%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP010+1 : 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 07:46:42 EDT 2024

% Result   : Theorem 4.23s 2.00s
% Output   : Refutation 4.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :    9 (   2 unt;   5 typ;   0 def)
%            Number of atoms       :    6 (   0 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   60 (   6   ~;   0   |;   0   &;  52   @)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    8 (   0   ^   8   !;   0   ?;   8   :)

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

thf(s_type,type,
    s: $i > $i > $i ).

thf(tyop_2Emin_2Ebool_type,type,
    tyop_2Emin_2Ebool: $i ).

thf(c_2Ecardinal_2Ecardleq_2E2_type,type,
    c_2Ecardinal_2Ecardleq_2E2: $i > $i > $i ).

thf(tyop_2Emin_2Efun_type,type,
    tyop_2Emin_2Efun: $i > $i > $i ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) )
    <=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) )
      <=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ 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
% 0.03/0.12  % Problem  : ITP010+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May  6 14:48:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.93/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.99  % [INFO] 	 Parsing done (138ms). 
% 1.23/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.91/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.91/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.94/1.24  % [INFO] 	 Scanning for conjecture ... 
% 2.15/1.33  % [INFO] 	 Found a conjecture and 39 axioms. Running axiom selection ... 
% 2.27/1.40  % [INFO] 	 Axiom selection finished. Selected 39 axioms (removed 0 axioms). 
% 2.61/1.47  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.61/1.47  % [INFO] 	 Type checking passed. 
% 2.61/1.48  % [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 ... 
% 4.23/2.00  % [INFO] 	 Killing All external provers ... 
% 4.23/2.00  % Time passed: 1485ms (effective reasoning time: 993ms)
% 4.23/2.00  % 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)>
% 4.23/2.00  % Axioms used in derivation (0): 
% 4.23/2.00  % No. of inferences in proof: 4
% 4.23/2.00  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1485 ms resp. 993 ms w/o parsing
% 4.23/2.03  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.23/2.03  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------