%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP170^1 : 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 : n032.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 04:02:42 EDT 2023

% Result   : Theorem 0.16s 0.39s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_traffic,type,
    traffic: $tType ).

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

thf(ty_real_int,type,
    real_int: $tType ).

thf(ty_view_e774982825t_unit,type,
    view_e774982825t_unit: $tType ).

thf(ty_real,type,
    real: $tType ).

thf(ty_c,type,
    c: cars ).

thf(ty_left,type,
    left: real_int > real ).

thf(ty_right,type,
    right: real_int > real ).

thf(ty_v,type,
    v: view_e774982825t_unit ).

thf(ty_regular_regular,type,
    regular_regular: cars > traffic > cars > real ).

thf(ty_eigen__0,type,
    eigen__0: cars > real ).

thf(ty_ext_Product_unit,type,
    ext_Product_unit: view_e774982825t_unit > real_int ).

thf(ty_ord_less_real,type,
    ord_less_real: real > real > $o ).

thf(ty_ts,type,
    ts: traffic ).

thf(ty_one_one_real,type,
    one_one_real: real ).

thf(ty_space,type,
    space: ( cars > traffic > cars > real ) > traffic > view_e774982825t_unit > cars > real_int ).

thf(ty_len,type,
    len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).

thf(ty_d,type,
    d: cars ).

thf(ty_real_length,type,
    real_length: real_int > real ).

thf(ty_eigen__1,type,
    eigen__1: cars > real ).

thf(ty_zero_zero_real,type,
    zero_zero_real: real ).

thf(sP1,plain,
    ( sP1
  <=> ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ d ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ d ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ d ) ) @ ( right @ ( ext_Product_unit @ v ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: cars] :
        ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ ts @ X1 ) ) )
       => ~ ( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ X1 ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
           => ~ ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: traffic,X2: cars] :
        ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ v @ X1 @ X2 ) ) )
       => ~ ( ( ord_less_real @ ( left @ ( space @ regular_regular @ X1 @ v @ X2 ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
           => ~ ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ X1 @ v @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: view_e774982825t_unit,X2: traffic,X3: cars] :
        ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ X1 @ X2 @ X3 ) ) )
       => ~ ( ( ord_less_real @ ( left @ ( space @ regular_regular @ X2 @ X1 @ X3 ) ) @ ( right @ ( ext_Product_unit @ X1 ) ) )
           => ~ ( ord_less_real @ ( left @ ( ext_Product_unit @ X1 ) ) @ ( right @ ( space @ regular_regular @ X2 @ X1 @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP3
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP1
     => ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(conj_0,conjecture,
    ~ sP7 ).

thf(h0,negated_conjecture,
    sP7,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ! [X1: cars] :
      ( ( eigen__1 @ X1 )
      = one_one_real ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ c ) ) @ ( right @ ( ext_Product_unit @ v ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ c ) ),
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP7
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | ~ sP1
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP4
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP6
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_4_v_H__d,axiom,
    sP1 ).

thf(fact_3_hmlsl_Olen__non__empty__inside,axiom,
    sP6 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h1,h0])],[1,2,3,4,5,h1,fact_4_v_H__d,fact_3_hmlsl_Olen__non__empty__inside]) ).

thf(fact_9_v_H__rel__c,axiom,
    ~ ( ( ord_less_real @ ( left @ ( space @ regular_regular @ ts @ v @ c ) ) @ ( right @ ( ext_Product_unit @ v ) ) )
     => ~ ( ord_less_real @ ( left @ ( ext_Product_unit @ v ) ) @ ( right @ ( space @ regular_regular @ ts @ v @ c ) ) ) ) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[fact_9_v_H__rel__c,6,h4,h5]) ).

thf(fact_32__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ps_O_A_092_060forall_062c_O_Aps_Ac_A_061_A1_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [X1: cars > real] :
        ~ ! [X2: cars] :
            ( ( X1 @ X2 )
            = one_one_real ) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[fact_32__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ps_O_A_092_060forall_062c_O_Aps_Ac_A_061_A1_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,7,h3]) ).

thf(h6,assumption,
    ! [X1: cars] :
      ( ( eigen__0 @ X1 )
      = one_one_real ),
    introduced(assumption,[]) ).

thf(9,plain,
    ( sP7
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP8
    | ~ sP1
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP4
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP5
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP6
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h6,h2,h0])],[9,10,11,12,13,h2,fact_4_v_H__d,fact_3_hmlsl_Olen__non__empty__inside]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h2,h0]),tab_negimp(discharge,[h4,h5])],[fact_9_v_H__rel__c,14,h4,h5]) ).

thf(16,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[fact_32__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ps_O_A_092_060forall_062c_O_Aps_Ac_A_061_A1_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,15,h6]) ).

thf(17,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,8,16,h1,h2]) ).

thf(0,theorem,
    ~ sP7,
    inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ITP170^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.11  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.31  % Computer : n032.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sun Aug 27 16:51:45 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.39  % SZS status Theorem
% 0.16/0.39  % Mode: cade22sinegrackle2x6978
% 0.16/0.39  % Steps: 180
% 0.16/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------