%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP152^1 : 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 : 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  : 300s
% DateTime : Thu Aug 31 04:02:34 EDT 2023

% Result   : Theorem 0.20s 0.42s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_set_Product_prod_a_a,type,
    set_Product_prod_a_a: $tType ).

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

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

thf(ty_carrier,type,
    carrier: set_a ).

thf(ty_x,type,
    x: a ).

thf(ty_relation,type,
    relation: set_Product_prod_a_a ).

thf(ty_y,type,
    y: a ).

thf(ty_product_Pair_a_a,type,
    product_Pair_a_a: a > a > 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_member_a,type,
    member_a: a > set_a > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( member_a @ x @ carrier ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( sP1
     => ! [X1: a] :
          ( ( member_a @ X1 @ carrier )
         => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ x @ X1 ) @ relation )
           => ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ x ) @ relation ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( member_a @ y @ carrier )
     => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
       => ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a] :
        ( ( member_a @ X1 @ carrier )
       => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ x @ X1 ) @ relation )
         => ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ x ) @ relation ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( member_a @ y @ carrier ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ sP6
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: a] :
        ( ( member_a @ X1 @ carrier )
       => ! [X2: a] :
            ( ( member_a @ X2 @ carrier )
           => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ relation )
             => ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ X1 ) @ relation ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(conj_3,conjecture,
    sP8 ).

thf(h0,negated_conjecture,
    ~ sP8,
    inference(assume_negation,[status(cth)],[conj_3]) ).

thf(h1,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP8
    | sP6
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | ~ sP5
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(4,plain,
    ( ~ sP2
    | ~ sP1
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP9
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(conj_1,axiom,
    sP5 ).

thf(conj_0,axiom,
    sP1 ).

thf(fact_3_compl,axiom,
    sP9 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,h1,h2,conj_1,conj_0,fact_3_compl]) ).

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

thf(0,theorem,
    sP8,
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP152^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % 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  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 12:58:23 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  % Mode: cade22sinegrackle2x6978
% 0.20/0.42  % Steps: 105
% 0.20/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------