%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP195^1 : 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 : n002.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 04:02:50 EDT 2023

% Result   : Theorem 0.20s 0.45s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_real,type,
    real: $tType ).

thf(ty_poly_real,type,
    poly_real: $tType ).

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

thf(ty_zero_zero_real,type,
    zero_zero_real: real ).

thf(ty_pderiv_real,type,
    pderiv_real: poly_real > poly_real ).

thf(ty_sturm_469514713_r_pos,type,
    sturm_469514713_r_pos: poly_real > real > $o ).

thf(ty_poly_real2,type,
    poly_real2: poly_real > real > real ).

thf(ty_p,type,
    p: poly_real ).

thf(ty_x,type,
    x: real ).

thf(sP1,plain,
    ( sP1
  <=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ( poly_real2 @ p @ x )
       != zero_zero_real )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( sP1
     => ( sturm_469514713_r_pos @ p @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( ( ( poly_real2 @ p @ x )
          = zero_zero_real )
       => ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sturm_469514713_r_pos @ p @ x ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( poly_real2 @ p @ x )
      = zero_zero_real ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(conj_0,conjecture,
    sP5 != sP4 ).

thf(h0,negated_conjecture,
    sP5 = sP4,
    inference(assume_negation,[status(cth)],[conj_0]) ).

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

thf(h2,assumption,
    sP4,
    introduced(assumption,[]) ).

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

thf(h4,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP6
     => ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(fact_0_False,axiom,
    ~ sP6 ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h9,h7,h8,h5,h1,h2,h0])],[h7,fact_0_False]) ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h9,h7,h8,h5,h1,h2,h0])],[h10,h9]) ).

thf(fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,axiom,
    ( sP5
   => sP1 ) ).

thf(3,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h9,h7,h8,h5,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,1,2,h3,h10]) ).

thf(4,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h1,h7,h8,h5,h1,h2,h0])],[h1,h3]) ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h1,h7,h8,h5,h1,h2,h0])],[h7,fact_0_False]) ).

thf(6,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h7,h8,h5,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,4,5,h3,h10]) ).

thf(fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,axiom,
    sP3 ).

thf(7,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h7,h8,h5,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h1])],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,3,6,h9,h1]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,7,h7,h8]) ).

thf(h11,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(9,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h9,h11,h9,h6,h1,h2,h0])],[h1,h3]) ).

thf(10,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h9,h11,h9,h6,h1,h2,h0])],[h10,h9]) ).

thf(11,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h9,h11,h9,h6,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,9,10,h3,h10]) ).

thf(12,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h1,h11,h9,h6,h1,h2,h0])],[h1,h3]) ).

thf(13,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h1,h11,h9,h6,h1,h2,h0])],[h10,h9]) ).

thf(14,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h11,h9,h6,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h10])],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,12,13,h3,h10]) ).

thf(15,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h11,h9,h6,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h1])],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,11,14,h9,h1]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h1,h2,h0]),tab_negimp(discharge,[h11,h9])],[h6,15,h11,h9]) ).

thf(17,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h2,8,16,h5,h6]) ).

thf(18,plain,
    ( ~ sP2
    | sP6
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP4
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP3
    | ~ sP1
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h0])],[18,19,20,fact_0_False,fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,h4,h3]) ).

thf(22,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h0]),tab_bq(discharge,[h1,h2]),tab_bq(discharge,[h3,h4])],[h0,17,21,h1,h2,h3,h4]) ).

thf(0,theorem,
    sP5 != sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : ITP195^1 : TPTP v8.1.2. Released v7.5.0.
% 0.08/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n002.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 : Sun Aug 27 12:56:48 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  % Mode: cade22sinegrackle2x6978
% 0.20/0.45  % Steps: 19
% 0.20/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------