TSTP Solution File: ITP111^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP111^1 : 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 : n017.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 04:02:10 EDT 2023

% Result   : Theorem 0.19s 0.45s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_set_a,type,
    set_a: $tType ).

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

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

thf(ty_eigen__2,type,
    eigen__2: extended_ereal ).

thf(ty_lower_191460856_ereal,type,
    lower_191460856_ereal: a > ( a > extended_ereal ) > $o ).

thf(ty_eigen__4,type,
    eigen__4: extended_ereal ).

thf(ty_x0,type,
    x0: a ).

thf(ty_ord_le2001149050_ereal,type,
    ord_le2001149050_ereal: extended_ereal > extended_ereal > $o ).

thf(ty_eigen__3,type,
    eigen__3: extended_ereal ).

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

thf(ty_uminus1208298309_ereal,type,
    uminus1208298309_ereal: extended_ereal > extended_ereal ).

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

thf(ty_topolo1276428101open_a,type,
    topolo1276428101open_a: set_a > $o ).

thf(ty_extend1289208545_ereal,type,
    extend1289208545_ereal: extended_ereal ).

thf(ty_eigen__0,type,
    eigen__0: extended_ereal ).

thf(sP1,plain,
    ( sP1
  <=> ( lower_191460856_ereal @ x0 @ f ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ( f @ x0 )
        = extend1289208545_ereal )
     => ( sP1
        = ( ! [X1: extended_ereal] :
              ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
             => ~ ! [X2: set_a] :
                    ( ~ ( ( topolo1276428101open_a @ X2 )
                       => ~ ( member_a @ x0 @ X2 ) )
                   => ~ ! [X3: a] :
                          ( ( member_a @ X3 @ X2 )
                         => ( ord_le2001149050_ereal @ X1 @ ( f @ X3 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( f @ x0 )
      = extend1289208545_ereal ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( f @ x0 )
      = ( uminus1208298309_ereal @ extend1289208545_ereal ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP1
      = ( ! [X1: extended_ereal] :
            ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
           => ~ ! [X2: set_a] :
                  ( ~ ( ( topolo1276428101open_a @ X2 )
                     => ~ ( member_a @ x0 @ X2 ) )
                 => ~ ! [X3: a] :
                        ( ( member_a @ X3 @ X2 )
                       => ( ord_le2001149050_ereal @ X1 @ ( f @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ord_le2001149050_ereal @ eigen__0 @ ( f @ x0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP4
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: extended_ereal] :
        ( ( ord_le2001149050_ereal @ X1 @ ( f @ x0 ) )
       => ~ ! [X2: set_a] :
              ( ~ ( ( topolo1276428101open_a @ X2 )
                 => ~ ( member_a @ x0 @ X2 ) )
             => ~ ! [X3: a] :
                    ( ( member_a @ X3 @ X2 )
                   => ( ord_le2001149050_ereal @ X1 @ ( f @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: set_a] :
        ( ~ ( ( topolo1276428101open_a @ X1 )
           => ~ ( member_a @ x0 @ X1 ) )
       => ~ ! [X2: a] :
              ( ( member_a @ X2 @ X1 )
             => ( ord_le2001149050_ereal @ eigen__0 @ ( f @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ~ sP3
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ~ sP4
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP6
     => ~ sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(conj_0,conjecture,
    ( sP1 != ~ sP8 ) ).

thf(h0,negated_conjecture,
    ( sP1 = ~ sP8 ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP12,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP12
    | ~ sP6
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | ~ sP1
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP7
    | ~ sP4
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
    sP7 ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h6,h7,h5,h1,h2,h0])],[1,2,3,4,h1,h6,h7,fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,h8]) ).

thf(h10,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(6,plain,
    ( ~ sP2
    | ~ sP3
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP12
    | ~ sP6
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP8
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP5
    | ~ sP1
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
    sP2 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h9,h6,h7,h5,h1,h2,h0])],[6,7,8,9,h1,h6,h7,fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,h10]) ).

thf(h12,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(11,plain,
    ( ~ sP12
    | ~ sP6
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP8
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h12,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[11,12,h6,h7,h4]) ).

thf(14,plain,
    ( ~ sP12
    | ~ sP6
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP8
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h4,h11,h12,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[14,15,h6,h7,h4]) ).

thf(17,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h2,h11,h12,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[h4,h2]) ).

thf(18,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h12,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_bq(discharge,[h1,h4]),tab_bq(discharge,[h3,h2])],[h11,16,17,h1,h4,h3,h2]) ).

thf(19,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h12,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h11])],[fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,13,18,h13,h11]) ).

thf(20,plain,
    ( ~ sP12
    | ~ sP6
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP8
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h1,h4,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[20,21,h6,h7,h4]) ).

thf(23,plain,
    ( ~ sP12
    | ~ sP6
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP8
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h4,h11,h1,h4,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[23,24,h6,h7,h4]) ).

thf(h14,assumption,
    ~ ( ( ord_le2001149050_ereal @ eigen__2 @ ( f @ x0 ) )
     => ~ ! [X1: set_a] :
            ( ~ ( ( topolo1276428101open_a @ X1 )
               => ~ ( member_a @ x0 @ X1 ) )
           => ~ ! [X2: a] :
                  ( ( member_a @ X2 @ X1 )
                 => ( ord_le2001149050_ereal @ eigen__2 @ ( f @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ord_le2001149050_ereal @ eigen__2 @ ( f @ x0 ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ! [X1: set_a] :
      ( ~ ( ( topolo1276428101open_a @ X1 )
         => ~ ( member_a @ x0 @ X1 ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ X1 )
           => ( ord_le2001149050_ereal @ eigen__2 @ ( f @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(26,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h16,h14,h3,h2,h11,h1,h4,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[h1,h3]) ).

