%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP052^1 : 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 : n011.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 04:01:47 EDT 2023

% Result   : Theorem 0.19s 0.46s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_product_prod_nat_nat,type,
    product_prod_nat_nat: $tType ).

thf(ty_list_P559422087at_nat,type,
    list_P559422087at_nat: $tType ).

thf(ty_capacity,type,
    capacity: $tType ).

thf(ty_nat,type,
    nat: $tType ).

thf(ty_isMaxFlow_capacity,type,
    isMaxFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).

thf(ty_t,type,
    t: nat ).

thf(ty_f,type,
    f: product_prod_nat_nat > capacity ).

thf(ty_eigen__8,type,
    eigen__8: list_P559422087at_nat ).

thf(ty_inf_in586391887at_nat,type,
    inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).

thf(ty_isSimp1359852763pacity,type,
    isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).

thf(ty_augmen1090971539pacity,type,
    augmen1090971539pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > $o ).

thf(ty_eigen__9,type,
    eigen__9: list_P559422087at_nat ).

thf(ty_s,type,
    s: nat ).

thf(ty_bot_bo2130386637at_nat,type,
    bot_bo2130386637at_nat: set_Pr1986765409at_nat ).

thf(ty_converse_nat_nat,type,
    converse_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).

thf(ty_c,type,
    c: product_prod_nat_nat > capacity ).

thf(ty_eigen__10,type,
    eigen__10: list_P559422087at_nat ).

thf(ty_p,type,
    p: list_P559422087at_nat ).

thf(ty_residu203630698pacity,type,
    residu203630698pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).

thf(ty_set_Pr2131844118at_nat,type,
    set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).

thf(sP1,plain,
    ( sP1
  <=> ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ p @ t ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: list_P559422087at_nat] :
        ~ ( augmen1090971539pacity @ c @ s @ t @ f @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( augmen1090971539pacity @ c @ s @ t @ f @ p ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: list_P559422087at_nat,X2: nat] :
        ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X1 @ X2 )
       => ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X1 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X1 ) ) )
          = bot_bo2130386637at_nat ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( isMaxFlow_capacity @ c @ s @ t @ f ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: nat,X2: list_P559422087at_nat,X3: nat] :
        ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ X1 @ X2 @ X3 )
       => ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X2 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X2 ) ) )
          = bot_bo2130386637at_nat ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
      = bot_bo2130386637at_nat ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(sP9,plain,
    ( sP9
  <=> ( sP3 = sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: nat] :
        ( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ p @ X1 )
       => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: list_P559422087at_nat] :
        ( ( augmen1090971539pacity @ c @ s @ t @ f @ X1 )
        = ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X1 @ t ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(conj_1,conjecture,
    sP7 ).

thf(h0,negated_conjecture,
    ~ sP7,
    inference(assume_negation,[status(cth)],[conj_1]) ).

thf(h1,assumption,
    sP5,
    introduced(assumption,[]) ).

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

thf(h3,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h2,h1,h1,h2,h0])],[h1,h3]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(conj_0,axiom,
    sP3 ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h2,h1,h1,h2,h0])],[2,conj_0,h2]) ).

thf(fact_7_fofu__I__II,axiom,
    ( sP5
   => sP2 ) ).

thf(4,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h2,h1,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h2])],[fact_7_fofu__I__II,1,3,h3,h2]) ).

thf(h5,assumption,
    augmen1090971539pacity @ c @ s @ t @ f @ eigen__8,
    introduced(assumption,[]) ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h5,h4,h3,h1,h2,h0])],[h1,h3]) ).

thf(6,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h2,h5,h4,h3,h1,h2,h0])],[h1,h3]) ).

thf(7,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h5,h4,h3,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h2])],[fact_7_fofu__I__II,5,6,h3,h2]) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__8)],[h4,7,h5]) ).

thf(fact_8_noAugPath__iff__maxFlow,axiom,
    sP2 = sP5 ).

thf(9,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h1,h2,h0]),tab_bq(discharge,[h2,h1]),tab_bq(discharge,[h4,h3])],[fact_8_noAugPath__iff__maxFlow,4,8,h2,h1,h4,h3]) ).

thf(h6,assumption,
    augmen1090971539pacity @ c @ s @ t @ f @ eigen__9,
    introduced(assumption,[]) ).

thf(10,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h2,h1,h6,h3,h4,h0])],[h1,h3]) ).

thf(11,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h2,h2,h1,h6,h3,h4,h0])],[h1,h3]) ).

thf(12,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h2,h1,h6,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h2])],[fact_7_fofu__I__II,10,11,h3,h2]) ).

thf(h7,assumption,
    augmen1090971539pacity @ c @ s @ t @ f @ eigen__10,
    introduced(assumption,[]) ).

thf(13,plain,
    ( ~ sP8
    | ~ sP1
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP10
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP4
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP9
    | ~ sP3
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP6
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP11
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_1_cf_OisSPath__nt__parallel__pf,axiom,
    sP6 ).

thf(fact_5_isAugmentingPath__def,axiom,
    sP11 ).

thf(19,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h7,h4,h3,h6,h3,h4,h0])],[13,14,15,16,17,18,h0,conj_0,fact_1_cf_OisSPath__nt__parallel__pf,fact_5_isAugmentingPath__def]) ).

thf(20,plain,
    ( ~ sP2
    | ~ sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h7,h4,h3,h6,h3,h4,h0])],[20,conj_0,h2]) ).

thf(22,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h7,h4,h3,h6,h3,h4,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h2])],[fact_7_fofu__I__II,19,21,h3,h2]) ).

thf(23,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h6,h3,h4,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__10)],[h4,22,h7]) ).

thf(24,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h6,h3,h4,h0]),tab_bq(discharge,[h2,h1]),tab_bq(discharge,[h4,h3])],[fact_8_noAugPath__iff__maxFlow,12,23,h2,h1,h4,h3]) ).

thf(25,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__9)],[h4,24,h6]) ).

thf(fact_54_ford__fulkerson_I1_J,axiom,
    sP5 = sP2 ).

thf(26,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h0]),tab_bq(discharge,[h1,h2]),tab_bq(discharge,[h3,h4])],[fact_54_ford__fulkerson_I1_J,9,25,h1,h2,h3,h4]) ).

thf(0,theorem,
    sP7,
    inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP052^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n011.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  : 300
% 0.13/0.33  % DateTime : Sun Aug 27 16:45:55 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.46  % SZS status Theorem
% 0.19/0.46  % Mode: cade22sinegrackle2x6978
% 0.19/0.46  % Steps: 431
% 0.19/0.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------