TSTP Solution File: SYO500^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO500^1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %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  : 600s
% DateTime : Thu Jul 21 17:35:10 EDT 2022

% Result   : Theorem 0.20s 0.46s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    3
% Syntax   : Number of formulae    :  127 (  14 unt;   2 typ;   0 def)
%            Number of atoms       : 1992 ( 444 equ;   0 cnn)
%            Maximal formula atoms :    6 (  15 avg)
%            Number of connectives : 1011 (  32   ~; 300   |;   0   &; 679   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0   ^   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_f,type,
    f: $o > $o ).

thf(tp_x,type,
    x: $o ).

thf(1,conjecture,
    ( ( f @ ( f @ ( f @ x ) ) )
    = ( f @ x ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = ( f @ x ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = ( f @ x ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
       != ( f @ x ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
       != ( f @ x ) ) )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = ( f @ x ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
          | ( f @ x ) )
      | ~ ( ~ ( f @ ( f @ ( f @ x ) ) )
          | ~ ( f @ x ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = ( f @ x ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
          | ( f @ x ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ~ ( ~ ( f @ ( f @ ( f @ x ) ) )
          | ~ ( f @ x ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      | ( f @ x ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ~ ( f @ ( f @ ( f @ x ) ) )
      | ~ ( f @ x ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ( ~ ( f @ ( f @ ( f @ x ) ) ) )
      = $true )
    | ( ( ~ ( f @ x ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( ~ ( f @ x ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ( f @ x )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(17,plain,
    ( ( ( f @ x )
      = $true )
    | ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ x ) )
      = $false ) ),
    inference(fac_restr,[status(thm)],[13]) ).

thf(18,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( ( f @ x )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false ) ),
    inference(fac_restr,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
            | ( f @ x ) )
        | ~ ( ~ ( f @ ( f @ ( f @ x ) ) )
            | ~ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ x ) )
      = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ( ~ ( ( f @ x )
            | ( f @ ( f @ ( f @ x ) ) ) )
        | ~ ( ~ ( f @ x )
            | ~ ( f @ ( f @ ( f @ x ) ) ) ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ( ( f @ x )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ( ~ ( ( f @ ( f @ ( f @ x ) ) )
            | ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(26,plain,
    ( ( ( ~ ( ~ ( f @ x )
            | ~ ( f @ ( f @ ( f @ x ) ) ) ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(27,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        | ( f @ x ) )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(30,plain,
    ( ( ( ~ ( f @ x )
        | ~ ( f @ ( f @ ( f @ x ) ) ) )
      = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(31,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ x )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(34,plain,
    ( ( ( ~ ( f @ x ) )
      = $true )
    | ( ( ~ ( f @ ( f @ ( f @ x ) ) ) )
      = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(36,plain,
    ( ( ( f @ x )
      = $false )
    | ( ( ~ ( f @ ( f @ ( f @ x ) ) ) )
      = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(38,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ( ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[20]) ).

thf(40,plain,
    ( ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[20]) ).

thf(41,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(extuni,[status(esa)],[22]) ).

thf(42,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[22]) ).

thf(43,plain,
    ( ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[8]) ).

thf(44,plain,
    ( ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[8]) ).

thf(45,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(sim,[status(thm)],[31]) ).

thf(46,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $false ) ),
    inference(sim,[status(thm)],[38]) ).

thf(47,plain,
    ( ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[8]) ).

thf(48,plain,
    ( ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[8]) ).

thf(51,plain,
    ( ( ( f @ x )
      = $true )
    | ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ x ) )
      = $false ) ),
    inference(fac_restr,[status(thm)],[13]) ).

thf(52,plain,
    ( ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(extuni,[status(esa)],[51]) ).

thf(53,plain,
    ( ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(extuni,[status(esa)],[51]) ).

thf(54,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ x ) )
      = $false )
    | ( ( f @ x )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $true ) ),
    inference(res,[status(thm)],[16,13]) ).

thf(57,plain,
    ( ( ( ( f @ x )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(res,[status(thm)],[16,13]) ).

thf(58,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( ( f @ x )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false ) ),
    inference(fac_restr,[status(thm)],[16]) ).

thf(59,plain,
    ( ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(extuni,[status(esa)],[57]) ).

thf(60,plain,
    ( ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[57]) ).

