TSTP Solution File: SEV059^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV059^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n015.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 : Thu Aug 31 19:32:28 EDT 2023

% Result   : Theorem 14.71s 14.95s
% Output   : Proof 14.71s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_b,type,
    b: $tType ).

thf(ty_eigen__0,type,
    eigen__0: b ).

thf(ty_c_less_,type,
    c_less_: a > a > $o ).

thf(ty_cF,type,
    cF: b > b ).

thf(ty_cG,type,
    cG: b > b ).

thf(ty_cA,type,
    cA: b > a ).

thf(sP1,plain,
    ( sP1
  <=> ( cG
      = ( ^ [X1: b] : ( cF @ ( cF @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( c_less_ @ ( cA @ ( cF @ eigen__0 ) ) @ ( cA @ ( cF @ ( cF @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ ( ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cF @ eigen__0 ) ) )
         => ~ sP2 )
     => ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cF @ ( cF @ eigen__0 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cF @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ! [X1: b] :
        ( ( cG @ X1 )
        = ( cF @ ( cF @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( cG @ eigen__0 )
      = ( cF @ ( cF @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: a] :
        ( ~ ( sP4
           => ~ ( c_less_ @ ( cA @ ( cF @ eigen__0 ) ) @ X1 ) )
       => ( c_less_ @ ( cA @ eigen__0 ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP4
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( c_less_ @ ( cA @ eigen__0 ) @ X1 )
           => ~ ( c_less_ @ X1 @ X2 ) )
       => ( c_less_ @ ( cA @ eigen__0 ) @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cF @ ( cF @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cF @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( c_less_ @ ( cA @ eigen__0 ) @ ( cA @ ( cG @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ( cA @ ( cF @ ( cF @ eigen__0 ) ) )
      = ( cA @ ( cG @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: a,X2: a,X3: a] :
        ( ~ ( ( c_less_ @ X1 @ X2 )
           => ~ ( c_less_ @ X2 @ X3 ) )
       => ( c_less_ @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(cTHM89A_pme,conjecture,
    ( ~ ( ~ ( sP16
           => ~ sP12 )
       => ~ sP1 )
   => ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cG @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( sP16
             => ~ sP12 )
         => ~ sP1 )
     => ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cG @ X1 ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM89A_pme]) ).

thf(h1,assumption,
    ~ ( ~ ( sP16
         => ~ sP12 )
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cG @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP16
     => ~ sP12 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP16,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP7
    | sP5
    | ~ sP7
    | sP14 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP11
    | sP13
    | ~ sP15
    | sP14 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP9
    | ~ sP4
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP9
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(6,plain,
    ( ~ sP10
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP15
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP12
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP16
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ~ sP14,
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP12
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP6
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP1
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h5,h6,h4,h7]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h2,14,h7]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,15,h5,h6]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,16,h3,h4]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,17,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ( sP16
           => ~ sP12 )
       => ~ sP1 )
   => ! [X1: b] : ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cG @ X1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV059^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n015.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  : 300
% 0.13/0.34  % DateTime : Thu Aug 24 03:46:05 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 14.71/14.95  % SZS status Theorem
% 14.71/14.95  % Mode: cade22grackle2xfee4
% 14.71/14.95  % Steps: 87673
% 14.71/14.95  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------