%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP227^3 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n025.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  : 600s
% DateTime : Sun Jul 17 00:29:47 EDT 2022

% Result   : Theorem 0.62s 0.90s
% Output   : Proof 0.62s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_vEBT_VEBT,type,
    vEBT_VEBT: $tType ).

thf(ty_list_VEBT_VEBT,type,
    list_VEBT_VEBT: $tType ).

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

thf(ty_set_VEBT_VEBT,type,
    set_VEBT_VEBT: $tType ).

thf(ty_num,type,
    num: $tType ).

thf(ty_nth_VEBT_VEBT,type,
    nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(ty_vEBT_VEBT_high,type,
    vEBT_VEBT_high: nat > nat > nat ).

thf(ty_numeral_numeral_nat,type,
    numeral_numeral_nat: num > nat ).

thf(ty_treeList,type,
    treeList: list_VEBT_VEBT ).

thf(ty_bit0,type,
    bit0: num > num ).

thf(ty_member_VEBT_VEBT,type,
    member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).

thf(ty_mi,type,
    mi: nat ).

thf(ty_na,type,
    na: nat ).

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

thf(ty_set_VEBT_VEBT2,type,
    set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).

thf(ty_xa,type,
    xa: nat ).

thf(ty_vEBT_VEBT_low,type,
    vEBT_VEBT_low: nat > nat > nat ).

thf(ty_one,type,
    one: num ).

thf(ty_vEBT_V8194947554948674370ptions,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(ty_power_power_nat,type,
    power_power_nat: nat > nat > nat ).

thf(ty_ord_less_eq_nat,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(ty_ma,type,
    ma: nat ).

thf(ty_m,type,
    m: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( xa = mi ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( xa = ma ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( mi = ma ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(conj_0,conjecture,
    ~ ( ~ sP1
     => sP2 ) ).

thf(h0,negated_conjecture,
    ( ~ sP1
   => sP2 ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

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

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

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

thf(h4,assumption,
    ! [X1: nat] :
      ( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
     => ~ ( ( ( ( vEBT_VEBT_high @ ma @ na )
              = X1 )
           => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
         => ~ ! [X2: nat] :
                ( ~ ( ( ( vEBT_VEBT_high @ X2 @ na )
                      = X1 )
                   => ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
               => ~ ( ( ord_less_nat @ mi @ X2 )
                   => ~ ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h6,assumption,
    ! [X1: vEBT_VEBT] :
      ( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
     => ! [X2: nat] :
          ~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h5,h3,h1,h0])],[h3,h5]) ).

thf(fact_0_False,axiom,
    ~ ( ~ sP1
     => sP2 ) ).

thf(2,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,1,h7,h8]) ).

thf(3,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h6,h3,h1,h0])],[h1,h7]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,3,h7,h8]) ).

thf(fact_2__C5_Ohyps_C_I6_J,axiom,
    ( sP3
   => ! [X1: vEBT_VEBT] :
        ( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
       => ! [X2: nat] :
            ~ ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ) ) ).

thf(5,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_2__C5_Ohyps_C_I6_J,2,4,h5,h6]) ).

thf(6,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h5,h4,h1,h0])],[h1,h7]) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h4,h1,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,6,h7,h8]) ).

thf(8,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h6,h4,h1,h0])],[h1,h7]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h4,h1,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,8,h7,h8]) ).

thf(10,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_2__C5_Ohyps_C_I6_J,7,9,h5,h6]) ).

thf(fact_89__C5_Ohyps_C_I9_J,axiom,
    ( ~ sP3
   => ! [X1: nat] :
        ( ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
       => ~ ( ( ( ( vEBT_VEBT_high @ ma @ na )
                = X1 )
             => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
           => ~ ! [X2: nat] :
                  ( ~ ( ( ( vEBT_VEBT_high @ X2 @ na )
                        = X1 )
                     => ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
                 => ~ ( ( ord_less_nat @ mi @ X2 )
                     => ~ ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ) ) ).

thf(11,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_89__C5_Ohyps_C_I9_J,5,10,h3,h4]) ).

thf(12,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h5,h3,h2,h0])],[h3,h5]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h3,h2,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,12,h7,h8]) ).

thf(14,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h6,h3,h2,h0])],[h2,h8]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h3,h2,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,14,h7,h8]) ).

thf(16,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h3,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_2__C5_Ohyps_C_I6_J,13,15,h5,h6]) ).

thf(17,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h5,h4,h2,h0])],[h2,h8]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,17,h7,h8]) ).

thf(19,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h6,h4,h2,h0])],[h2,h8]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h4,h2,h0]),tab_negimp(discharge,[h7,h8])],[fact_0_False,19,h7,h8]) ).

thf(21,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h4,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_2__C5_Ohyps_C_I6_J,18,20,h5,h6]) ).

thf(22,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_89__C5_Ohyps_C_I9_J,16,21,h3,h4]) ).

thf(23,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,11,22,h1,h2]) ).

thf(0,theorem,
    ~ ( ~ sP1
     => sP2 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ITP227^3 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jun  3 16:06:45 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.62/0.90  % SZS status Theorem
% 0.62/0.90  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.62/0.90  % Inferences: 0
% 0.62/0.90  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------