thf(63,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ x )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[54]) ).

thf(64,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ x )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[54]) ).

thf(65,plain,
    ( ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[58]) ).

thf(66,plain,
    ( ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[58]) ).

thf(69,plain,
    ( ( ( ( f @ x )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ x )
      = $false ) ),
    inference(res,[status(thm)],[39,16]) ).

thf(71,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ x ) )
      = $false )
    | ( ( f @ x )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(res,[status(thm)],[39,16]) ).

thf(72,plain,
    ( ( ( ( f @ x )
        = ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(res,[status(thm)],[39,16]) ).

thf(76,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(extuni,[status(esa)],[72]) ).

thf(77,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $true )
    | ( ( f @ x )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[71]) ).

thf(79,plain,
    ( ( ( f @ x )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(extuni,[status(esa)],[69]) ).

thf(85,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(sim,[status(thm)],[77]) ).

thf(86,plain,
    ( ( ( f @ x )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(sim,[status(thm)],[79]) ).

thf(97,plain,
    ( ( ( ( f @ x )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ x )
      = $false ) ),
    inference(res,[status(thm)],[40,16]) ).

thf(98,plain,
    ( ( ( ( f @ x )
        = ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(res,[status(thm)],[40,16]) ).

thf(102,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( ( f @ x )
      = $true )
    | ( x = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(res,[status(thm)],[40,13]) ).

thf(106,plain,
    ( ( ( f @ x )
      = $true )
    | ( x = $false )
    | ( ( f @ x )
      = $true )
    | ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(extuni,[status(esa)],[102]) ).

thf(110,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[98]) ).

thf(112,plain,
    ( ( ( f @ x )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[97]) ).

thf(121,plain,
    ( ( ( f @ x )
      = $true )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(sim,[status(thm)],[106]) ).

thf(122,plain,
    ( ( ( f @ x )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(sim,[status(thm)],[112]) ).

thf(123,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true ) ),
    inference(res,[status(thm)],[41,41]) ).

thf(125,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(res,[status(thm)],[41,41]) ).

thf(133,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ x )
      = $true )
    | ( x = $true ) ),
    inference(res,[status(thm)],[41,39]) ).

thf(134,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ x ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(res,[status(thm)],[41,39]) ).

thf(135,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $false ) ),
    inference(res,[status(thm)],[41,16]) ).

thf(137,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(res,[status(thm)],[41,16]) ).

thf(139,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ x ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $true ) ),
    inference(res,[status(thm)],[41,13]) ).

thf(140,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(res,[status(thm)],[41,13]) ).

thf(143,plain,
    ( ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[140]) ).

thf(144,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[139]) ).

thf(146,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[137]) ).

thf(151,plain,
    ( ( ( f @ x )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[135]) ).

thf(152,plain,
    ( ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[134]) ).

thf(154,plain,
    ( ( x = $true )
    | ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ x )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[133]) ).

thf(156,plain,
    ( ( x = $true )
    | ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(extuni,[status(esa)],[133]) ).

thf(162,plain,
    ( ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(extuni,[status(esa)],[125]) ).

thf(164,plain,
    ( ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(extuni,[status(esa)],[125]) ).

thf(166,plain,
    ( ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ x )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[123]) ).

thf(168,plain,
    ( ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(extuni,[status(esa)],[123]) ).

thf(170,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true ) ),
    inference(sim,[status(thm)],[144]) ).

thf(171,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(sim,[status(thm)],[146]) ).

thf(172,plain,
    ( ( ( f @ x )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(sim,[status(thm)],[151]) ).

thf(173,plain,
    ( ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(sim,[status(thm)],[152]) ).

thf(174,plain,
    ( ( x = $true )
    | ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(sim,[status(thm)],[156]) ).

thf(175,plain,
    ( ( x = $true )
    | ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(sim,[status(thm)],[154]) ).

thf(176,plain,
    ( ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(sim,[status(thm)],[164]) ).

thf(177,plain,
    ( ( ( f @ ( f @ x ) )
      = $true )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(sim,[status(thm)],[162]) ).

thf(178,plain,
    ( ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(sim,[status(thm)],[168]) ).

thf(179,plain,
    ( ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(sim,[status(thm)],[166]) ).

thf(186,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(res,[status(thm)],[42,40]) ).

