%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP243^3 : 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 : n028.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 00:30:00 EDT 2022

% Result   : Theorem 52.58s 52.42s
% Output   : Proof 52.58s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_set_nat,type,
    set_nat: $tType ).

thf(ty_vEBT_VEBT,type,
    vEBT_VEBT: $tType ).

thf(ty_option_nat,type,
    option_nat: $tType ).

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

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

thf(ty_vEBT_vebt_succ,type,
    vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).

thf(ty_summary,type,
    summary: 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_vEBT_VEBT_set_vebt,type,
    vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(ty_vEBT_is_succ_in_set,type,
    vEBT_is_succ_in_set: set_nat > nat > nat > $o ).

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

thf(ty_deg,type,
    deg: nat ).

thf(ty_xa,type,
    xa: nat ).

thf(ty_one,type,
    one: num ).

thf(ty_some_nat,type,
    some_nat: nat > option_nat ).

thf(ty_divide_divide_nat,type,
    divide_divide_nat: nat > nat > nat ).

thf(ty_sc,type,
    sc: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
      = ( some_nat @ sc ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: nat,X2: nat] :
        ( ( ( vEBT_vebt_succ @ summary @ X1 )
          = ( some_nat @ X2 ) )
        = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: nat] :
        ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
          = ( some_nat @ X1 ) )
        = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP1 = sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(conj_0,conjecture,
    sP4 ).

thf(h0,negated_conjecture,
    ~ sP4,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP5
    | ~ sP1
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_0__C4_Ohyps_C_I3_J,axiom,
    sP2 ).

thf(fact_1__092_060open_062vebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Asc_092_060close_062,axiom,
    sP1 ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,fact_0__C4_Ohyps_C_I3_J,fact_1__092_060open_062vebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Asc_092_060close_062,h0]) ).

thf(0,theorem,
    sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP243^3 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n028.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  : 600
% 0.13/0.34  % DateTime : Fri Jun  3 04:29:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 52.58/52.42  % SZS status Theorem
% 52.58/52.42  % Mode: mode9:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 52.58/52.42  % Inferences: 500
% 52.58/52.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------