TSTP Solution File: SWW520_5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW520_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 18:25:32 EDT 2024

% Result   : Theorem 6.19s 2.44s
% Output   : Refutation 6.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   11 (   2 unt;   0 typ;   0 def)
%            Number of atoms       :   44 (   4 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  131 (  12   ~;   5   |;   3   &; 106   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   23 (   0   ^  20   !;   3   ?;  23   :)

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

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

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

thf(hoare_1633586161_valid_type,type,
    hoare_1633586161_valid: 
      !>[TA: $tType] : ( nat > ( hoare_28830079triple @ TA ) > $o ) ).

thf(bot_bot_type,type,
    bot_bot: 
      !>[TA: $tType] : TA ).

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

thf(ga_type,type,
    ga: fun @ ( hoare_28830079triple @ a ) @ bool ).

thf(sk2_type,type,
    sk2: hoare_28830079triple @ a ).

thf(1,conjecture,
    ! [A: nat] :
      ( ? [B: hoare_28830079triple @ a] :
          ( ( member @ ( hoare_28830079triple @ a ) @ B @ ga )
          & ~ ( hoare_1633586161_valid @ a @ A @ B ) )
      | ! [B: hoare_28830079triple @ a] :
          ( ( member @ ( hoare_28830079triple @ a ) @ B @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) )
         => ( hoare_1633586161_valid @ a @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ! [A: nat] :
        ( ? [B: hoare_28830079triple @ a] :
            ( ( member @ ( hoare_28830079triple @ a ) @ B @ ga )
            & ~ ( hoare_1633586161_valid @ a @ A @ B ) )
        | ! [B: hoare_28830079triple @ a] :
            ( ( member @ ( hoare_28830079triple @ a ) @ B @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) )
           => ( hoare_1633586161_valid @ a @ A @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(128,plain,
    ~ ! [A: nat] :
        ( ? [B: hoare_28830079triple @ a] :
            ( ( member @ ( hoare_28830079triple @ a ) @ B @ ga )
            & ~ ( hoare_1633586161_valid @ a @ A @ B ) )
        | ! [B: hoare_28830079triple @ a] :
            ( ( member @ ( hoare_28830079triple @ a ) @ B @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) )
           => ( hoare_1633586161_valid @ a @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(130,plain,
    member @ ( hoare_28830079triple @ a ) @ sk2 @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ),
    inference(cnf,[status(esa)],[128]) ).

thf(56,axiom,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ( B
        = ( bot_bot @ ( fun @ TA @ bool ) ) )
     => ~ ( member @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_equals0D) ).

thf(303,plain,
    ! [TA: $tType,A: TA,B: fun @ TA @ bool] :
      ( ( B
        = ( bot_bot @ ( fun @ TA @ bool ) ) )
     => ~ ( member @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(304,plain,
    ! [TA: $tType,B: fun @ TA @ bool,A: TA] :
      ( ( B
       != ( bot_bot @ ( fun @ TA @ bool ) ) )
      | ~ ( member @ TA @ A @ B ) ),
    inference(cnf,[status(esa)],[303]) ).

thf(305,plain,
    ! [TA: $tType,B: fun @ TA @ bool,A: TA] :
      ( ( B
       != ( bot_bot @ ( fun @ TA @ bool ) ) )
      | ~ ( member @ TA @ A @ B ) ),
    inference(lifteq,[status(thm)],[304]) ).

thf(306,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
    inference(simp,[status(thm)],[305]) ).

thf(536,plain,
    $false,
    inference(rewrite,[status(thm)],[130,306]) ).

thf(537,plain,
    $false,
    inference(simp,[status(thm)],[536]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SWW520_5 : TPTP v8.2.0. Released v6.0.0.
% 0.11/0.13  % Command  : run_Leo-III %s %d SAT
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jun 19 09:45:10 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.55/1.05  % [INFO] 	 Parsing done (178ms). 
% 1.55/1.06  % [INFO] 	 Running in sequential loop mode. 
% 2.14/1.26  % [INFO] 	 nitpick registered as external prover. 
% 2.14/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.43/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ... 
% 2.62/1.42  % [INFO] 	 Axiom selection finished. Selected 125 axioms (removed 0 axioms). 
% 3.10/1.54  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.10/1.56  % [INFO] 	 Type checking passed. 
% 3.10/1.56  % [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 ... 
% 3.90/1.90  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 3.90/1.90  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 6.19/2.44  % [INFO] 	 Killing All external provers ... 
% 6.19/2.44  % Time passed: 1898ms (effective reasoning time: 1377ms)
% 6.19/2.44  % 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)>
% 6.19/2.44  % Axioms used in derivation (1): fact_11_equals0D
% 6.19/2.44  % No. of inferences in proof: 11
% 6.19/2.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1898 ms resp. 1377 ms w/o parsing
% 6.19/2.46  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.19/2.46  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------