%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO392^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 21 08:56:37 EDT 2024

% Result   : Theorem 3.65s 2.30s
% Output   : Refutation 3.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   16 (   7 unt;   7 typ;   5 def)
%            Number of atoms       :   44 (   5 equ;   0 cnn)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :   41 (   4   ~;   1   |;   0   &;  36   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :    8 (   7   ^   1   !;   0   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: $i > $o,B: $i] :
          ~ ( A @ B ) ) ) ).

thf(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ A ) ) ) ) ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid_def,definition,
    ( mvalid
    = ( '!' @ $i ) ) ).

thf(mbox_k_type,type,
    mbox_k: ( $i > $o ) > $i > $o ).

thf(mbox_k_def,definition,
    ( mbox_k
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_k @ B @ C )
          | ( A @ C ) ) ) ) ).

thf(mdia_k_type,type,
    mdia_k: ( $i > $o ) > $i > $o ).

thf(mdia_k_def,definition,
    ( mdia_k
    = ( ^ [A: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ A ) ) ) ) ) ).

thf(p_type,type,
    p: $i > $o ).

thf(1,conjecture,
    mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    $false,
    inference(simp,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYO392^1 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 10:32:24 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.19/1.13  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.87/1.38  % [INFO] 	 Parsing done (248ms). 
% 1.87/1.40  % [INFO] 	 Running in sequential loop mode. 
% 2.63/1.84  % [INFO] 	 eprover registered as external prover. 
% 2.63/1.85  % [INFO] 	 cvc4 registered as external prover. 
% 2.63/1.85  % [INFO] 	 Scanning for conjecture ... 
% 2.95/2.06  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 3.18/2.09  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 3.18/2.09  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.28/2.10  % [INFO] 	 Type checking passed. 
% 3.28/2.10  % [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 ... 
% 3.65/2.29  % [INFO] 	 Killing All external provers ... 
% 3.65/2.30  % Time passed: 1758ms (effective reasoning time: 892ms)
% 3.65/2.30  % 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)>
% 3.65/2.30  % Axioms used in derivation (0): 
% 3.65/2.30  % No. of inferences in proof: 4
% 3.65/2.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1758 ms resp. 892 ms w/o parsing
% 3.65/2.36  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.65/2.36  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------