thf(27,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h3,h2,h11,h1,h4,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,26,h15,h16]) ).

thf(28,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h11,h1,h4,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__2)],[h2,27,h14]) ).

thf(29,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h1,h4,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_bq(discharge,[h1,h4]),tab_bq(discharge,[h3,h2])],[h11,25,28,h1,h4,h3,h2]) ).

thf(30,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h4,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h11])],[fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,22,29,h13,h11]) ).

thf(h17,assumption,
    ~ ( ( ord_le2001149050_ereal @ eigen__3 @ ( f @ x0 ) )
     => ~ ! [X1: set_a] :
            ( ~ ( ( topolo1276428101open_a @ X1 )
               => ~ ( member_a @ x0 @ X1 ) )
           => ~ ! [X2: a] :
                  ( ( member_a @ X2 @ X1 )
                 => ( ord_le2001149050_ereal @ eigen__3 @ ( f @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ord_le2001149050_ereal @ eigen__3 @ ( f @ x0 ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ! [X1: set_a] :
      ( ~ ( ( topolo1276428101open_a @ X1 )
         => ~ ( member_a @ x0 @ X1 ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ X1 )
           => ( ord_le2001149050_ereal @ eigen__3 @ ( f @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(31,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h18,h19,h17,h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[h1,h3]) ).

thf(32,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h1,h4,h11,h18,h19,h17,h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[h1,h3]) ).

thf(h20,assumption,
    ~ ( ( ord_le2001149050_ereal @ eigen__4 @ ( f @ x0 ) )
     => ~ ! [X1: set_a] :
            ( ~ ( ( topolo1276428101open_a @ X1 )
               => ~ ( member_a @ x0 @ X1 ) )
           => ~ ! [X2: a] :
                  ( ( member_a @ X2 @ X1 )
                 => ( ord_le2001149050_ereal @ eigen__4 @ ( f @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    ord_le2001149050_ereal @ eigen__4 @ ( f @ x0 ),
    introduced(assumption,[]) ).

thf(h22,assumption,
    ! [X1: set_a] :
      ( ~ ( ( topolo1276428101open_a @ X1 )
         => ~ ( member_a @ x0 @ X1 ) )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ X1 )
           => ( ord_le2001149050_ereal @ eigen__4 @ ( f @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(33,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h21,h22,h20,h3,h2,h11,h18,h19,h17,h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0])],[h1,h3]) ).

thf(34,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h3,h2,h11,h18,h19,h17,h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,33,h21,h22]) ).

thf(35,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h11,h18,h19,h17,h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__4)],[h2,34,h20]) ).

thf(36,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h18,h19,h17,h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_bq(discharge,[h1,h4]),tab_bq(discharge,[h3,h2])],[h11,32,35,h1,h4,h3,h2]) ).

thf(37,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h18,h19,h17,h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h11])],[fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,31,36,h13,h11]) ).

thf(38,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h17,h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,37,h18,h19]) ).

thf(39,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__3)],[h2,38,h17]) ).

thf(40,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_bq(discharge,[h1,h4]),tab_bq(discharge,[h3,h2])],[h11,30,39,h1,h4,h3,h2]) ).

thf(41,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h4,h11,h9,h6,h7,h5,h1,h2,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h11])],[fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,19,40,h12,h11]) ).

thf(42,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h2,h11,h9,h6,h7,h5,h1,h2,h0])],[h1,h3]) ).

thf(43,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h9,h6,h7,h5,h1,h2,h0]),tab_bq(discharge,[h1,h4]),tab_bq(discharge,[h3,h2])],[h11,41,42,h1,h4,h3,h2]) ).

thf(44,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h9,h6,h7,h5,h1,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h9,10,43,h10,h11]) ).

thf(fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,axiom,
    sP11 ).

thf(45,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h1,h2,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,5,44,h8,h9]) ).

thf(46,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,45,h6,h7]) ).

thf(47,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,46,h5]) ).

thf(48,plain,
    ( ~ sP10
    | sP3
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(49,plain,
    ( ~ sP2
    | ~ sP3
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(50,plain,
    ( ~ sP5
    | sP1
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
    ( ~ sP7
    | ~ sP4
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
    ( ~ sP11
    | sP4
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(53,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h0])],[48,49,50,51,52,fact_0__092_060open_062f_Ax0_A_061_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,fact_1__092_060open_062f_Ax0_A_061_A_N_A_092_060infinity_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,fact_2__092_060open_062_092_060lbrakk_062f_Ax0_A_092_060noteq_062_A_N_A_092_060infinity_062_059_Af_Ax0_A_092_060noteq_062_A_092_060infinity_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Alsc__at_Ax0_Af_A_061_A_I_092_060forall_062C_060f_Ax0_O_A_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062y_092_060in_062T_O_AC_A_060_Af_Ay_J_J_092_060close_062,h4,h3]) ).

thf(54,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h0]),tab_bq(discharge,[h1,h2]),tab_bq(discharge,[h3,h4])],[h0,47,53,h1,h2,h3,h4]) ).

thf(0,theorem,
    ( sP1 != ~ sP8 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[54,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : ITP111^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n017.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  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 10:18:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  % Mode: cade22sinegrackle2x6978
% 0.19/0.45  % Steps: 192
% 0.19/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------