%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SET764^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n020.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 15:18:32 EDT 2023

% Result   : Theorem 0.19s 0.42s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(def_in,definition,
    ( in
    = ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).

thf(def_is_a,definition,
    ( is_a
    = ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).

thf(def_emptyset,definition,
    ( emptyset
    = ( ^ [X1: $i] : sP1 ) ) ).

thf(def_unord_pair,definition,
    ( unord_pair
    = ( ^ [X1: $i,X2: $i,X3: $i] :
          ( ( X3 = X1 )
          | ( X3 = X2 ) ) ) ) ).

thf(def_singleton,definition,
    ( singleton
    = ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).

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

thf(def_excl_union,definition,
    ( excl_union
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( ( X1 @ X3 )
            & ( (~) @ ( X2 @ X3 ) ) )
          | ( ( (~) @ ( X1 @ X3 ) )
            & ( X2 @ X3 ) ) ) ) ) ).

thf(def_intersection,definition,
    ( intersection
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X1 @ X3 )
          & ( X2 @ X3 ) ) ) ) ).

thf(def_setminus,definition,
    ( setminus
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X1 @ X3 )
          & ( (~) @ ( X2 @ X3 ) ) ) ) ) ).

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

thf(def_disjoint,definition,
    ( disjoint
    = ( ^ [X1: $i > $o,X2: $i > $o] :
          ( ( intersection @ X1 @ X2 )
          = emptyset ) ) ) ).

thf(def_subset,definition,
    ( subset
    = ( ^ [X1: $i > $o,X2: $i > $o] :
        ! [X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( X1 @ X3 )
          @ ( X2 @ X3 ) ) ) ) ).

thf(def_meets,definition,
    ( meets
    = ( ^ [X1: $i > $o,X2: $i > $o] :
        ? [X3: $i] :
          ( ( X1 @ X3 )
          & ( X2 @ X3 ) ) ) ) ).

thf(def_misses,definition,
    ( misses
    = ( ^ [X1: $i > $o,X2: $i > $o] :
          ( (~)
          @ ? [X3: $i] :
              ( ( X1 @ X3 )
              & ( X2 @ X3 ) ) ) ) ) ).

thf(def_fun_image,definition,
    ( fun_image
    = ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
        ? [X4: $i] :
          ( ( X2 @ X4 )
          & ( X3
            = ( X1 @ X4 ) ) ) ) ) ).

thf(def_fun_composition,definition,
    ( fun_composition
    = ( ^ [X1: $i > $i,X2: $i > $i,X3: $i] : ( X2 @ ( X1 @ X3 ) ) ) ) ).

thf(def_fun_inv_image,definition,
    ( fun_inv_image
    = ( ^ [X1: $i > $i,X2: $i > $o,X3: $i] :
        ? [X4: $i] :
          ( ( X2 @ X4 )
          & ( X4
            = ( X1 @ X3 ) ) ) ) ) ).

thf(def_fun_injective,definition,
    ( fun_injective
    = ( ^ [X1: $i > $i] :
        ! [X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( ( X1 @ X2 )
            = ( X1 @ X3 ) )
          @ ( X2 = X3 ) ) ) ) ).

thf(def_fun_surjective,definition,
    ( fun_surjective
    = ( ^ [X1: $i > $i] :
        ! [X2: $i] :
        ? [X3: $i] :
          ( X2
          = ( X1 @ X3 ) ) ) ) ).

thf(def_fun_bijective,definition,
    ( fun_bijective
    = ( ^ [X1: $i > $i] :
          ( ( fun_injective @ X1 )
          & ( fun_surjective @ X1 ) ) ) ) ).

thf(def_fun_decreasing,definition,
    ( fun_decreasing
    = ( ^ [X1: $i > $i,X2: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( X2 @ X3 @ X4 )
          @ ( X2 @ ( X1 @ X4 ) @ ( X1 @ X3 ) ) ) ) ) ).

thf(def_fun_increasing,definition,
    ( fun_increasing
    = ( ^ [X1: $i > $i,X2: $i > $i > $o] :
        ! [X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( X2 @ X3 @ X4 )
          @ ( X2 @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) ) ) ).

thf(thm,conjecture,
    ~ sP1 ).

thf(h0,negated_conjecture,
    sP1,
    inference(assume_negation,[status(cth)],[thm]) ).

thf(1,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,h0]) ).

thf(0,theorem,
    ~ sP1,
    inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET764^4 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n020.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 : Sat Aug 26 12:54:14 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  % Mode: cade22grackle2xfee4
% 0.19/0.42  % Steps: 1
% 0.19/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------