thf(188,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(res,[status(thm)],[42,40]) ).

thf(200,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $true ) ),
    inference(res,[status(thm)],[42,13]) ).

thf(201,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(res,[status(thm)],[42,13]) ).

thf(203,plain,
    ( ( ( ( f @ ( f @ ( f @ x ) ) )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(res,[status(thm)],[42,13]) ).

thf(204,plain,
    ( ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[203]) ).

thf(207,plain,
    ( ( ( f @ x )
      = $true )
    | ( x = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(extuni,[status(esa)],[201]) ).

thf(210,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[200]) ).

thf(224,plain,
    ( ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[188]) ).

thf(226,plain,
    ( ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[186]) ).

thf(233,plain,
    ( ( ( f @ x )
      = $true )
    | ( x = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(sim,[status(thm)],[207]) ).

thf(234,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( x = $false ) ),
    inference(sim,[status(thm)],[210]) ).

thf(235,plain,
    ( ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(sim,[status(thm)],[224]) ).

thf(236,plain,
    ( ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( ( f @ x )
      = $false ) ),
    inference(sim,[status(thm)],[226]) ).

thf(248,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $false ) ),
    inference(res,[status(thm)],[43,16]) ).

thf(250,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ x ) )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $false ) ),
    inference(res,[status(thm)],[43,16]) ).

thf(254,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $true )
    | ( x = $true ) ),
    inference(extuni,[status(esa)],[250]) ).

thf(259,plain,
    ( ( ( f @ x )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $false )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[248]) ).

thf(268,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $false )
    | ( x = $true )
    | ( ( f @ x )
      = $true ) ),
    inference(sim,[status(thm)],[254]) ).

thf(269,plain,
    ( ( ( f @ x )
      = $false )
    | ( x = $true )
    | ( ( f @ ( f @ x ) )
      = $false ) ),
    inference(sim,[status(thm)],[259]) ).

thf(275,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ x ) )
      = $false )
    | ( x = $false )
    | ( ( f @ ( f @ ( f @ x ) ) )
      = $true ) ),
    inference(res,[status(thm)],[44,13]) ).

thf(277,plain,
    ( ( ( ( f @ ( f @ x ) )
        = ( f @ ( f @ ( f @ x ) ) ) )
      = $false )
    | ( x = $false )
    | ( ( f @ x )
      = $true ) ),
    inference(res,[status(thm)],[44,13]) ).

thf(281,plain,
    ( ( ( f @ x )
      = $true )
    | ( x = $false )
    | ( ( f @ x )
      = $true )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(extuni,[status(esa)],[277]) ).

thf(284,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( x = $false )
    | ( ( f @ x )
      = $false )
    | ( x = $false ) ),
    inference(extuni,[status(esa)],[275]) ).

thf(287,plain,
    ( ( ( f @ x )
      = $true )
    | ( x = $false )
    | ( ( f @ ( f @ x ) )
      = $true ) ),
    inference(sim,[status(thm)],[281]) ).

thf(288,plain,
    ( ( ( f @ ( f @ ( f @ x ) ) )
      = $true )
    | ( x = $false )
    | ( ( f @ x )
      = $false ) ),
    inference(sim,[status(thm)],[284]) ).

thf(289,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[8,288,287,269,268,236,235,234,233,204,179,178,177,176,175,174,173,172,171,170,143,122,121,110,86,85,76,66,65,64,63,60,59,53,52,48,47,46,45,44,43,16,13]) ).

thf(290,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[289]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYO500^1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n020.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 : Fri Jul  8 23:10:28 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.20/0.46  
% 0.20/0.46  ********************************
% 0.20/0.46  *   All subproblems solved!    *
% 0.20/0.46  ********************************
% 0.20/0.46  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:289,loop_count:10,foatp_calls:3,translation:fof_full)
% 0.20/0.47  
% 0.20/0.47  %**** Beginning of derivation protocol ****
% 0.20/0.47  % SZS output start CNFRefutation
% See solution above
% 0.20/0.47  
% 0.20/0.47  %**** End of derivation protocol ****
% 0.20/0.47  %**** no. of clauses in derivation: 125 ****
% 0.20/0.47  %**** clause counter: 289 ****
% 0.20/0.47  
% 0.20/0.47  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:289,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------