%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM663^1 : 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 : n029.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 13:54:51 EDT 2022

% Result   : Theorem 0.19s 0.46s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_z,type,
    z: nat ).

thf(ty_y,type,
    y: nat ).

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

thf(ty_x,type,
    x: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( z = z ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: nat,X2: nat,X3: nat] :
        ( ( less @ X1 @ X2 )
       => ( ( less @ X2 @ X3 )
         => ( less @ X1 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

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

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

thf(sP6,plain,
    ( sP6
  <=> ( sP4
     => ( ( less @ y @ z )
       => ( less @ x @ z ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: nat,X2: nat] :
        ( ( less @ x @ X1 )
       => ( ( less @ X1 @ X2 )
         => ( less @ x @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( x = y )
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( less @ x @ z ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( less @ y @ z )
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

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

thf(sP12,plain,
    ( sP12
  <=> ! [X1: nat] :
        ( ( x = X1 )
       => ( X1 = x ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: nat,X2: nat] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( less @ y @ z ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(satz16a,conjecture,
    sP9 ).

thf(h0,negated_conjecture,
    ~ sP9,
    inference(assume_negation,[status(cth)],[satz16a]) ).

thf(h1,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | ~ sP4
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP10
    | ~ sP14
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(k,axiom,
    sP14 ).

thf(satz15,axiom,
    sP2 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1,k,satz15,h0]) ).

thf(7,plain,
    sP1,
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP14
    | sP9
    | ~ sP5
    | ~ sP1 ),
    inference(mating_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP8
    | ~ sP11
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP12
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP13
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    sP13,
    inference(eq_sym,[status(thm)],]) ).

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

thf(l,axiom,
    ( ~ sP4
   => sP11 ) ).

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,
    sP9,
    inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM663^1 : TPTP v8.1.0. Released v3.7.0.
% 0.13/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n029.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 15:32:12 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.46  % SZS status Theorem
% 0.19/0.46  % Mode: mode213
% 0.19/0.46  % Inferences: 1463
% 0.19/0.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------