TSTP Solution File: CSR144^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : CSR144^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -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  : 300s
% DateTime : Wed Aug 30 21:33:34 EDT 2023

% Result   : Theorem 20.21s 20.53s
% Output   : Proof 20.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   87
% Syntax   : Number of formulae    :   93 (  13 unt;   9 typ;   2 def)
%            Number of atoms       :  253 (  13 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  318 (  79   ~;  63   |;   0   &; 131   @)
%                                         (  36 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  46 usr;  41 con; 0-2 aty)
%            Number of variables   :   28 (   2   ^;  26   !;   0   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_believes_THFTYPE_IiooI,type,
    believes_THFTYPE_IiooI: $i > $o > $o ).

thf(ty_wife_THFTYPE_IiioI,type,
    wife_THFTYPE_IiioI: $i > $i > $o ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

thf(ty_husband_THFTYPE_IiioI,type,
    husband_THFTYPE_IiioI: $i > $i > $o ).

thf(ty_lMax_THFTYPE_i,type,
    lMax_THFTYPE_i: $i ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_considers_THFTYPE_IiooI,type,
    considers_THFTYPE_IiooI: $i > $o > $o ).

thf(ty_inverse_THFTYPE_IIiioIIiioIoI,type,
    inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

thf(ty_holdsDuring_THFTYPE_IiooI,type,
    holdsDuring_THFTYPE_IiooI: $i > $o > $o ).

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

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i] :
        ~ ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X1 @ lMax_THFTYPE_i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( holdsDuring_THFTYPE_IiooI @ eigen__0 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: $i] :
        ( ( husband_THFTYPE_IiioI @ X1 @ X2 )
        = ( wife_THFTYPE_IiioI @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ $false )
      = ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i )
      = ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( holdsDuring_THFTYPE_IiooI @ eigen__0 @ sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i )
      = sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i )
      = ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i] :
        ( ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X1 )
        = ( wife_THFTYPE_IiioI @ X1 @ lMax_THFTYPE_i ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 )
     => ~ ! [X1: $i] :
            ~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i] :
        ~ ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ( believes_THFTYPE_IiooI @ X1 @ ~ sP7 )
       => ~ ! [X2: $i] :
              ~ ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ X1 @ ~ sP7 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( sP12
      = ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( ~ sP7
      = ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: $o,X2: $i] :
        ( ( believes_THFTYPE_IiooI @ X2 @ X1 )
       => ~ ! [X3: $i] :
              ~ ( holdsDuring_THFTYPE_IiooI @ X3 @ ( considers_THFTYPE_IiooI @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: $i] : ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( holdsDuring_THFTYPE_IiooI @ eigen__1 @ sP24 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ! [X1: $i] :
        ( ( believes_THFTYPE_IiooI @ X1 @ sP7 )
       => ~ ! [X2: $i] :
              ~ ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ X1 @ sP7 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( holdsDuring_THFTYPE_IiooI @ eigen__1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( sP10 = sP29 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ! [X1: $i > $i > $o] :
        ( ( inverse_THFTYPE_IIiioIIiioIoI @ X1 @ wife_THFTYPE_IiioI )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 @ X3 )
            = ( wife_THFTYPE_IiioI @ X3 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ! [X1: $i] :
        ~ ( holdsDuring_THFTYPE_IiooI @ X1 @ sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( wife_THFTYPE_IiioI @ lMax_THFTYPE_i @ lMax_THFTYPE_i ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: $i > $i > $o,X2: $i > $i > $o] :
        ( ( inverse_THFTYPE_IIiioIIiioIoI @ X2 @ X1 )
       => ! [X3: $i,X4: $i] :
            ( ( X2 @ X3 @ X4 )
            = ( X1 @ X4 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( sP9
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( sP2
     => ~ sP32 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(con,conjecture,
    ~ sP23 ).

thf(h1,negated_conjecture,
    sP23,
    inference(assume_negation,[status(cth)],[con]) ).

thf(1,plain,
    ( sP14
    | ~ sP33
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP21
    | sP7
    | ~ sP33 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP25
    | sP27
    | ~ sP6
    | sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP11
    | sP3
    | ~ sP30
    | sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP29
    | sP24
    | ~ sP14
    | sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP24
    | sP29
    | ~ sP21
    | sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP10
    | sP29
    | sP33
    | sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP29
    | sP10
    | sP33
    | sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP4
    | ~ sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP4
    | ~ sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP6
    | ~ sP24
    | ~ sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP6
    | sP24
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP30
    | ~ sP10
    | ~ sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP30
    | sP10
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP13
    | ~ sP33
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP13
    | sP33
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP20
    | sP13 ),
    inference(symeq,[status(thm)],]) ).

thf(18,plain,
    ( sP8
    | ~ sP12
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ~ sP7,
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP16
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP15
    | sP28
    | ~ sP8
    | sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP15
    | sP2
    | sP12
    | sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP5
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( sP18
    | sP25 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(25,plain,
    ( sP32
    | sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(26,plain,
    ( ~ sP35
    | ~ sP9
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP17
    | ~ sP28
    | ~ sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP36
    | ~ sP2
    | ~ sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP31
    | sP35 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP19
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP26
    | sP36 ),
    inference(all_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP34
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP22
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP22
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP23
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(ax,axiom,
    sP9 ).

thf(ax_001,axiom,
    sP34 ).

thf(ax_002,axiom,
    sP22 ).

thf(ax_003,axiom,
    sP1 ).

thf(37,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,ax,ax_001,ax_002,ax_003,h1]) ).

thf(38,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[37,h0]) ).

thf(0,theorem,
    ~ sP23,
    inference(contra,[status(thm),contra(discharge,[h1])],[37,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : CSR144^1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n029.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  : 300
% 0.12/0.33  % DateTime : Mon Aug 28 08:52:26 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 20.21/20.53  % SZS status Theorem
% 20.21/20.53  % Mode: cade22grackle2x798d
% 20.21/20.53  % Steps: 966
% 20.21/20.53  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------