TSTP Solution File: SEU930^5 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU930^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 : Tue May 21 03:44:16 EDT 2024

% Result   : Theorem 5.59s 2.52s
% Output   : Refutation 5.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   22 (   9 unt;   3 typ;   0 def)
%            Number of atoms       :   40 (  39 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   95 (  13   ~;   9   |;   3   &;  61   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (  10   ^  14   !;   0   ?;  24   :)

% Comments : 
%------------------------------------------------------------------------------
thf(f_type,type,
    f: $i > $i ).

thf(g_type,type,
    g: $i > $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(1,conjecture,
    ( ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
      = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) )
   => ! [A: $i] :
        ( ( ( ( g @ A )
            = A )
          & ! [B: $i] :
              ( ( ( g @ B )
                = B )
             => ( B = A ) ) )
       => ( ( f @ A )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM171A_pme) ).

thf(2,negated_conjecture,
    ~ ( ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
        = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) )
     => ! [A: $i] :
          ( ( ( ( g @ A )
              = A )
            & ! [B: $i] :
                ( ( ( g @ B )
                  = B )
               => ( B = A ) ) )
         => ( ( f @ A )
            = A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
        = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) )
     => ! [A: $i] :
          ( ( ( ( g @ A )
              = A )
            & ! [B: $i] :
                ( ( ( g @ B )
                  = B )
               => ( B = A ) ) )
         => ( ( f @ A )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ( ( g @ sk1 )
    = sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ( ( g @ sk1 )
    = sk1 ),
    inference(lifteq,[status(thm)],[6]) ).

thf(7,plain,
    ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
    = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ( ( ^ [A: $i] : ( g @ ( f @ A ) ) )
    = ( ^ [A: $i] : ( f @ ( g @ A ) ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(12,plain,
    ! [A: $i] :
      ( ( g @ ( f @ A ) )
      = ( f @ ( g @ A ) ) ),
    inference(func_ext,[status(esa)],[11]) ).

thf(5,plain,
    ! [A: $i] :
      ( ( ( g @ A )
       != A )
      | ( A = sk1 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: $i] :
      ( ( ( g @ A )
       != A )
      | ( A = sk1 ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ( ( f @ ( g @ A ) )
       != B )
      | ( B = sk1 )
      | ( ( g @ ( f @ A ) )
       != ( g @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,9]) ).

thf(43,plain,
    ! [A: $i] :
      ( ( ( f @ ( g @ A ) )
       != ( f @ A ) )
      | ( ( f @ A )
        = sk1 ) ),
    inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( C )),bind(B,$thf( f @ C ))]]) ).

thf(44,plain,
    ! [A: $i] :
      ( ( ( f @ ( g @ A ) )
       != ( f @ A ) )
      | ( ( f @ A )
        = sk1 ) ),
    inference(simp,[status(thm)],[43]) ).

thf(417,plain,
    ! [A: $i] :
      ( ( ( f @ sk1 )
       != ( f @ A ) )
      | ( ( f @ A )
        = sk1 )
      | ( ( g @ sk1 )
       != ( g @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10,44]) ).

thf(418,plain,
    ( ( ( f @ sk1 )
     != ( f @ sk1 ) )
    | ( ( f @ sk1 )
      = sk1 ) ),
    inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( sk1 ))]]) ).

thf(428,plain,
    ( ( f @ sk1 )
    = sk1 ),
    inference(simp,[status(thm)],[418]) ).

thf(4,plain,
    ( ( f @ sk1 )
   != sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ( ( f @ sk1 )
   != sk1 ),
    inference(lifteq,[status(thm)],[4]) ).

thf(430,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[428,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SEU930^5 : TPTP v8.2.0. Released v4.0.0.
% 0.17/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n027.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sun May 19 15:23:54 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.95/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.06  % [INFO] 	 Parsing done (145ms). 
% 1.35/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.37  % [INFO] 	 nitpick registered as external prover. 
% 1.80/1.37  % [INFO] 	 Scanning for conjecture ... 
% 1.99/1.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.99/1.46  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.99/1.46  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.99/1.47  % [INFO] 	 Type checking passed. 
% 1.99/1.47  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 5.59/2.52  % [INFO] 	 Killing All external provers ... 
% 5.59/2.52  % Time passed: 1968ms (effective reasoning time: 1436ms)
% 5.59/2.52  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.59/2.52  % Axioms used in derivation (0): 
% 5.59/2.52  % No. of inferences in proof: 19
% 5.59/2.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1968 ms resp. 1436 ms w/o parsing
% 5.59/2.56  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.59/2.56  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------