%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP093^1 : 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 : n018.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 00:29:04 EDT 2022

% Result   : Theorem 0.35s 0.55s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_pair_p125712459t_unit,type,
    pair_p125712459t_unit: $tType ).

thf(ty_product_prod_a_a,type,
    product_prod_a_a: $tType ).

thf(ty_nat,type,
    nat: $tType ).

thf(ty_set_Product_prod_a_a,type,
    set_Product_prod_a_a: $tType ).

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

thf(ty_finite_finite_a,type,
    finite_finite_a: set_a > $o ).

thf(ty_collec645855634od_a_a,type,
    collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).

thf(ty_member449909584od_a_a,type,
    member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).

thf(ty_produc1833107820_a_a_o,type,
    produc1833107820_a_a_o: ( a > a > $o ) > product_prod_a_a > $o ).

thf(ty_finite_card_a,type,
    finite_card_a: set_a > nat ).

thf(ty_n,type,
    n: nat ).

thf(ty_pair_p1047056820t_unit,type,
    pair_p1047056820t_unit: pair_p125712459t_unit > set_a ).

thf(ty_product_Sigma_a_a,type,
    product_Sigma_a_a: set_a > ( a > set_a ) > set_Product_prod_a_a ).

thf(ty_ord_le1824328871od_a_a,type,
    ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).

thf(ty_finite179568208od_a_a,type,
    finite179568208od_a_a: set_Product_prod_a_a > $o ).

thf(ty_g,type,
    g: pair_p125712459t_unit ).

thf(ty_pair_p133601421t_unit,type,
    pair_p133601421t_unit: pair_p125712459t_unit > set_Product_prod_a_a ).

thf(ty_product_Pair_a_a,type,
    product_Pair_a_a: a > a > product_prod_a_a ).

thf(sP1,plain,
    ( sP1
  <=> ( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
      @ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
        @ ^ [X1: a] : ( pair_p1047056820t_unit @ g ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: set_Product_prod_a_a,X2: set_Product_prod_a_a] :
        ( ( ord_le1824328871od_a_a @ X1 @ X2 )
       => ( ( finite179568208od_a_a @ X2 )
         => ( finite179568208od_a_a @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( finite179568208od_a_a
        @ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
          @ ^ [X1: a] : ( pair_p1047056820t_unit @ g ) ) )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( finite179568208od_a_a
      @ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
        @ ^ [X1: a] : ( pair_p1047056820t_unit @ g ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP1
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: set_Product_prod_a_a] :
        ( ( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g ) @ X1 )
       => ( ( finite179568208od_a_a @ X1 )
         => sP3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(conj_0,conjecture,
    sP3 ).

thf(h0,negated_conjecture,
    ~ sP3,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ~ ( ( finite_finite_a @ ( pair_p1047056820t_unit @ g ) )
     => ( ( finite_card_a @ ( pair_p1047056820t_unit @ g ) )
       != n ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( ( pair_p133601421t_unit @ g )
    = ( collec645855634od_a_a
      @ ( produc1833107820_a_a_o
        @ ^ [X1: a,X2: a] :
            ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 )
                @ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
                  @ ^ [X3: a] : ( pair_p1047056820t_unit @ g ) ) )
             => ( X1 = X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    finite_finite_a @ ( pair_p1047056820t_unit @ g ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ( ( finite_card_a @ ( pair_p1047056820t_unit @ g ) )
    = n ),
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP7
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | ~ sP1
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP4
    | ~ sP5
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP2
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_19_finite__subset,axiom,
    sP2 ).

thf(fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062,axiom,
    sP1 ).

thf(fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062,axiom,
    sP5 ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h1,h2,h0])],[1,2,3,4,h0,fact_19_finite__subset,fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062,fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,5,h3,h4]) ).

thf(fact_348_calculation,axiom,
    ~ ( ~ ( ( finite_finite_a @ ( pair_p1047056820t_unit @ g ) )
         => ( ( finite_card_a @ ( pair_p1047056820t_unit @ g ) )
           != n ) )
     => ( ( pair_p133601421t_unit @ g )
       != ( collec645855634od_a_a
          @ ( produc1833107820_a_a_o
            @ ^ [X1: a,X2: a] :
                ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 )
                    @ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
                      @ ^ [X3: a] : ( pair_p1047056820t_unit @ g ) ) )
                 => ( X1 = X2 ) ) ) ) ) ) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_348_calculation,6,h1,h2]) ).

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP093^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n018.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 06:30:01 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.35/0.55  % SZS status Theorem
% 0.35/0.55  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.35/0.55  % Inferences: 38
% 0.35/0.55  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------