%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU967^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n013.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 17:38:01 EDT 2023

% Result   : Theorem 0.21s 0.41s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cG_0,type,
    cG_0: ( ( $i > $i ) > $o ) > $i > $i ).

thf(ty_cP_0,type,
    cP_0: $i > $o ).

thf(ty_cY_0,type,
    cY_0: ( ( $i > $i ) > $o ) > $i ).

thf(ty_cH_0,type,
    cH_0: ( ( $i > $i ) > $o ) > $i > $i ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: ( $i > $i ) > $i > $o] :
        ~ ( ~ ( ~ ! [X2: $i] :
                    ~ ( X1
                      @ ( cG_0
                        @ ^ [X3: $i > $i] :
                            ~ ! [X4: $i] :
                                ~ ( X1 @ X3 @ X4 ) )
                      @ X2 )
             => ! [X2: $i] :
                  ~ ( X1
                    @ ( cH_0
                      @ ^ [X3: $i > $i] :
                          ~ ! [X4: $i] :
                              ~ ( X1 @ X3 @ X4 ) )
                    @ X2 ) )
         => ~ ( ~ ! [X2: $i] :
                    ~ ( X1
                      @ ^ [X3: $i] :
                          ( cG_0
                          @ ^ [X4: $i > $i] :
                              ~ ! [X5: $i] :
                                  ~ ( X1 @ X4 @ X5 )
                          @ ( cH_0
                            @ ^ [X4: $i > $i] :
                                ~ ! [X5: $i] :
                                    ~ ( X1 @ X4 @ X5 )
                            @ X3 ) )
                      @ X2 )
             => ~ ( ( cP_0
                    @ ( cY_0
                      @ ^ [X2: $i > $i] :
                          ~ ! [X3: $i] :
                              ~ ( X1 @ X2 @ X3 ) ) )
                 => ( cP_0
                    @ ( cG_0
                      @ ^ [X2: $i > $i] :
                          ~ ! [X3: $i] :
                              ~ ( X1 @ X2 @ X3 )
                      @ ( cY_0
                        @ ^ [X2: $i > $i] :
                            ~ ! [X3: $i] :
                                ~ ( X1 @ X2 @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(cBUGWFFA_pme,conjecture,
    ~ sP2 ).

thf(h0,negated_conjecture,
    sP2,
    inference(assume_negation,[status(cth)],[cBUGWFFA_pme]) ).

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

thf(2,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0]) ).

thf(0,theorem,
    ~ sP2,
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU967^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Wed Aug 23 19:37:32 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.41  % SZS status Theorem
% 0.21/0.41  % Mode: cade22grackle2xfee4
% 0.21/0.41  % Steps: 25
% 0.21/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------