TSTP Solution File: SWW492_5 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW492_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n021.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 18:25:28 EDT 2024

% Result   : Theorem 7.26s 3.24s
% Output   : Refutation 7.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   17 (   8 unt;   0 typ;   0 def)
%            Number of atoms       :   60 (  37 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  142 (  27   ~;   7   |;   2   &;  94   @)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    3 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    5 (   0   ^   4   !;   1   ?;   5   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

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

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

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

thf(suc_type,type,
    suc: nat > nat ).

thf(degree_type,type,
    degree: 
      !>[TA: $tType] : ( ( poly @ TA ) > nat ) ).

thf(p_type,type,
    p: poly @ a ).

thf(1,conjecture,
    ~ ( ( ( p
         != ( zero_zero @ ( poly @ a ) ) )
       => ( ( suc @ ( degree @ a @ p ) )
          = ( zero_zero @ nat ) ) )
    <=> ( p
       != ( zero_zero @ ( poly @ a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ~ ( ( ( p
           != ( zero_zero @ ( poly @ a ) ) )
         => ( ( suc @ ( degree @ a @ p ) )
            = ( zero_zero @ nat ) ) )
      <=> ( p
         != ( zero_zero @ ( poly @ a ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(128,plain,
    ~ ~ ( ( ( ( p
             != ( zero_zero @ ( poly @ a ) ) )
           => ( ( suc @ ( degree @ a @ p ) )
              = ( zero_zero @ nat ) ) )
         => ( p
           != ( zero_zero @ ( poly @ a ) ) ) )
        & ( ( p
           != ( zero_zero @ ( poly @ a ) ) )
         => ( ( p
             != ( zero_zero @ ( poly @ a ) ) )
           => ( ( suc @ ( degree @ a @ p ) )
              = ( zero_zero @ nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(129,plain,
    ( ( ( ( p
         != ( zero_zero @ ( poly @ a ) ) )
       => ( ( suc @ ( degree @ a @ p ) )
          = ( zero_zero @ nat ) ) )
     => ( p
       != ( zero_zero @ ( poly @ a ) ) ) )
    & ( ( p
       != ( zero_zero @ ( poly @ a ) ) )
     => ( ( p
         != ( zero_zero @ ( poly @ a ) ) )
       => ( ( suc @ ( degree @ a @ p ) )
          = ( zero_zero @ nat ) ) ) ) ),
    inference(polarity_switch,[status(thm)],[128]) ).

thf(130,plain,
    ( ( p
      = ( zero_zero @ ( poly @ a ) ) )
    | ( p
      = ( zero_zero @ ( poly @ a ) ) )
    | ( ( suc @ ( degree @ a @ p ) )
      = ( zero_zero @ nat ) ) ),
    inference(cnf,[status(esa)],[129]) ).

thf(133,plain,
    ( ( p
      = ( zero_zero @ ( poly @ a ) ) )
    | ( p
      = ( zero_zero @ ( poly @ a ) ) )
    | ( ( suc @ ( degree @ a @ p ) )
      = ( zero_zero @ nat ) ) ),
    inference(lifteq,[status(thm)],[130]) ).

thf(134,plain,
    ( ( p
      = ( zero_zero @ ( poly @ a ) ) )
    | ( ( suc @ ( degree @ a @ p ) )
      = ( zero_zero @ nat ) ) ),
    inference(simp,[status(thm)],[133]) ).

thf(131,plain,
    ( ( p
     != ( zero_zero @ ( poly @ a ) ) )
    | ( p
     != ( zero_zero @ ( poly @ a ) ) ) ),
    inference(cnf,[status(esa)],[129]) ).

thf(135,plain,
    ( ( p
     != ( zero_zero @ ( poly @ a ) ) )
    | ( p
     != ( zero_zero @ ( poly @ a ) ) ) ),
    inference(lifteq,[status(thm)],[131]) ).

thf(136,plain,
    ( p
   != ( zero_zero @ ( poly @ a ) ) ),
    inference(simp,[status(thm)],[135]) ).

thf(569,plain,
    ( ( suc @ ( degree @ a @ p ) )
    = ( zero_zero @ nat ) ),
    inference(simplifyReflect,[status(thm)],[134,136]) ).

thf(53,axiom,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nat_Osimps_I2_J) ).

thf(301,plain,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(302,plain,
    ~ ? [A: nat] :
        ( ( zero_zero @ nat )
        = ( suc @ A ) ),
    inference(miniscope,[status(thm)],[301]) ).

thf(303,plain,
    ! [A: nat] :
      ( ( zero_zero @ nat )
     != ( suc @ A ) ),
    inference(cnf,[status(esa)],[302]) ).

thf(304,plain,
    ! [A: nat] :
      ( ( suc @ A )
     != ( zero_zero @ nat ) ),
    inference(lifteq,[status(thm)],[303]) ).

thf(605,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[569,304]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SWW492_5 : TPTP v8.2.0. Released v6.0.0.
% 0.00/0.09  % Command  : run_Leo-III %s %d SAT
% 0.09/0.29  % Computer : n021.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Wed Jun 19 05:44:40 EDT 2024
% 0.09/0.29  % CPUTime  : 
% 0.94/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.41/1.14  % [INFO] 	 Parsing done (255ms). 
% 1.41/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.45/1.50  % [INFO] 	 nitpick registered as external prover. 
% 2.51/1.50  % [INFO] 	 Scanning for conjecture ... 
% 2.78/1.64  % [INFO] 	 Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ... 
% 2.96/1.75  % [INFO] 	 Axiom selection finished. Selected 125 axioms (removed 0 axioms). 
% 3.51/1.94  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.51/1.96  % [INFO] 	 Type checking passed. 
% 3.51/1.97  % [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 ... 
% 4.04/2.20  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 4.04/2.21  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 7.26/3.24  % [INFO] 	 Killing All external provers ... 
% 7.26/3.24  % Time passed: 2790ms (effective reasoning time: 2078ms)
% 7.26/3.24  % 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)>
% 7.26/3.24  % Axioms used in derivation (1): fact_4_nat_Osimps_I2_J
% 7.26/3.24  % No. of inferences in proof: 17
% 7.26/3.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2790 ms resp. 2078 ms w/o parsing
% 7.26/3.27  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.26/3.27  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------