%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : ITP010^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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  7 10:35:43 EDT 2024

% Result   : Theorem 3.54s 2.03s
% Output   : Refutation 3.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   11 (   2 unt;   7 typ;   0 def)
%            Number of atoms       :   12 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :   54 (   6   ~;   0   |;   0   &;  44   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :    8 (   0   ^   8   !;   0   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
thf(del_type,type,
    del: $tType ).

thf(bool_type,type,
    bool: del ).

thf(arr_type,type,
    arr: del > del > del ).

thf(mem_type,type,
    mem: $i > del > $o ).

thf(ap_type,type,
    ap: $i > $i > $i ).

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

thf(c_2Ecardinal_2Ecardleq_type,type,
    c_2Ecardinal_2Ecardleq: del > del > $i ).

thf(1,conjecture,
    ! [A: del,B: del,C: $i] :
      ( ( mem @ C @ ( arr @ A @ bool ) )
     => ! [D: $i] :
          ( ( mem @ D @ ( arr @ B @ bool ) )
         => ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A @ B ) @ C ) @ D ) ) )
            = ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A @ B ) @ C ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).

thf(2,negated_conjecture,
    ~ ! [A: del,B: del,C: $i] :
        ( ( mem @ C @ ( arr @ A @ bool ) )
       => ! [D: $i] :
            ( ( mem @ D @ ( arr @ B @ bool ) )
           => ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A @ B ) @ C ) @ D ) ) )
              = ( ~ ( p @ ( ap @ ( ap @ ( c_2Ecardinal_2Ecardleq @ A @ B ) @ C ) @ D ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(42,plain,
    ~ $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(43,plain,
    $false,
    inference(simp,[status(thm)],[42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : ITP010^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n028.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May  6 22:12:54 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.91/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.35/1.02  % [INFO] 	 Parsing done (168ms). 
% 1.35/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.31  % [INFO] 	 nitpick registered as external prover. 
% 1.78/1.32  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.41  % [INFO] 	 Found a conjecture and 39 axioms. Running axiom selection ... 
% 2.34/1.47  % [INFO] 	 Axiom selection finished. Selected 39 axioms (removed 0 axioms). 
% 2.52/1.53  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.52/1.54  % [INFO] 	 Type checking passed. 
% 2.52/1.54  % [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 ... 
% 3.54/2.03  % [INFO] 	 Killing All external provers ... 
% 3.54/2.03  % Time passed: 1567ms (effective reasoning time: 993ms)
% 3.54/2.03  % 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)>
% 3.54/2.03  % Axioms used in derivation (0): 
% 3.54/2.03  % No. of inferences in proof: 4
% 3.54/2.03  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1567 ms resp. 993 ms w/o parsing
% 3.54/2.06  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.54/2.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------