TSTP Solution File: NUM739^1 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM739^1 : 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 : n018.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 13:55:54 EDT 2022

% Result   : Theorem 0.19s 0.41s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_frac,type,
    frac: $tType ).

thf(ty_z,type,
    z: frac ).

thf(ty_u,type,
    u: frac ).

thf(ty_y,type,
    y: frac ).

thf(ty_eq,type,
    eq: frac > frac > $o ).

thf(ty_moref,type,
    moref: frac > frac > $o ).

thf(ty_x,type,
    x: frac ).

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

thf(sP2,plain,
    ( sP2
  <=> ( moref @ z @ u ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eq @ y @ u ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP3
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( moref @ x @ y )
     => ( ( eq @ x @ z )
       => sP4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: frac] :
        ( ( eq @ y @ x )
       => ( ( eq @ x @ X1 )
         => ( eq @ y @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: frac,X2: frac,X3: frac] :
        ( ( eq @ X1 @ X2 )
       => ( ( eq @ X2 @ X3 )
         => ( eq @ X1 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP1
     => ( sP3
       => ( eq @ z @ u ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

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

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

thf(sP11,plain,
    ( sP11
  <=> ! [X1: frac] :
        ( ( moref @ x @ y )
       => ( ( eq @ x @ z )
         => ( ( eq @ y @ X1 )
           => ( moref @ z @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

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

thf(sP13,plain,
    ( sP13
  <=> ( ( eq @ x @ z )
     => ( eq @ y @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: frac] :
        ( ( eq @ y @ X1 )
       => ( eq @ X1 @ y ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: frac,X2: frac,X3: frac] :
        ( ( moref @ x @ X1 )
       => ( ( eq @ x @ X2 )
         => ( ( eq @ X1 @ X3 )
           => ( moref @ X2 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( moref @ x @ y ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( eq @ y @ z )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( sP3
     => ( eq @ z @ u ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( sP9
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ! [X1: frac,X2: frac] :
        ( ( eq @ z @ X1 )
       => ( ( eq @ X1 @ X2 )
         => ( eq @ z @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: frac,X2: frac,X3: frac,X4: frac] :
        ( ( moref @ X1 @ X2 )
       => ( ( eq @ X1 @ X3 )
         => ( ( eq @ X2 @ X4 )
           => ( moref @ X3 @ X4 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: frac] :
        ( sP1
       => ( ( eq @ y @ X1 )
         => ( eq @ z @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( eq @ z @ u ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( sP10
     => sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( eq @ x @ z ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP25
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( eq @ y @ z ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ! [X1: frac,X2: frac] :
        ( sP16
       => ( ( eq @ x @ X1 )
         => ( ( eq @ y @ X2 )
           => ( moref @ X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: frac,X2: frac] :
        ( ( eq @ X1 @ X2 )
       => ( eq @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: frac,X2: frac] :
        ( ( eq @ y @ X1 )
       => ( ( eq @ X1 @ X2 )
         => ( eq @ y @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(satz46,conjecture,
    ( ~ sP2
   => sP23 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ sP2
     => sP23 ),
    inference(assume_negation,[status(cth)],[satz46]) ).

thf(h1,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP23,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP16,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP11
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | ~ sP16
    | sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP26
    | ~ sP25
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP15
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP28
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP21
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP4
    | ~ sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(e,axiom,
    sP25 ).

thf(f,axiom,
    sP3 ).

thf(satz44,axiom,
    sP21 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h1,h2,h0])],[1,2,3,4,5,6,7,h3,e,f,satz44,h1]) ).

thf(9,plain,
    ( ~ sP12
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP19
    | ~ sP9
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP29
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP30
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP6
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP24
    | ~ sP10
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP13
    | ~ sP25
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP7
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP29
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP14
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP17
    | ~ sP27
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP7
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP20
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP22
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP8
    | ~ sP1
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP18
    | ~ sP3
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(satz39,axiom,
    sP7 ).

thf(satz38,axiom,
    sP29 ).

thf(25,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h1,h2,h0])],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,h4,e,f,satz39,satz38,h2]) ).

thf(m,axiom,
    ( ~ sP16
   => sP9 ) ).

thf(26,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[m,8,25,h3,h4]) ).

thf(27,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,26,h1,h2]) ).

thf(0,theorem,
    ( ~ sP2
   => sP23 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[27,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM739^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Thu Jul  7 01:45:39 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  % Mode: mode213
% 0.19/0.41  % Inferences: 449
% 0.19/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------