TSTP Solution File: SWW499_5 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW499_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n026.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 : Mon Jun 24 18:25:29 EDT 2024

% Result   : Theorem 213.17s 37.83s
% Output   : Refutation 213.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   27 (  19 unt;   0 typ;   0 def)
%            Number of atoms       :   40 (  25 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  191 (  14   ~;   6   |;   2   &; 164   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :   25 (   0   ^  17   !;   8   ?;  25   :)

% Comments : 
%------------------------------------------------------------------------------
thf(complex_type,type,
    complex: $tType ).

thf(bool_type,type,
    bool: $tType ).

thf(int_type,type,
    int: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(real_type,type,
    real: $tType ).

thf(times_times_type,type,
    times_times: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(zero_zero_type,type,
    zero_zero: 
      !>[TA: $tType] : TA ).

thf(bit0_type,type,
    bit0: int > int ).

thf(bit1_type,type,
    bit1: int > int ).

thf(pls_type,type,
    pls: int ).

thf(number_number_of_type,type,
    number_number_of: 
      !>[TA: $tType] : ( int > TA ) ).

thf(even_odd_even_type,type,
    even_odd_even: 
      !>[TA: $tType] : ( TA > $o ) ).

thf(na_type,type,
    na: nat ).

thf(sk1_type,type,
    sk1: nat > nat ).

thf(191,axiom,
    even_odd_even @ nat @ na,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_e) ).

thf(703,plain,
    even_odd_even @ nat @ na,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(142,axiom,
    ! [A: nat] :
      ( ( even_odd_even @ nat @ A )
    <=> ? [B: nat] :
          ( A
          = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_even__mult__two__ex) ).

thf(515,plain,
    ! [A: nat] :
      ( ( ( even_odd_even @ nat @ A )
       => ? [B: nat] :
            ( A
            = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) )
      & ( ? [B: nat] :
            ( A
            = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
       => ( even_odd_even @ nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(516,plain,
    ( ! [A: nat] :
        ( ( even_odd_even @ nat @ A )
       => ? [B: nat] :
            ( A
            = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) )
    & ! [A: nat] :
        ( ? [B: nat] :
            ( A
            = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
       => ( even_odd_even @ nat @ A ) ) ),
    inference(miniscope,[status(thm)],[515]) ).

thf(518,plain,
    ! [A: nat] :
      ( ~ ( even_odd_even @ nat @ A )
      | ( A
        = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( sk1 @ A ) ) ) ),
    inference(cnf,[status(esa)],[516]) ).

thf(521,plain,
    ! [A: nat] :
      ( ( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( sk1 @ A ) )
        = A )
      | ~ ( even_odd_even @ nat @ A ) ),
    inference(lifteq,[status(thm)],[518]) ).

thf(103,axiom,
    ( ( zero_zero @ int )
    = ( number_number_of @ int @ pls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zero__is__num__zero) ).

thf(383,plain,
    ( ( zero_zero @ int )
    = ( number_number_of @ int @ pls ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(384,plain,
    ( ( number_number_of @ int @ pls )
    = ( zero_zero @ int ) ),
    inference(lifteq,[status(thm)],[383]) ).

thf(87,axiom,
    ! [A: int] :
      ( ( number_number_of @ int @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_number__of__is__id) ).

thf(324,plain,
    ! [A: int] :
      ( ( number_number_of @ int @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(325,plain,
    ! [A: int] :
      ( ( number_number_of @ int @ A )
      = A ),
    inference(cnf,[status(esa)],[324]) ).

thf(326,plain,
    ! [A: int] :
      ( ( number_number_of @ int @ A )
      = A ),
    inference(lifteq,[status(thm)],[325]) ).

thf(4253,plain,
    ( pls
    = ( zero_zero @ int ) ),
    inference(rewrite,[status(thm)],[384,326]) ).

thf(14764,plain,
    ! [A: nat] :
      ( ( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ ( zero_zero @ int ) ) ) ) @ ( sk1 @ A ) )
        = A )
      | ~ ( even_odd_even @ nat @ A ) ),
    inference(rewrite,[status(thm)],[521,4253]) ).

thf(1,conjecture,
    ? [A: nat] :
      ( na
      = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ? [A: nat] :
        ( na
        = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(192,plain,
    ~ ? [A: nat] :
        ( na
        = ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(193,plain,
    ! [A: nat] :
      ( na
     != ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
    inference(cnf,[status(esa)],[192]) ).

thf(194,plain,
    ! [A: nat] :
      ( na
     != ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) ),
    inference(lifteq,[status(thm)],[193]) ).

thf(4288,plain,
    ! [A: nat] :
      ( na
     != ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ ( zero_zero @ int ) ) ) ) @ A ) ),
    inference(rewrite,[status(thm)],[194,4253]) ).

thf(14816,plain,
    ! [B: nat,A: nat] :
      ( ~ ( even_odd_even @ nat @ A )
      | ( A != na )
      | ( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ ( zero_zero @ int ) ) ) ) @ ( sk1 @ A ) )
       != ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ ( zero_zero @ int ) ) ) ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14764,4288]) ).

thf(14817,plain,
    ! [A: nat] :
      ( ~ ( even_odd_even @ nat @ A )
      | ( A != na ) ),
    inference(pattern_uni,[status(thm)],[14816:[bind(A,$thf( C )),bind(B,$thf( sk1 @ C ))]]) ).

thf(14991,plain,
    ~ ( even_odd_even @ nat @ na ),
    inference(simp,[status(thm)],[14817]) ).

thf(35348,plain,
    $false,
    inference(rewrite,[status(thm)],[703,14991]) ).

thf(35349,plain,
    $false,
    inference(simp,[status(thm)],[35348]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW499_5 : TPTP v8.2.0. Released v6.0.0.
% 0.11/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n026.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
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jun 19 07:09:10 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.94/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.63/1.08  % [INFO] 	 Parsing done (185ms). 
% 1.63/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.88/1.28  % [INFO] 	 nitpick registered as external prover. 
% 1.88/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.37  % [INFO] 	 Found a conjecture (or negated_conjecture) and 191 axioms. Running axiom selection ... 
% 2.32/1.45  % [INFO] 	 Axiom selection finished. Selected 189 axioms (removed 2 axioms). 
% 2.83/1.56  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.83/1.58  % [INFO] 	 Type checking passed. 
% 2.83/1.58  % [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 ... 
% 213.17/37.83  % [INFO] 	 Killing All external provers ... 
% 213.17/37.83  % Time passed: 37290ms (effective reasoning time: 36740ms)
% 213.17/37.83  % 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)>
% 213.17/37.83  % Axioms used in derivation (4): fact_0_e, fact_25_even__mult__two__ex, fact_37_zero__is__num__zero, fact_35_number__of__is__id
% 213.17/37.83  % No. of inferences in proof: 27
% 213.17/37.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 37290 ms resp. 36740 ms w/o parsing
% 213.17/37.85  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 213.17/37.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------