%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SYO053^2 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n029.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 20:50:01 EDT 2024

% Result   : Theorem 3.02s 1.61s
% Output   : Refutation 3.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   10 (   6 unt;   0 typ;   3 def)
%            Number of atoms       :   20 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   30 (  11   ~;   0   |;   0   &;  19   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-3 aty)
%            Number of variables   :   13 (   3   ^   6   !;   4   ?;  13   :)

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

thf(mtrue_type,type,
    mtrue: $i > $o ).

thf(mtrue_def,definition,
    ( mtrue
    = ( ^ [A: $i] : $true ) ) ).

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

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

thf(1,conjecture,
    ? [A: $i > $i > $o] :
      ~ ( mvalid @ ( mdia @ A @ mtrue ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ? [A: $i > $i > $o] :
        ~ ( mvalid @ ( mdia @ A @ mtrue ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ~ ~ ~ ~ ! [A: $i > $i > $o,B: $i] :
            ? [C: $i] : ( A @ B @ C ),
    inference(miniscope,[status(thm)],[3]) ).

thf(5,plain,
    ! [B: $i,A: $i > $i > $o] : ( A @ B @ ( sk1 @ B @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(7,plain,
    $false,
    inference(prim_subst,[status(thm)],[5:[bind(A,$thf( ^ [C: $i] : ^ [D: $i] : $false ))]]) ).

thf(12,plain,
    $false,
    inference(simp,[status(thm)],[7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO053^2 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n029.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 : Sun Jun 23 09:14:40 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.87/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.99  % [INFO] 	 Parsing done (136ms). 
% 1.20/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.87/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.87/1.21  % [INFO] 	 Scanning for conjecture ... 
% 2.21/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.21/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.21/1.33  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.21/1.33  % [INFO] 	 Type checking passed. 
% 2.21/1.33  % [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 ... 
% 2.80/1.60  % [INFO] 	 Killing All external provers ... 
% 3.02/1.61  % Time passed: 1089ms (effective reasoning time: 606ms)
% 3.02/1.61  % 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)>
% 3.02/1.61  % Axioms used in derivation (0): 
% 3.02/1.61  % No. of inferences in proof: 7
% 3.02/1.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1089 ms resp. 606 ms w/o parsing
% 3.02/1.63  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.02/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------