%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SCT171^2 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n017.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 14:19:29 EDT 2023

% Result   : Theorem 0.20s 0.47s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_arrow_1429601828e_indi,type,
    arrow_1429601828e_indi: $tType ).

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

thf(ty_arrow_475358991le_alt,type,
    arrow_475358991le_alt: $tType ).

thf(ty_produc1501160679le_alt,type,
    produc1501160679le_alt: $tType ).

thf(ty_arrow_789600939_above,type,
    arrow_789600939_above: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o ).

thf(ty_plus_plus_nat,type,
    plus_plus_nat: nat > nat > nat ).

thf(ty_d,type,
    d: arrow_475358991le_alt ).

thf(ty_c,type,
    c: arrow_475358991le_alt ).

thf(ty_member377231867_alt_o,type,
    member377231867_alt_o: ( produc1501160679le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).

thf(ty_one_one_nat,type,
    one_one_nat: nat ).

thf(ty_eigen__2,type,
    eigen__2: produc1501160679le_alt > $o ).

thf(ty_eigen__4,type,
    eigen__4: produc1501160679le_alt > $o ).

thf(ty_eigen__3,type,
    eigen__3: produc1501160679le_alt > $o ).

thf(ty_ord_less_nat,type,
    ord_less_nat: nat > nat > $o ).

thf(ty_lba,type,
    lba: produc1501160679le_alt > $o ).

thf(ty_lab,type,
    lab: produc1501160679le_alt > $o ).

thf(ty_member214075476le_alt,type,
    member214075476le_alt: produc1501160679le_alt > ( produc1501160679le_alt > $o ) > $o ).

thf(ty_b,type,
    b: arrow_475358991le_alt ).

thf(ty_h,type,
    h: arrow_1429601828e_indi > nat ).

thf(ty_arrow_2054445623_mkbot,type,
    arrow_2054445623_mkbot: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > produc1501160679le_alt > $o ).

thf(ty_f,type,
    f: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ).

thf(ty_if_Pro1561232536_alt_o,type,
    if_Pro1561232536_alt_o: $o > ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ).

thf(ty_eigen__0,type,
    eigen__0: produc1501160679le_alt > $o ).

thf(ty_p,type,
    p: arrow_1429601828e_indi > produc1501160679le_alt > $o ).

thf(ty_a,type,
    a: arrow_475358991le_alt ).

thf(ty_arrow_823908191le_Lin,type,
    arrow_823908191le_Lin: ( produc1501160679le_alt > $o ) > $o ).

thf(ty_eigen__1,type,
    eigen__1: produc1501160679le_alt > $o ).

thf(ty_e,type,
    e: arrow_475358991le_alt ).

thf(ty_arrow_55669061_mktop,type,
    arrow_55669061_mktop: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > produc1501160679le_alt > $o ).

thf(ty_produc1347929815le_alt,type,
    produc1347929815le_alt: arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt ).

thf(ty_n,type,
    n: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d )
      @ ( f
        @ ^ [X1: arrow_1429601828e_indi] :
            ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X1 ) @ e )
            @ ( if_Pro1561232536_alt_o
              @ ( ( h @ X1 )
                = n )
              @ ( arrow_789600939_above @ ( p @ X1 ) @ c @ e )
              @ ( arrow_2054445623_mkbot @ ( p @ X1 ) @ e ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
      @ ( f
        @ ^ [X1: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ ( plus_plus_nat @ n @ one_one_nat ) ) @ lab @ lba ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
      @ ( f
        @ ^ [X1: arrow_1429601828e_indi] :
            ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X1 ) @ e )
            @ ( if_Pro1561232536_alt_o
              @ ( ( h @ X1 )
                = n )
              @ ( arrow_789600939_above @ ( p @ X1 ) @ c @ e )
              @ ( arrow_2054445623_mkbot @ ( p @ X1 ) @ e ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(conj_0,conjecture,
    sP1 ).

thf(h0,negated_conjecture,
    ~ sP1,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    member377231867_alt_o @ eigen__0 @ arrow_823908191le_Lin,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e )
    @ ( f
      @ ^ [X1: arrow_1429601828e_indi] :
          ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X1 ) @ e )
          @ ( if_Pro1561232536_alt_o
            @ ( ( h @ X1 )
              = n )
            @ ( arrow_789600939_above @ ( p @ X1 ) @ c @ e )
            @ ( arrow_2054445623_mkbot @ ( p @ X1 ) @ e ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e )
      @ ( f
        @ ^ [X1: arrow_1429601828e_indi] :
            ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X1 ) @ e )
            @ ( if_Pro1561232536_alt_o
              @ ( ( h @ X1 )
                = n )
              @ ( arrow_789600939_above @ ( p @ X1 ) @ c @ e )
              @ ( arrow_2054445623_mkbot @ ( p @ X1 ) @ e ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ eigen__1 )
     => ~ ( member377231867_alt_o @ eigen__1 @ arrow_823908191le_Lin ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ eigen__1,
    introduced(assumption,[]) ).

thf(h8,assumption,
    member377231867_alt_o @ eigen__1 @ arrow_823908191le_Lin,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ eigen__2 )
     => ~ ( member377231867_alt_o @ eigen__2 @ arrow_823908191le_Lin ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ eigen__2,
    introduced(assumption,[]) ).

thf(h11,assumption,
    member377231867_alt_o @ eigen__2 @ arrow_823908191le_Lin,
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
    @ ( f
      @ ^ [X1: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ lab @ lba ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
      @ ( f
        @ ^ [X1: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ lab @ lba ) ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h16,h17,h12,h13,h10,h11,h9,h7,h8,h6,h2,h3,h1,h0])],[h16,h0]) ).

