%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO066^4.001 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 08:59:10 EDT 2024

% Result   : Theorem 3.15s 1.85s
% Output   : Refutation 3.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   19 (   8 unt;   7 typ;   3 def)
%            Number of atoms       :   34 (   3 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   33 (   4   ~;   1   |;   0   &;  26   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :    8 (   3   ^   5   !;   0   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
thf(irel_type,type,
    irel: $i > $i > $o ).

thf(iatom_type,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(iatom_def,definition,
    ( iatom
    = ( ^ [A: $i > $o] : A ) ) ).

thf(ior_type,type,
    ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(ior_def,definition,
    ( ior
    = ( ^ [A: $i > $o,B: $i > $o] : ( mor @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).

thf(ivalid_type,type,
    ivalid: ( $i > $o ) > $o ).

thf(ivalid_def,definition,
    ( ivalid
    = ( '!' @ $i ) ) ).

thf(o11_type,type,
    o11: $i > $o ).

thf(o21_type,type,
    o21: $i > $o ).

thf(sk2_type,type,
    sk2: $i ).

thf(1,conjecture,
    ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o21 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ! [A: $i] :
        ( ! [B: $i] :
            ( ( irel @ A @ B )
           => ( o11 @ B ) )
        | ! [B: $i] :
            ( ( irel @ A @ B )
           => ( o21 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    ~ ( o11 @ sk2 ),
    inference(cnf,[status(esa)],[7]) ).

thf(5,axiom,
    ivalid @ ( iatom @ o11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).

thf(16,plain,
    ! [A: $i] : ( o11 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(17,plain,
    ! [A: $i] : ( o11 @ A ),
    inference(cnf,[status(esa)],[16]) ).

thf(88,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[10,17]) ).

thf(89,plain,
    $false,
    inference(simp,[status(thm)],[88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO066^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n018.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 09:38:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.90/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.17/0.98  % [INFO] 	 Parsing done (134ms). 
% 1.35/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.25  % [INFO] 	 nitpick registered as external prover. 
% 1.78/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.99/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.05/1.36  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.05/1.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.05/1.37  % [INFO] 	 Type checking passed. 
% 2.05/1.37  % [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 ... 
% 3.15/1.85  % [INFO] 	 Killing All external provers ... 
% 3.15/1.85  % Time passed: 1338ms (effective reasoning time: 847ms)
% 3.15/1.85  % 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)>
% 3.15/1.85  % Axioms used in derivation (1): axiom1
% 3.15/1.85  % No. of inferences in proof: 9
% 3.15/1.85  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1338 ms resp. 847 ms w/o parsing
% 3.19/1.89  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.19/1.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------