5
       => ~ sP7 )
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: nat] :
        ~ ( ( ( x = X1 )
           => ~ ( more @ x @ X1 ) )
         => ( ( ( more @ x @ X1 )
             => ~ ( less @ x @ X1 ) )
           => ~ ( ( less @ x @ X1 )
               => ( x != X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(satz10d,conjecture,
    ~ sP7 ).

thf(h0,negated_conjecture,
    sP7,
    inference(assume_negation,[status(cth)],[satz10d]) ).

thf(h1,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP3
    | ~ sP7
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP9
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP12
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP13
    | ~ sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP1
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(satz10b,axiom,
    sP1 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1,satz10b,h0]) ).

thf(7,plain,
    ( ~ sP7
    | sP6
    | ~ sP5
    | ~ sP4 ),
    inference(mating_rule,[status(thm)],]) ).

thf(8,plain,
    sP4,
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP2
    | ~ sP4
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP10
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP8
    | ~ sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP1
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h0])],[7,8,9,10,11,12,h2,satz10b,h0]) ).

thf(l,axiom,
    ( ~ sP11
   => sP5 ) ).

thf(14,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[l,6,13,h1,h2]) ).

thf(0,theorem,
    ~ sP7,
    inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : NUM653^1 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jul  5 20:07:18 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % Mode: mode213
% 0.13/0.38  % Inferences: 93
% 0.13/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------