TSTP Solution File: ITP039^2 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP039^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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  : 300s
% DateTime : Tue May  7 07:47:19 EDT 2024

% Result   : Theorem 11.74s 4.02s
% Output   : Refutation 11.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   19 (   4 unt;  15 typ;   0 def)
%            Number of atoms       :   48 (   6 equ;   0 cnn)
%            Maximal formula atoms :    1 (  12 avg)
%            Number of connectives :  334 (   2   ~;   0   |;   0   &; 324   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   2 avg)
%            Number of types       :    9 (   8 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   9 con; 0-6 aty)
%            Number of variables   :   30 (   0   ^  16   !;   0   ?;  30   :)
%                                         (  14  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(product_unit_type,type,
    product_unit: $tType ).

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

thf(sz_type,type,
    sz: $tType ).

thf(sf_type,type,
    sf: $tType ).

thf(sc_type,type,
    sc: $tType ).

thf(c_type,type,
    c: $tType ).

thf(b_type,type,
    b: $tType ).

thf(a_type,type,
    a: $tType ).

thf(denotational_Iagree_type,type,
    denotational_Iagree: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( set @ ( sum_sum @ TC @ ( sum_sum @ TB @ TA ) ) ) > $o ) ).

thf(denotational_Vagree_type,type,
    denotational_Vagree: 
      !>[TA: $tType] : ( ( product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) ) > ( product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) ) > ( set @ ( sum_sum @ TA @ TA ) ) > $o ) ).

thf(denotational_fml_sem_type,type,
    denotational_fml_sem: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( denota1663640101rp_ext @ TC @ TB @ TA @ product_unit ) > ( formula @ TC @ TB @ TA ) > ( set @ ( product_prod @ ( finite_Cartesian_vec @ real @ TA ) @ ( finite_Cartesian_vec @ real @ TA ) ) ) ) ).

thf(static_FVF_type,type,
    static_FVF: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( formula @ TC @ TB @ TA ) > ( set @ ( sum_sum @ TA @ TA ) ) ) ).

thf(static_SIGF_type,type,
    static_SIGF: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( formula @ TC @ TB @ TA ) > ( set @ ( sum_sum @ TC @ ( sum_sum @ TB @ TA ) ) ) ) ).

thf(member_type,type,
    member: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).

thf(phi_type,type,
    phi: formula @ a @ b @ c ).

thf(1,conjecture,
    ( ( ! [A: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),B: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),C: denota1663640101rp_ext @ a @ b @ c @ product_unit,D: denota1663640101rp_ext @ a @ b @ c @ product_unit] :
          ( ( denotational_Iagree @ a @ b @ c @ C @ D @ ( static_SIGF @ a @ b @ c @ phi ) )
         => ( ( denotational_Vagree @ c @ A @ B @ ( static_FVF @ a @ b @ c @ phi ) )
           => ( ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ A @ ( denotational_fml_sem @ a @ b @ c @ C @ phi ) )
              = ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ B @ ( denotational_fml_sem @ a @ b @ c @ D @ phi ) ) ) ) ) )
    = ( ! [A: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),B: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),C: denota1663640101rp_ext @ a @ b @ c @ product_unit,D: denota1663640101rp_ext @ a @ b @ c @ product_unit] :
          ( ( denotational_Iagree @ a @ b @ c @ C @ D @ ( static_SIGF @ a @ b @ c @ phi ) )
         => ( ( denotational_Vagree @ c @ A @ B @ ( static_FVF @ a @ b @ c @ phi ) )
           => ( ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ A @ ( denotational_fml_sem @ a @ b @ c @ C @ phi ) )
              = ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ B @ ( denotational_fml_sem @ a @ b @ c @ D @ phi ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( ! [A: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),B: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),C: denota1663640101rp_ext @ a @ b @ c @ product_unit,D: denota1663640101rp_ext @ a @ b @ c @ product_unit] :
          ( ( denotational_Iagree @ a @ b @ c @ C @ D @ ( static_SIGF @ a @ b @ c @ phi ) )
         => ( ( denotational_Vagree @ c @ A @ B @ ( static_FVF @ a @ b @ c @ phi ) )
           => ( ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ A @ ( denotational_fml_sem @ a @ b @ c @ C @ phi ) )
              = ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ B @ ( denotational_fml_sem @ a @ b @ c @ D @ phi ) ) ) ) ) )
   != ( ! [A: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),B: product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ),C: denota1663640101rp_ext @ a @ b @ c @ product_unit,D: denota1663640101rp_ext @ a @ b @ c @ product_unit] :
          ( ( denotational_Iagree @ a @ b @ c @ C @ D @ ( static_SIGF @ a @ b @ c @ phi ) )
         => ( ( denotational_Vagree @ c @ A @ B @ ( static_FVF @ a @ b @ c @ phi ) )
           => ( ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ A @ ( denotational_fml_sem @ a @ b @ c @ C @ phi ) )
              = ( member @ ( product_prod @ ( finite_Cartesian_vec @ real @ c ) @ ( finite_Cartesian_vec @ real @ c ) ) @ B @ ( denotational_fml_sem @ a @ b @ c @ D @ phi ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(281,plain,
    ~ $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(282,plain,
    $false,
    inference(simp,[status(thm)],[281]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : ITP039^2 : TPTP v8.1.2. Released v7.5.0.
% 0.04/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n020.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 14:34:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.94/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.90/1.10  % [INFO] 	 Parsing done (260ms). 
% 1.90/1.11  % [INFO] 	 Running in sequential loop mode. 
% 2.60/1.32  % [INFO] 	 eprover registered as external prover. 
% 2.60/1.32  % [INFO] 	 cvc4 registered as external prover. 
% 2.76/1.32  % [INFO] 	 Scanning for conjecture ... 
% 3.08/1.44  % [INFO] 	 Found a conjecture and 281 axioms. Running axiom selection ... 
% 3.43/1.54  % [INFO] 	 Axiom selection finished. Selected 278 axioms (removed 3 axioms). 
% 4.51/1.83  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.61/1.85  % [INFO] 	 Type checking passed. 
% 4.61/1.86  % [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 ... 
% 11.74/4.01  % [INFO] 	 Killing All external provers ... 
% 11.74/4.01  % Time passed: 3497ms (effective reasoning time: 2900ms)
% 11.74/4.01  % 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)>
% 11.74/4.01  % Axioms used in derivation (0): 
% 11.74/4.01  % No. of inferences in proof: 4
% 11.74/4.02  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3497 ms resp. 2900 ms w/o parsing
% 11.97/4.05  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.97/4.05  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------