TSTP Solution File: SYO414^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO414^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 08:56:42 EDT 2024

% Result   : Theorem 3.80s 2.36s
% Output   : Refutation 4.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   19 (   6 unt;  10 typ;   5 def)
%            Number of atoms       :   72 (   5 equ;   0 cnn)
%            Maximal formula atoms :   19 (   8 avg)
%            Number of connectives :  101 (  22   ~;  12   |;   0   &;  67   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :   13 (   6   ^   7   !;   0   ?;  13   :)

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

thf(mand_type,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).

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

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

thf(rel_k_type,type,
    rel_k: $i > $i > $o ).

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(q_type,type,
    q: $i > $o ).

thf(r_type,type,
    r: $i > $o ).

thf(1,conjecture,
    mvalid @ ( mimplies @ ( mdia_k @ ( mimplies @ p @ ( mand @ q @ r ) ) ) @ ( mand @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ q ) ) @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ r ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mimplies @ ( mdia_k @ ( mimplies @ p @ ( mand @ q @ r ) ) ) @ ( mand @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ q ) ) @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ r ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i] :
        ( ! [B: $i] :
            ( ~ ( rel_k @ A @ B )
            | ~ ( ~ ( p @ B )
                | ~ ( ~ ( q @ B )
                    | ~ ( r @ B ) ) ) )
        | ~ ( ~ ( ~ ! [B: $i] :
                      ( ~ ( rel_k @ A @ B )
                      | ( p @ B ) )
                | ~ ! [B: $i] :
                      ( ~ ( rel_k @ A @ B )
                      | ~ ( q @ B ) ) )
            | ~ ( ~ ! [B: $i] :
                      ( ~ ( rel_k @ A @ B )
                      | ( p @ B ) )
                | ~ ! [B: $i] :
                      ( ~ ( rel_k @ A @ B )
                      | ~ ( r @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(15,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SYO414^1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n016.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 : Mon May 20 09:59:24 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.09/1.03  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.61/1.26  % [INFO] 	 Parsing done (230ms). 
% 1.61/1.28  % [INFO] 	 Running in sequential loop mode. 
% 2.31/1.66  % [INFO] 	 eprover registered as external prover. 
% 2.31/1.66  % [INFO] 	 cvc4 registered as external prover. 
% 2.31/1.67  % [INFO] 	 Scanning for conjecture ... 
% 2.75/1.85  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.75/1.88  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.75/1.89  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.75/1.89  % [INFO] 	 Type checking passed. 
% 2.75/1.89  % [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 ... 
% 3.80/2.35  % External prover 'e' found a proof!
% 3.80/2.35  % [INFO] 	 Killing All external provers ... 
% 3.80/2.36  % Time passed: 1853ms (effective reasoning time: 1073ms)
% 3.80/2.36  % 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)>
% 3.80/2.36  % Axioms used in derivation (0): 
% 3.80/2.36  % No. of inferences in proof: 4
% 3.80/2.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1853 ms resp. 1073 ms w/o parsing
% 4.03/2.41  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.03/2.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------