%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP225^1 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n021.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 : Sun Jul 17 00:29:46 EDT 2022

% Result   : Theorem 28.57s 28.57s
% Output   : Proof 28.57s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_suc,type,
    suc: nat > nat ).

thf(ty_na,type,
    na: nat ).

thf(ty_zero_zero_nat,type,
    zero_zero_nat: nat ).

thf(ty_ord_less_nat,type,
    ord_less_nat: nat > nat > $o ).

thf(ty_m,type,
    m: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( ( ( suc @ na )
        = zero_zero_nat )
     => ( zero_zero_nat
        = ( suc @ na ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: nat] :
        ( ( ( suc @ na )
          = X1 )
       => ( X1
          = ( suc @ na ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ! [X1: nat,X2: nat] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( zero_zero_nat
      = ( suc @ na ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( suc @ na )
      = zero_zero_nat ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: nat] :
        ( ( ord_less_nat @ zero_zero_nat @ X1 )
        = ( ~ ! [X2: nat] :
                ( X1
               != ( suc @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( m = zero_zero_nat ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: nat] :
        ( ( ( X1 != zero_zero_nat ) )
        = ( ord_less_nat @ zero_zero_nat @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( ~ sP9 )
      = ( ord_less_nat @ zero_zero_nat @ m ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ord_less_nat @ zero_zero_nat @ m ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP2
      = ( ~ ! [X1: nat] :
              ( zero_zero_nat
             != ( suc @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: nat] :
        ( zero_zero_nat
       != ( suc @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( m
      = ( suc @ na ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(conj_0,conjecture,
    sP12 ).

thf(h0,negated_conjecture,
    ~ sP12,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP14
    | ~ sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | sP7
    | ~ sP15
    | ~ sP4 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | ~ sP7
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP13
    | sP2
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP11
    | sP9
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP10
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP5
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP8
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    sP5,
    inference(eq_sym,[status(thm)],]) ).

thf(fact_8974_zero__natural_Orsp,axiom,
    sP4 ).

thf(fact_107_less__numeral__extra_I3_J,axiom,
    ~ sP2 ).

thf(fact_79_gr0__conv__Suc,axiom,
    sP8 ).

thf(fact_4__C3_Ohyps_C_I3_J,axiom,
    sP15 ).

thf(fact_0_bot__nat__0_Onot__eq__extremum,axiom,
    sP10 ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,h0,fact_8974_zero__natural_Orsp,fact_107_less__numeral__extra_I3_J,fact_79_gr0__conv__Suc,fact_4__C3_Ohyps_C_I3_J,fact_0_bot__nat__0_Onot__eq__extremum]) ).

thf(0,theorem,
    sP12,
    inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP225^1 : TPTP v8.1.0. Released v8.1.0.
% 0.13/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Fri Jun  3 08:42:32 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 28.57/28.57  % SZS status Theorem
% 28.57/28.57  % Mode: mode9a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 28.57/28.57  % Inferences: 9837
% 28.57/28.57  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------