%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM750^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n006.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 : Mon Jul 18 13:56:04 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_frac,type,
    frac: $tType ).

thf(ty_pf,type,
    pf: frac > frac > frac ).

thf(ty_z,type,
    z: frac ).

thf(ty_y,type,
    y: frac ).

thf(ty_eq,type,
    eq: frac > frac > $o ).

thf(ty_x,type,
    x: frac ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: frac] : ( eq @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( eq @ x @ y )
     => ( ( eq @ z @ z )
       => ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: frac,X2: frac,X3: frac] :
        ( ( eq @ x @ X1 )
       => ( ( eq @ X2 @ X3 )
         => ( eq @ ( pf @ x @ X2 ) @ ( pf @ X1 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eq @ z @ z ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP4
     => ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: frac,X2: frac] :
        ( ( eq @ x @ y )
       => ( ( eq @ X1 @ X2 )
         => ( eq @ ( pf @ x @ X1 ) @ ( pf @ y @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: frac,X2: frac,X3: frac,X4: frac] :
        ( ( eq @ X1 @ X2 )
       => ( ( eq @ X3 @ X4 )
         => ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: frac] :
        ( ( eq @ x @ y )
       => ( ( eq @ z @ X1 )
         => ( eq @ ( pf @ x @ z ) @ ( pf @ y @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( eq @ x @ y ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(satz62b,conjecture,
    sP8 ).

thf(h0,negated_conjecture,
    ~ sP8,
    inference(assume_negation,[status(cth)],[satz62b]) ).

thf(1,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(6,plain,
    ( ~ sP2
    | ~ sP10
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP5
    | ~ sP4
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(e,axiom,
    sP10 ).

thf(satz56,axiom,
    sP7 ).

thf(satz37,axiom,
    sP1 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,e,satz56,satz37,h0]) ).

thf(0,theorem,
    sP8,
    inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM750^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jul  6 11:50:21 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 6
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------