thf(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    sP4 ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h18,h19,h12,h13,h10,h11,h9,h7,h8,h6,h2,h3,h1,h0])],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h19]) ).

thf(fact_14_PW,axiom,
    sP1 = sP4 ).

thf(3,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h8,h6,h2,h3,h1,h0]),tab_bq(discharge,[h16,h17]),tab_bq(discharge,[h18,h19])],[fact_14_PW,1,2,h16,h17,h18,h19]) ).

thf(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    sP2 ).

thf(4,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h16,h17,h14,h15,h10,h11,h9,h7,h8,h6,h2,h3,h1,h0])],[fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h14]) ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h18,h19,h14,h15,h10,h11,h9,h7,h8,h6,h2,h3,h1,h0])],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h19]) ).

thf(6,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h15,h10,h11,h9,h7,h8,h6,h2,h3,h1,h0]),tab_bq(discharge,[h16,h17]),tab_bq(discharge,[h18,h19])],[fact_14_PW,4,5,h16,h17,h18,h19]) ).

thf(fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( sP2
    = ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
      @ ( f
        @ ^ [X1: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ lab @ lba ) ) ) ) ).

thf(7,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h2,h3,h1,h0]),tab_bq(discharge,[h12,h13]),tab_bq(discharge,[h14,h15])],[fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,3,6,h12,h13,h14,h15]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,7,h10,h11]) ).

thf(fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [X1: produc1501160679le_alt > $o] :
        ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ X1 )
       => ~ ( member377231867_alt_o @ X1 @ arrow_823908191le_Lin ) ) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,8,h9]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,9,h7,h8]) ).

thf(fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [X1: produc1501160679le_alt > $o] :
        ( ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ X1 )
       => ~ ( member377231867_alt_o @ X1 @ arrow_823908191le_Lin ) ) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,10,h6]) ).

thf(h20,assumption,
    ~ ( ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ eigen__3 )
     => ~ ( member377231867_alt_o @ eigen__3 @ arrow_823908191le_Lin ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ eigen__3,
    introduced(assumption,[]) ).

thf(h22,assumption,
    member377231867_alt_o @ eigen__3 @ arrow_823908191le_Lin,
    introduced(assumption,[]) ).

thf(h23,assumption,
    ~ ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ eigen__4 )
     => ~ ( member377231867_alt_o @ eigen__4 @ arrow_823908191le_Lin ) ),
    introduced(assumption,[]) ).

thf(h24,assumption,
    member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ eigen__4,
    introduced(assumption,[]) ).

thf(h25,assumption,
    member377231867_alt_o @ eigen__4 @ arrow_823908191le_Lin,
    introduced(assumption,[]) ).

thf(fact_181_n_I3_J,axiom,
    sP3 ).

thf(12,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h16,h17,h12,h13,h24,h25,h23,h21,h22,h20,h4,h5,h1,h0])],[fact_181_n_I3_J,h5]) ).

thf(13,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h18,h19,h12,h13,h24,h25,h23,h21,h22,h20,h4,h5,h1,h0])],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h19]) ).

thf(14,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h12,h13,h24,h25,h23,h21,h22,h20,h4,h5,h1,h0]),tab_bq(discharge,[h16,h17]),tab_bq(discharge,[h18,h19])],[fact_14_PW,12,13,h16,h17,h18,h19]) ).

thf(15,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h16,h17,h14,h15,h24,h25,h23,h21,h22,h20,h4,h5,h1,h0])],[fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h14]) ).

thf(16,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h18,h19,h14,h15,h24,h25,h23,h21,h22,h20,h4,h5,h1,h0])],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,h19]) ).

thf(17,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h15,h24,h25,h23,h21,h22,h20,h4,h5,h1,h0]),tab_bq(discharge,[h16,h17]),tab_bq(discharge,[h18,h19])],[fact_14_PW,15,16,h16,h17,h18,h19]) ).

thf(18,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h4,h5,h1,h0]),tab_bq(discharge,[h12,h13]),tab_bq(discharge,[h14,h15])],[fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,14,17,h12,h13,h14,h15]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h4,h5,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,18,h24,h25]) ).

thf(20,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h4,h5,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__4)],[fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,19,h23]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h4,h5,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,20,h21,h22]) ).

thf(22,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__3)],[fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,21,h20]) ).

thf(fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e )
      @ ( f
        @ ^ [X1: arrow_1429601828e_indi] :
            ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ X1 ) @ n ) @ ( arrow_55669061_mktop @ ( p @ X1 ) @ e )
            @ ( if_Pro1561232536_alt_o
              @ ( ( h @ X1 )
                = n )
              @ ( arrow_789600939_above @ ( p @ X1 ) @ c @ e )
              @ ( arrow_2054445623_mkbot @ ( p @ X1 ) @ e ) ) ) ) )
    = sP3 ) ).

thf(23,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h1,h0]),tab_bq(discharge,[h2,h3]),tab_bq(discharge,[h4,h5])],[fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,11,22,h2,h3,h4,h5]) ).

thf(fact_579_linear__alt,axiom,
    ~ ! [X1: produc1501160679le_alt > $o] :
        ~ ( member377231867_alt_o @ X1 @ arrow_823908191le_Lin ) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_579_linear__alt,23,h1]) ).

thf(0,theorem,
    sP1,
    inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SCT171^2 : TPTP v8.1.2. Released v5.3.0.
% 0.08/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 15:05:39 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  % SZS status Theorem
% 0.20/0.47  % Mode: cade22sinegrackle2x6978
% 0.20/0.47  % Steps: 0
% 0.20/0.47  % SZS output start Proof
% See solution above
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