%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : AGT038^1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n012.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 : Wed Aug 30 15:55:06 EDT 2023

% Result   : Theorem 0.22s 0.42s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_mu,type,
    mu: $tType ).

thf(ty_possibly_likes,type,
    possibly_likes: mu > mu > $i > $o ).

thf(ty_a3,type,
    a3: $i > $i > $o ).

thf(ty_pepsi,type,
    pepsi: mu ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_likes,type,
    likes: mu > mu > $i > $o ).

thf(ty_piotr,type,
    piotr: mu ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ( ( a3 @ X1 @ X2 )
           => ~ ( likes @ piotr @ pepsi @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i,X2: mu,X3: mu] :
        ( ~ ! [X4: $i] :
              ( ( a3 @ X1 @ X4 )
             => ~ ( likes @ X2 @ X3 @ X4 ) )
       => ( possibly_likes @ X2 @ X3 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( a3 @ eigen__0 @ X1 )
       => ~ ( likes @ piotr @ pepsi @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( possibly_likes @ piotr @ pepsi @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ sP3
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: mu,X2: mu] :
        ( ~ ! [X3: $i] :
              ( ( a3 @ eigen__0 @ X3 )
             => ~ ( likes @ X1 @ X2 @ X3 ) )
       => ( possibly_likes @ X1 @ X2 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: mu] :
        ( ~ ! [X2: $i] :
              ( ( a3 @ eigen__0 @ X2 )
             => ~ ( likes @ piotr @ X1 @ X2 ) )
       => ( possibly_likes @ piotr @ X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(def_mnot,definition,
    ( mnot
    = ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

thf(def_mor,definition,
    ( mor
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X1 @ X3 )
          | ( X2 @ X3 ) ) ) ) ).

thf(def_mimplies,definition,
    ( mimplies
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).

thf(def_mforall_ind,definition,
    ( mforall_ind
    = ( ^ [X1: mu > $i > $o,X2: $i] :
        ! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).

thf(def_mbox,definition,
    ( mbox
    = ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
        ! [X4: $i] :
          ( ( (~) @ ( X1 @ X3 @ X4 ) )
          | ( X2 @ X4 ) ) ) ) ).

thf(def_mdia,definition,
    ( mdia
    = ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).

thf(def_mvalid,definition,
    ( mvalid
    = ( ^ [X1: $i > $o] :
        ! [X2: $i] : ( X1 @ X2 ) ) ) ).

thf(conj,conjecture,
    ! [X1: $i] : ( possibly_likes @ piotr @ pepsi @ X1 ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i] : ( possibly_likes @ piotr @ pepsi @ X1 ),
    inference(assume_negation,[status(cth)],[conj]) ).

thf(h1,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP5
    | sP3
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP1
    | ~ sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(axiom_user_communication_5,axiom,
    sP2 ).

thf(axiom_a3_2,axiom,
    sP1 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1,axiom_user_communication_5,axiom_a3_2]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).

thf(0,theorem,
    ! [X1: $i] : ( possibly_likes @ piotr @ pepsi @ X1 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : AGT038^1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.15  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36  % Computer : n012.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun Aug 27 17:13:25 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.22/0.42  % SZS status Theorem
% 0.22/0.42  % Mode: cade22sinegrackle2x6978
% 0.22/0.42  % Steps: 72
% 0.22/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------