%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP110^1 : 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 : n021.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 04:02:09 EDT 2023

% Result   : Theorem 0.19s 0.43s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_extended_ereal,type,
    extended_ereal: $tType ).

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

thf(ty_f,type,
    f: a > extended_ereal ).

thf(ty_eigen__1,type,
    eigen__1: a ).

thf(ty_lower_311861424x_on_a,type,
    lower_311861424x_on_a: set_a > ( a > extended_ereal ) > $o ).

thf(ty_top_top_set_a,type,
    top_top_set_a: set_a ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(ty_convex_a,type,
    convex_a: set_a > $o ).

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

thf(ty_lower_1391529426main_a,type,
    lower_1391529426main_a: ( a > extended_ereal ) > set_a ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a > extended_ereal] :
        ( ( lower_311861424x_on_a @ top_top_set_a @ X1 )
       => ( convex_a @ ( lower_1391529426main_a @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( convex_a @ ( lower_1391529426main_a @ f ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( lower_311861424x_on_a @ top_top_set_a @ f ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP3
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(conj_0,conjecture,
    sP3 = sP2 ).

thf(h0,negated_conjecture,
    sP3 != sP2,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    sP3,
    introduced(assumption,[]) ).

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

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

thf(h4,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h5,assumption,
    member_a @ eigen__0 @ top_top_set_a,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_2_convex__domain,axiom,
    sP1 ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h1,h2,h0])],[1,2,h1,h4,fact_2_convex__domain]) ).

thf(4,plain,
    ( ~ sP4
    | ~ sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h5,h1,h2,h0])],[4,5,h1,h2,fact_2_convex__domain]) ).

thf(fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_AUNIV_Af_092_060close_062,axiom,
    ( sP2
   => sP3 ) ).

thf(7,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h5,h1,h2,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h1])],[fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_AUNIV_Af_092_060close_062,3,6,h4,h1]) ).

thf(fact_29_UNIV__witness,axiom,
    ~ ! [X1: a] :
        ~ ( member_a @ X1 @ top_top_set_a ) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[fact_29_UNIV__witness,7,h5]) ).

thf(h6,assumption,
    member_a @ eigen__1 @ top_top_set_a,
    introduced(assumption,[]) ).

thf(9,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h4,h6,h3,h4,h0])],[h4,h4]) ).

thf(10,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h1,h6,h3,h4,h0])],[h1,h3]) ).

thf(11,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h6,h3,h4,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h1])],[fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_AUNIV_Af_092_060close_062,9,10,h4,h1]) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[fact_29_UNIV__witness,11,h6]) ).

thf(13,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,8,12,h1,h2,h3,h4]) ).

thf(0,theorem,
    sP3 = sP2,
    inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP110^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.34  % Computer : n021.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Sun Aug 27 16:53:43 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  % Mode: cade22sinegrackle2x6978
% 0.19/0.43  % Steps: 134
% 0.19/0.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------