TSTP Solution File: SYO041^2 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO041^2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n027.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 19:29:46 EDT 2022

% Result   : Theorem 0.12s 0.38s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   70
% Syntax   : Number of formulae    :  106 (  51 unt;   4 typ;   0 def)
%            Number of atoms       :  269 (  35 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  177 (  74   ~;  52   |;   0   &;  17   @)
%                                         (  19 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  23 usr;  22 con; 0-2 aty)
%            Number of variables   :    3 (   0   ^   3   !;   0   ?;   3   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_y,type,
    y: $o ).

thf(ty_g,type,
    g: $o > $o ).

thf(ty_f,type,
    f: $o > $o ).

thf(ty_x,type,
    x: $o ).

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

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

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

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

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

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

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

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

thf(sP9,plain,
    ( sP9
  <=> ( ( f @ sP8 )
      = sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( x
      = ( f @ sP8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $o] :
        ( ( sP8 = X1 )
       => ( X1 = sP8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

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

thf(sP13,plain,
    ( sP13
  <=> ( g @ sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( sP8 = sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( sP8 = sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP12 = sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( sP4 = sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( g @ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( f @ sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(3,conjecture,
    ( ~ ( ~ ( ( sP12 != sP4 )
           => ( sP6 != sP4 ) )
       => ( sP18 != sP12 ) )
   => ( sP2 != sP13 ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ( sP12 != sP4 )
             => ( sP6 != sP4 ) )
         => ( sP18 != sP12 ) )
     => ( sP2 != sP13 ) ),
    inference(assume_negation,[status(cth)],[3]) ).

thf(h1,assumption,
    ~ ( ~ ( ( sP12 != sP4 )
         => ( sP6 != sP4 ) )
     => ( sP18 != sP12 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP2 = sP13,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ( sP12 != sP4 )
     => ( sP6 != sP4 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP18 = sP12,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP12 != sP4,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP6 = sP4,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP12,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP18,
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h16,h13,h7,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h8,h8]) ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h17,h18,h13,h7,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h8,h8]) ).

thf('3_001',plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h13,h7,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,1,2,h15,h16,h17,h18]) ).

thf(4,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h16,h14,h9,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h8,h8]) ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h17,h18,h14,h9,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h8,h8]) ).

thf(6,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h9,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,4,5,h15,h16,h17,h18]) ).

thf(7,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h7]),tab_bq(discharge,[h14,h9])],[h4,3,6,h13,h7,h14,h9]) ).

thf(8,plain,
    ( sP9
    | sP19
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP2
    | sP19
    | ~ sP9 ),
    inference(mating_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP1
    | ~ sP19
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP2
    | sP8
    | ~ sP1 ),
    inference(mating_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP14
    | ~ sP8
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP13
    | sP6
    | ~ sP14 ),
    inference(mating_rule,[status(thm)],]) ).

thf(14,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h15,h16,h13,h7,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[8,9,10,11,12,13,h12,h7,h15,h16]) ).

thf(15,plain,
    ( sP14
    | ~ sP8
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP7
    | ~ sP14
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP11
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP8
    | sP19
    | ~ sP16 ),
    inference(mating_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP10
    | ~ sP12
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP8
    | sP2
    | ~ sP10 ),
    inference(mating_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP17
    | sP4
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP3
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    sP3,
    inference(eq_sym,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP18
    | sP13
    | ~ sP17 ),
    inference(mating_rule,[status(thm)],]) ).

thf(25,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h17,h18,h13,h7,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[15,16,17,18,19,20,21,22,23,24,h10,h13,h7,h17,h18]) ).

thf(26,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h13,h7,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,14,25,h15,h16,h17,h18]) ).

thf(27,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h16,h14,h9,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h7,h9]) ).

thf(28,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h17,h18,h14,h9,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h7,h9]) ).

thf(29,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h9,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,27,28,h15,h16,h17,h18]) ).

thf(30,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h7]),tab_bq(discharge,[h14,h9])],[h4,26,29,h13,h7,h14,h9]) ).

thf(31,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h11,h8]),tab_bq(discharge,[h12,h10])],[h6,7,30,h11,h8,h12,h10]) ).

thf(32,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h16,h13,h7,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h7,h9]) ).

thf(33,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h17,h18,h13,h7,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h7,h9]) ).

thf(34,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h13,h7,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,32,33,h15,h16,h17,h18]) ).

thf(35,plain,
    ( sP14
    | sP8
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP19
    | sP8
    | ~ sP14 ),
    inference(mating_rule,[status(thm)],]) ).

thf(37,plain,
    ( sP1
    | sP19
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP2
    | sP8
    | ~ sP1 ),
    inference(mating_rule,[status(thm)],]) ).

thf(39,plain,
    ( sP15
    | ~ sP8
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP13
    | sP18
    | ~ sP15 ),
    inference(mating_rule,[status(thm)],]) ).

thf(41,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h9,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[35,36,37,38,39,40,h8,h14,h9,h15,h16]) ).

thf(42,plain,
    ( sP5
    | ~ sP8
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( ~ sP19
    | sP2
    | ~ sP5 ),
    inference(mating_rule,[status(thm)],]) ).

thf(44,plain,
    ( sP10
    | sP12
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( ~ sP8
    | sP2
    | ~ sP10 ),
    inference(mating_rule,[status(thm)],]) ).

thf(46,plain,
    ( sP16
    | sP12
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( ~ sP6
    | sP13
    | ~ sP16 ),
    inference(mating_rule,[status(thm)],]) ).

thf(48,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h17,h18,h14,h9,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[42,43,44,45,46,47,h11,h9,h17,h18]) ).

thf(49,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h9,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,41,48,h15,h16,h17,h18]) ).

thf(50,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h7]),tab_bq(discharge,[h14,h9])],[h4,34,49,h13,h7,h14,h9]) ).

thf(51,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h16,h13,h7,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).

thf(52,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h17,h18,h13,h7,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).

thf(53,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h13,h7,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,51,52,h15,h16,h17,h18]) ).

thf(54,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h16,h14,h9,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).

thf(55,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h17,h18,h14,h9,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).

thf(56,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h9,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,54,55,h15,h16,h17,h18]) ).

thf(57,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h7]),tab_bq(discharge,[h14,h9])],[h4,53,56,h13,h7,h14,h9]) ).

thf(58,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h11,h8]),tab_bq(discharge,[h12,h10])],[h6,50,57,h11,h8,h12,h10]) ).

thf(59,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h5,31,58,h7,h8,h9,h10]) ).

thf(60,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,59,h5,h6]) ).

thf(61,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,60,h3,h4]) ).

thf(62,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,61,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ( ( sP12 != sP4 )
           => ( sP6 != sP4 ) )
       => ( sP18 != sP12 ) )
   => ( sP2 != sP13 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[62,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYO041^2 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n027.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 : Sat Jul  9 04:20:16 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.38  % SZS status Theorem
% 0.12/0.38  % Mode: mode213
% 0.12/0.38  % Inferences: 123
% 0.12/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------