%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO554^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n016.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 : Thu Jul 21 19:33:23 EDT 2022

% Result   : Unsatisfiable 0.12s 0.37s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   37 (  14 unt;   4 typ;   0 def)
%            Number of atoms       :   61 (   9 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   48 (  17   ~;  13   |;   0   &;   3   @)
%                                         (  10 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;  14 con; 0-2 aty)
%            Number of variables   :    3 (   0   ^   3   !;   0   ?;   3   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_p,type,
    p: $i > $o ).

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

thf(ty_u,type,
    u: $i ).

thf(ty_t,type,
    t: $i ).

thf(sP1,plain,
    ( sP1
  <=> ( p @ t ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

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

thf(sP4,plain,
    ( sP4
  <=> ( sP2
     => ( t = s ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( t = s ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

thf(sP7,plain,
    ( sP7
  <=> ( t = u ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

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

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

thf(h0,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(h1,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | sP9
    | ~ sP5
    | ~ sP7 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP10
    | sP6
    | ~ sP9 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP4
    | ~ sP2
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP8
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP3
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    sP3,
    inference(eq_sym,[status(thm)],]) ).

thf(st,axiom,
    sP2 ).

thf(tu,axiom,
    sP7 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h0])],[1,2,3,4,5,6,h0,h2,st,tu]) ).

thf(8,plain,
    ( ~ sP10
    | sP1
    | ~ sP2 ),
    inference(mating_rule,[status(thm)],]) ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h0])],[8,h0,h3,st]) ).

thf(puv,axiom,
    ( sP6
   => ~ sP1 ) ).

thf(10,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[puv,7,9,h2,h3]) ).

thf(11,plain,
    ( ~ sP1
    | sP6
    | ~ sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(12,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1])],[11,h1,h2,tu]) ).

thf(13,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h1])],[h1,h3]) ).

thf(14,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[puv,12,13,h2,h3]) ).

thf(pst,axiom,
    ( ~ sP10
   => sP1 ) ).

thf(15,plain,
    $false,
    inference(tab_imp,[status(thm),tab_imp(discharge,[h0]),tab_imp(discharge,[h1])],[pst,10,14,h0,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO554^1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n016.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
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jul  9 14:17:10 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.37  % SZS status Unsatisfiable
% 0.12/0.37  % Mode: mode213
% 0.12/0.37  % Inferences: 17
% 0.12/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------