%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ALG254^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n029.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 : Thu Jul 14 17:57:46 EDT 2022

% Result   : Theorem 0.19s 0.40s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_subst,type,
    subst: $tType ).

thf(ty_id,type,
    id: subst ).

thf(ty_comp,type,
    comp: subst > subst > subst ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: subst] :
        ( ( comp @ id @ X1 )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( ! [X1: subst,X2: subst,X3: subst] :
              ( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
              = ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
         => ~ sP1 )
     => ~ ! [X1: subst] :
            ( ( comp @ X1 @ id )
            = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ! [X1: subst] :
          ( ( comp @ X1 @ id )
          = X1 )
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: subst] :
        ( ( comp @ X1 @ id )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ! [X1: subst,X2: subst,X3: subst] :
          ( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
          = ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP1
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ! [X1: subst,X2: subst,X3: subst] :
          ( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
          = ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: subst,X2: subst,X3: subst] :
        ( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
        = ( comp @ X1 @ ( comp @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(def_axidl,definition,
    axidl = sP1 ).

thf(def_axassoc,definition,
    axassoc = sP8 ).

thf(def_axidr,definition,
    axidr = sP4 ).

thf(def_substmonoid,definition,
    ( substmonoid
    = ( ~ sP2 ) ) ).

thf(def_substmonoid_lthm,definition,
    ( substmonoid_lthm
    = ( axidl
     => ( axassoc
       => ( axidr
         => substmonoid ) ) ) ) ).

thf(thm,conjecture,
    sP6 ).

thf(h0,negated_conjecture,
    ~ sP6,
    inference(assume_negation,[status(cth)],[thm]) ).

thf(1,plain,
    ( ~ sP7
    | ~ sP8
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP7
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP3
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP5
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP5
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP6
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP6
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0]) ).

thf(0,theorem,
    sP6,
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG254^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.12/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n029.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 : Wed Jun  8 06:37:36 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 0.19/0.40  % Inferences: 7
% 0.19/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------