TSTP Solution File: LCL700^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : LCL700^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 00:07:16 EDT 2024

% Result   : Theorem 3.05s 1.91s
% Output   : Refutation 3.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   17 (   7 unt;   7 typ;   6 def)
%            Number of atoms       :   31 (   6 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   61 (   8   ~;   4   |;   0   &;  44   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   49 (  49   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   24 (  11   ^  13   !;   0   ?;  24   :)

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

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

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

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(mforall_prop_def,definition,
    ( mforall_prop
    = ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
        ! [C: $i > $o] : ( A @ C @ B ) ) ) ).

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ! [D: $i] :
          ( ~ ( A @ C @ D )
          | ( B @ D ) ) ) ) ).

thf(mdia_type,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mdia_def,definition,
    ( mdia
    = ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

thf(msymmetric_def,definition,
    ( msymmetric
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i] :
          ( ( A @ B @ C )
         => ( A @ C @ B ) ) ) ) ).

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

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

thf(1,conjecture,
    ! [A: $i > $i > $o] :
      ( ( msymmetric @ A )
     => ( mvalid
        @ ( mforall_prop
          @ ^ [B: $i > $o] : ( mimplies @ B @ ( mbox @ A @ ( mdia @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o] :
        ( ( msymmetric @ A )
       => ( mvalid
          @ ( mforall_prop
            @ ^ [B: $i > $o] : ( mimplies @ B @ ( mbox @ A @ ( mdia @ A @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i > $i > $o] :
        ( ! [B: $i,C: $i] :
            ( ( A @ B @ C )
           => ( A @ C @ B ) )
       => ! [B: $i,C: $i > $o] :
            ( ~ ( C @ B )
            | ! [D: $i] :
                ( ~ ( A @ B @ D )
                | ~ ! [E: $i] :
                      ( ~ ( A @ D @ E )
                      | ~ ( C @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(14,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : LCL700^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.09/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon May 20 01:00:54 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.82/0.81  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.13/0.99  % [INFO] 	 Parsing done (168ms). 
% 1.13/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.84/1.31  % [INFO] 	 eprover registered as external prover. 
% 1.84/1.31  % [INFO] 	 cvc4 registered as external prover. 
% 1.84/1.33  % [INFO] 	 Scanning for conjecture ... 
% 2.21/1.47  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.27/1.49  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.27/1.49  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.27/1.50  % [INFO] 	 Type checking passed. 
% 2.27/1.50  % [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 ... 
% 3.05/1.91  % External prover 'e' found a proof!
% 3.05/1.91  % [INFO] 	 Killing All external provers ... 
% 3.05/1.91  % Time passed: 1431ms (effective reasoning time: 909ms)
% 3.05/1.91  % 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)>
% 3.05/1.91  % Axioms used in derivation (0): 
% 3.05/1.91  % No. of inferences in proof: 4
% 3.05/1.91  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1431 ms resp. 909 ms w/o parsing
% 3.23/1.95  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.23/1.95  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------