TSTP Solution File: NUM830^5 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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  7 08:00:57 EDT 2024

% Result   : Theorem 2.85s 1.83s
% Output   : Refutation 2.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   17 (   5 unt;   9 typ;   4 def)
%            Number of atoms       :   28 (  15 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :   84 (   2   ~;   0   |;   9   &;  70   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   12 (   0   ^  12   !;   0   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(n_type,type,
    n: $tType ).

thf(c0_type,type,
    c0: n ).

thf(cS_type,type,
    cS: n > n ).

thf(c_plus_type,type,
    c_plus: n > n > n ).

thf(c_star_type,type,
    c_star: n > n > n ).

thf(cPA_1_type,type,
    cPA_1: $o ).

thf(cPA_1_def,definition,
    ( cPA_1
    = ( ! [A: n] :
          ( ( c_plus @ A @ c0 )
          = A ) ) ) ).

thf(cPA_2_type,type,
    cPA_2: $o ).

thf(cPA_2_def,definition,
    ( cPA_2
    = ( ! [A: n,B: n] :
          ( ( c_plus @ A @ ( cS @ B ) )
          = ( cS @ ( c_plus @ A @ B ) ) ) ) ) ).

thf(cPA_3_type,type,
    cPA_3: $o ).

thf(cPA_3_def,definition,
    ( cPA_3
    = ( ! [A: n] :
          ( ( c_star @ A @ c0 )
          = c0 ) ) ) ).

thf(cPA_4_type,type,
    cPA_4: $o ).

thf(cPA_4_def,definition,
    ( cPA_4
    = ( ! [A: n,B: n] :
          ( ( c_star @ A @ ( cS @ B ) )
          = ( c_plus @ ( c_star @ A @ B ) @ A ) ) ) ) ).

thf(1,conjecture,
    ( ( cPA_1
      & cPA_2
      & cPA_3
      & cPA_4 )
   => ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
      = ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_THM1) ).

thf(2,negated_conjecture,
    ~ ( ( cPA_1
        & cPA_2
        & cPA_3
        & cPA_4 )
     => ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
        = ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: n] :
            ( ( c_plus @ A @ c0 )
            = A )
        & ! [A: n,B: n] :
            ( ( c_plus @ A @ ( cS @ B ) )
            = ( cS @ ( c_plus @ A @ B ) ) )
        & ! [A: n] :
            ( ( c_star @ A @ c0 )
            = c0 )
        & ! [A: n,B: n] :
            ( ( c_star @ A @ ( cS @ B ) )
            = ( c_plus @ ( c_star @ A @ B ) @ A ) ) )
     => ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
        = ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(17,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.17/0.17  % Command  : run_Leo-III %s %d
% 0.18/0.39  % Computer : n023.cluster.edu
% 0.18/0.39  % Model    : x86_64 x86_64
% 0.18/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39  % Memory   : 8042.1875MB
% 0.18/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39  % CPULimit : 300
% 0.18/0.39  % WCLimit  : 300
% 0.18/0.39  % DateTime : Mon May  6 12:37:39 EDT 2024
% 0.18/0.39  % CPUTime  : 
% 0.95/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.33/1.07  % [INFO] 	 Parsing done (160ms). 
% 1.36/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.36  % [INFO] 	 eprover registered as external prover. 
% 1.84/1.36  % [INFO] 	 cvc4 registered as external prover. 
% 1.84/1.37  % [INFO] 	 Scanning for conjecture ... 
% 1.96/1.45  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.04/1.47  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.04/1.47  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.04/1.47  % [INFO] 	 Type checking passed. 
% 2.04/1.47  % [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 ... 
% 2.85/1.82  % External prover 'e' found a proof!
% 2.85/1.83  % [INFO] 	 Killing All external provers ... 
% 2.85/1.83  % Time passed: 1283ms (effective reasoning time: 746ms)
% 2.85/1.83  % 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)>
% 2.85/1.83  % Axioms used in derivation (0): 
% 2.85/1.83  % No. of inferences in proof: 4
% 2.85/1.83  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1283 ms resp. 746 ms w/o parsing
% 2.85/1.86  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.85/1.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------