TSTP Solution File: ITP072^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP072^1 : TPTP v8.1.0. Released v7.5.0.
% 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 00:28:59 EDT 2022

% Result   : Theorem 47.69s 47.76s
% Output   : Proof 47.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   49
% Syntax   : Number of formulae    :   55 (  12 unt;   6 typ;   2 def)
%            Number of atoms       :  128 (  28 equ;   3 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  125 (  28   ~;  24   |;   0   &;  49   @)
%                                         (  20 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   29 (  26 usr;  27 con; 0-2 aty)
%            Number of variables   :   21 (   6   ^  15   !;   0   ?;  21   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_hF_Mirabelle_hf,type,
    hF_Mirabelle_hf: $tType ).

thf(ty_eigen__2,type,
    eigen__2: hF_Mirabelle_hf ).

thf(ty_z,type,
    z: hF_Mirabelle_hf ).

thf(ty_eigen__0,type,
    eigen__0: hF_Mirabelle_hf ).

thf(ty_hF_Mirabelle_hmem,type,
    hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).

thf(ty_zero_z189798548lle_hf,type,
    zero_z189798548lle_hf: hF_Mirabelle_hf ).

thf(h0,assumption,
    ! [X1: hF_Mirabelle_hf > $o,X2: hF_Mirabelle_hf] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: hF_Mirabelle_hf] :
          ~ ~ ( hF_Mirabelle_hmem @ X1 @ z ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
         != ( hF_Mirabelle_hmem @ X1 @ z ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( (=)
      = ( ^ [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
          ! [X3: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ X3 @ X1 )
            = ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: hF_Mirabelle_hf] :
        ~ ( hF_Mirabelle_hmem @ X1 @ z ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( (=) @ X1 )
        = ( ^ [X2: hF_Mirabelle_hf] :
            ! [X3: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ X3 @ X1 )
              = ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( hF_Mirabelle_hmem @ eigen__2 @ zero_z189798548lle_hf ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__0 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( zero_z189798548lle_hf = z ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP6
      = ( ! [X1: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
            = ( hF_Mirabelle_hmem @ X1 @ z ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( (=) @ zero_z189798548lle_hf )
      = ( ^ [X1: hF_Mirabelle_hf] :
          ! [X2: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ X2 @ zero_z189798548lle_hf )
            = ( hF_Mirabelle_hmem @ X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP6
     => ( z = zero_z189798548lle_hf ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( z = zero_z189798548lle_hf ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( hF_Mirabelle_hmem @ eigen__0 @ z ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
        = ( hF_Mirabelle_hmem @ X1 @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( zero_z189798548lle_hf = X1 )
       => ( X1 = zero_z189798548lle_hf ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: hF_Mirabelle_hf] :
        ~ ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( sP10 = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( zero_z189798548lle_hf = X1 )
        = ( ! [X2: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ X2 @ zero_z189798548lle_hf )
              = ( hF_Mirabelle_hmem @ X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( hF_Mirabelle_hmem @ eigen__2 @ z ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( hF_Mirabelle_hmem @ eigen__0 @ zero_z189798548lle_hf ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( sP4 = sP18 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(conj_0,conjecture,
    sP15 ).

thf(h1,negated_conjecture,
    ~ sP15,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP14
    | ~ sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP14
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP11
    | sP19
    | ~ sP5
    | ~ sP10 ),
    inference(mating_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP2
    | ~ sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP20
    | sP4
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    sP5,
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP12
    | ~ sP20 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(8,plain,
    ( ~ sP7
    | sP6
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP17
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP8
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP3
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP2
    | sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(14,plain,
    ( ~ sP9
    | ~ sP6
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP13
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP16
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    sP16,
    inference(eq_sym,[status(thm)],]) ).

thf(18,plain,
    ( sP15
    | ~ sP10
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP15
    | sP10
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(fact_1_hemptyE,axiom,
    sP14 ).

thf(fact_0_hf__ext,axiom,
    sP1 ).

thf(20,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,fact_1_hemptyE,fact_0_hf__ext,h1]) ).

thf(21,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0]) ).

thf(0,theorem,
    sP15,
    inference(contra,[status(thm),contra(discharge,[h1])],[20,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ITP072^1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n021.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 : Fri Jun  3 21:42:03 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 47.69/47.76  % SZS status Theorem
% 47.69/47.76  % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 47.69/47.76  % Inferences: 5144
% 47.69/47.76  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------