TSTP Solution File: ITP148^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP148^1 : 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 : n031.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 04:02:33 EDT 2023

% Result   : Theorem 20.27s 20.58s
% Output   : Proof 20.27s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_complex,type,
    complex: $tType ).

thf(ty_set_a,type,
    set_a: $tType ).

thf(ty_set_complex,type,
    set_complex: $tType ).

thf(ty_a,type,
    a: $tType ).

thf(ty_path_pathfinish_a,type,
    path_pathfinish_a: ( real > a ) > a ).

thf(ty_inj_on_a_complex,type,
    inj_on_a_complex: ( a > complex ) > set_a > $o ).

thf(ty_comp_a_complex_real,type,
    comp_a_complex_real: ( a > complex ) > ( real > a ) > real > complex ).

thf(ty_path_s36253918omplex,type,
    path_s36253918omplex: ( real > complex ) > $o ).

thf(ty_top_top_set_complex,type,
    top_top_set_complex: set_complex ).

thf(ty_eigen__0,type,
    eigen__0: complex ).

thf(ty_path_p769714271omplex,type,
    path_p769714271omplex: ( real > complex ) > complex ).

thf(ty_eigen__1,type,
    eigen__1: a ).

thf(ty_path_p797330068omplex,type,
    path_p797330068omplex: ( real > complex ) > complex ).

thf(ty_member_a,type,
    member_a: a > set_a > $o ).

thf(ty_bij_betw_a_complex,type,
    bij_betw_a_complex: ( a > complex ) > set_a > set_complex > $o ).

thf(ty_real_V1477106445omplex,type,
    real_V1477106445omplex: ( a > complex ) > $o ).

thf(ty_poinca1910941596x_of_a,type,
    poinca1910941596x_of_a: a > complex ).

thf(ty_member_complex,type,
    member_complex: complex > set_complex > $o ).

thf(ty_top_top_set_a,type,
    top_top_set_a: set_a ).

thf(ty_path_arc_complex,type,
    path_arc_complex: ( real > complex ) > $o ).

thf(ty_path_pathstart_a,type,
    path_pathstart_a: ( real > a ) > a ).

thf(ty_c,type,
    c: real > a ).

thf(ty_path_arc_a,type,
    path_arc_a: ( real > a ) > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
      = ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( path_arc_complex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
      = ( path_arc_a @ c ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( inj_on_a_complex @ poinca1910941596x_of_a @ top_top_set_a ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( path_arc_a @ c )
     => ( ( path_pathfinish_a @ c )
       != ( path_pathstart_a @ c ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: a > complex,X2: real > a] :
        ( ( real_V1477106445omplex @ X1 )
       => ( ( inj_on_a_complex @ X1 @ top_top_set_a )
         => ( ( path_arc_complex @ ( comp_a_complex_real @ X1 @ X2 ) )
            = ( path_arc_a @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: real > a] :
        ( ( real_V1477106445omplex @ poinca1910941596x_of_a )
       => ( sP3
         => ( ( path_arc_complex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ X1 ) )
            = ( path_arc_a @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( real_V1477106445omplex @ poinca1910941596x_of_a )
     => ( sP3
       => sP2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( path_arc_complex
      = ( ^ [X1: real > complex] :
            ~ ( ( path_s36253918omplex @ X1 )
             => ( ( path_p769714271omplex @ X1 )
                = ( path_p797330068omplex @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( path_arc_complex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: real > complex] :
        ( ( path_arc_complex @ X1 )
        = ( ~ ( ( path_s36253918omplex @ X1 )
             => ( ( path_p769714271omplex @ X1 )
                = ( path_p797330068omplex @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP7
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP3
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( sP10
      = ( ~ ( ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
           => sP1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: real > a] :
        ( ( path_arc_a @ X1 )
       => ( ( path_pathfinish_a @ X1 )
         != ( path_pathstart_a @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( path_arc_a @ c ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: a > complex,X2: set_a,X3: set_complex] :
        ( ( bij_betw_a_complex @ X1 @ X2 @ X3 )
       => ( inj_on_a_complex @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: set_a,X2: set_complex] :
        ( ( bij_betw_a_complex @ poinca1910941596x_of_a @ X1 @ X2 )
       => ( inj_on_a_complex @ poinca1910941596x_of_a @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ( path_pathfinish_a @ c )
      = ( path_pathstart_a @ c ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: set_complex] :
        ( ( bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ X1 )
       => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( real_V1477106445omplex @ poinca1910941596x_of_a ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( sP19
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(conj_0,conjecture,
    sP1 ).

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

thf(h1,assumption,
    member_complex @ eigen__0 @ top_top_set_complex,
    introduced(assumption,[]) ).

thf(h2,assumption,
    member_a @ eigen__1 @ top_top_set_a,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP10
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP12
    | ~ sP7
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP23
    | ~ sP19
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP13
    | ~ sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP21
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP14
    | sP10
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP8
    | ~ sP22
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP18
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP11
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP4
    | ~ sP16
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP6
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP17
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP9
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP15
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP5
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_337_bij__betw__imp__inj__on,axiom,
    sP17 ).

thf(fact_250_complex__of__bij,axiom,
    sP7 ).

thf(fact_236_arc__simple__path,axiom,
    sP9 ).

thf(fact_222_arc__distinct__ends,axiom,
    sP15 ).

thf(fact_214_arc__linear__image__eq,axiom,
    sP5 ).

thf(fact_22_complex__of__linear,axiom,
    sP22 ).

thf(fact_2_a1,axiom,
    sP19 ).

thf(fact_0_assms_I2_J,axiom,
    sP20 ).

thf(16,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h0,fact_337_bij__betw__imp__inj__on,fact_250_complex__of__bij,fact_236_arc__simple__path,fact_222_arc__distinct__ends,fact_214_arc__linear__image__eq,fact_22_complex__of__linear,fact_2_a1,fact_0_assms_I2_J]) ).

thf(fact_227_UNIV__witness,axiom,
    ~ ! [X1: a] :
        ~ ( member_a @ X1 @ top_top_set_a ) ).

thf(17,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[fact_227_UNIV__witness,16,h2]) ).

thf(fact_228_UNIV__witness,axiom,
    ~ ! [X1: complex] :
        ~ ( member_complex @ X1 @ top_top_set_complex ) ).

thf(18,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_228_UNIV__witness,17,h1]) ).

thf(0,theorem,
    sP1,
    inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : ITP148^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n031.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 17:02:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 20.27/20.58  % SZS status Theorem
% 20.27/20.58  % Mode: cade22sinegrackle2xfaf3
% 20.27/20.58  % Steps: 1640
% 20.27/20.58  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------