TSTP Solution File: ITP168^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP168^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n007.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 04:02:41 EDT 2023

% Result   : Theorem 20.97s 21.16s
% Output   : Proof 20.97s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_view_e774982825t_unit,type,
    view_e774982825t_unit: $tType ).

thf(ty_traffic,type,
    traffic: $tType ).

thf(ty_cars,type,
    cars: $tType ).

thf(ty_ts3,type,
    ts3: traffic ).

thf(ty_ts_a,type,
    ts_a: traffic ).

thf(ty_eigen__0,type,
    eigen__0: cars ).

thf(ty_move,type,
    move: traffic > traffic > view_e774982825t_unit > view_e774982825t_unit ).

thf(ty_ts,type,
    ts: traffic ).

thf(ty_create_reservation,type,
    create_reservation: traffic > cars > traffic > $o ).

thf(ty_v,type,
    v: view_e774982825t_unit ).

thf(ty_abstract,type,
    abstract: traffic > traffic > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( create_reservation @ ts_a @ eigen__0 @ ts ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( abstract @ ts_a @ ts ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: view_e774982825t_unit] :
        ( ~ ( ( abstract @ ts3 @ ts_a )
           => ~ sP3 )
       => ( ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ X1 ) )
          = ( move @ ts3 @ ts @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( move @ ts3 @ ts_a @ v )
      = ( move @ ts3 @ ts @ v ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( move @ ts3 @ ts_a @ v )
      = ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: traffic,X2: traffic,X3: traffic] :
        ( ( abstract @ X1 @ X2 )
       => ( ~ ! [X4: cars] :
                ~ ( create_reservation @ X2 @ X4 @ X3 )
         => ( abstract @ X1 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: traffic,X2: traffic] :
        ( ( abstract @ ts_a @ X1 )
       => ( ~ ! [X3: cars] :
                ~ ( create_reservation @ X1 @ X3 @ X2 )
         => ( abstract @ ts_a @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ ( ( abstract @ ts3 @ ts_a )
         => ~ sP3 )
     => ( ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) )
        = ( move @ ts3 @ ts @ v ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: traffic] :
        ( ( abstract @ ts_a @ ts_a )
       => ( ~ ! [X2: cars] :
                ~ ( create_reservation @ ts_a @ X2 @ X1 )
         => ( abstract @ ts_a @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: traffic,X2: traffic,X3: traffic,X4: view_e774982825t_unit] :
        ( ~ ( ( abstract @ X1 @ X2 )
           => ~ ( abstract @ X2 @ X3 ) )
       => ( ( move @ X2 @ X3 @ ( move @ X1 @ X2 @ X4 ) )
          = ( move @ X1 @ X3 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) )
      = ( move @ ts3 @ ts @ v ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: traffic,X2: view_e774982825t_unit] :
        ( ~ ( ( abstract @ ts3 @ ts_a )
           => ~ ( abstract @ ts_a @ X1 ) )
       => ( ( move @ ts_a @ X1 @ ( move @ ts3 @ ts_a @ X2 ) )
          = ( move @ ts3 @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( abstract @ ts_a @ ts_a ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( abstract @ ts3 @ ts_a ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP14
     => ( ~ ! [X1: cars] :
              ~ ( create_reservation @ ts_a @ X1 @ ts )
       => sP3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ~ ! [X1: cars] :
            ~ ( create_reservation @ ts_a @ X1 @ ts )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( sP15
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: traffic] : ( abstract @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ! [X1: traffic,X2: traffic,X3: view_e774982825t_unit] :
        ( ~ ( ( abstract @ ts3 @ X1 )
           => ~ ( abstract @ X1 @ X2 ) )
       => ( ( move @ X1 @ X2 @ ( move @ ts3 @ X1 @ X3 ) )
          = ( move @ ts3 @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: cars] :
        ~ ( create_reservation @ ts_a @ X1 @ ts ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(conj_0,conjecture,
    sP5 ).

thf(h0,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP21
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP18
    | ~ sP15
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP17
    | sP21
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP9
    | sP18
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP16
    | ~ sP14
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP10
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP13
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ~ sP2,
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP6
    | sP5
    | sP2
    | ~ sP12 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP8
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP20
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP19
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP7
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP11
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_37_traffic_Oabstract_Orefl,axiom,
    sP19 ).

thf(fact_29_traffic_Ocr__res,axiom,
    sP7 ).

thf(fact_10_traffic_Omove__trans,axiom,
    sP11 ).

thf(fact_5__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,axiom,
    sP6 ).

thf(fact_0_cr__res_Ohyps_I1_J,axiom,
    sP15 ).

thf(16,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,h0,fact_37_traffic_Oabstract_Orefl,fact_29_traffic_Ocr__res,fact_10_traffic_Omove__trans,fact_5__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,h1,fact_0_cr__res_Ohyps_I1_J]) ).

thf(fact_1_cr__res_Ohyps_I2_J,axiom,
    ~ sP21 ).

thf(17,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_1_cr__res_Ohyps_I2_J,16,h1]) ).

thf(0,theorem,
    sP5,
    inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ITP168^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n007.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 : Sun Aug 27 15:26:42 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 20.97/21.16  % SZS status Theorem
% 20.97/21.16  % Mode: cade22sinegrackle2xfaf3
% 20.97/21.16  % Steps: 4537
% 20.97/21.16  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------