%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP144^1 : TPTP v8.1.0. Released v7.5.0.
% 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 00:29:16 EDT 2022

% Result   : Theorem 0.20s 0.38s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_b,type,
    b: $tType ).

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

thf(ty_q,type,
    q: a > b > $o ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(ty_hilbert_Eps_b,type,
    hilbert_Eps_b: ( b > $o ) > b ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a] :
        ( ( p @ X1 )
       => ~ ! [X2: b] :
              ~ ( q @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( p @ eigen__0 )
     => ~ ! [X1: b] :
            ~ ( q @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( p @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( q @ eigen__0 @ ( hilbert_Eps_b @ ( q @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: b] :
        ~ ( q @ eigen__0 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(conj_1,conjecture,
    ! [X1: a] :
      ( ( p @ X1 )
     => ( q @ X1 @ ( hilbert_Eps_b @ ( q @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a] :
        ( ( p @ X1 )
       => ( q @ X1 @ ( hilbert_Eps_b @ ( q @ X1 ) ) ) ),
    inference(assume_negation,[status(cth)],[conj_1]) ).

thf(h1,assumption,
    ~ ( sP3
     => sP4 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(fact_13_tfl__some,axiom,
    ! [X1: b > $o,X2: b] :
      ( ( X1 @ X2 )
     => ( X1 @ ( hilbert_Eps_b @ X1 ) ) ) ).

thf(1,plain,
    ( sP4
    | sP5 ),
    inference(choice_rule,[status(thm)],[fact_13_tfl__some]) ).

thf(2,plain,
    ( ~ sP1
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | ~ sP3
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(conj_0,axiom,
    sP1 ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,h2,h3,conj_0]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,4,h2,h3]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,5,h1]) ).

thf(0,theorem,
    ! [X1: a] :
      ( ( p @ X1 )
     => ( q @ X1 @ ( hilbert_Eps_b @ ( q @ X1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ITP144^1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13  % 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 02:38:54 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.38  % SZS status Theorem
% 0.20/0.38  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.20/0.38  % Inferences: 45
% 0.20/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------