%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO003^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Tue May 21 08:58:54 EDT 2024

% Result   : Theorem 2.35s 1.56s
% Output   : Refutation 2.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (  10 unt;   4 typ;   1 def)
%            Number of atoms       :   17 (   9 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   40 (   9   ~;   3   |;   3   &;  20   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :   14 (   2   ^  12   !;   0   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(leibeq_type,type,
    leibeq: $i > $i > $o ).

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

thf(sk1_type,type,
    sk1: $i ).

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

thf(sk3_type,type,
    sk3: $i > $o ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i > $o] :
      ( ( ( leibeq @ A @ B )
        & ( C @ A ) )
     => ( C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i > $o] :
        ( ( ( leibeq @ A @ B )
          & ( C @ A ) )
       => ( C @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(5,plain,
    sk3 @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk3 @ sk2 ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ( ( sk3 @ sk2 )
   != ( sk3 @ sk1 ) ),
    inference(paramod_ordered,[status(thm)],[5,4]) ).

thf(11,plain,
    sk2 != sk1,
    inference(simp,[status(thm)],[10]) ).

thf(6,plain,
    ! [A: $i > $o] :
      ( ~ ( A @ sk1 )
      | ( A @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ( ( sk1 != sk1 )
    | ( sk1 = sk2 ) ),
    inference(replace_leibeq,[status(thm)],[6:[bind(A,$thf( (=) @ $i @ sk1 ))]]) ).

thf(8,plain,
    ( ( sk1 != sk1 )
    | ( sk2 = sk1 ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(9,plain,
    sk2 = sk1,
    inference(simp,[status(thm)],[8]) ).

thf(13,plain,
    sk1 != sk1,
    inference(rewrite,[status(thm)],[11,9]) ).

thf(14,plain,
    $false,
    inference(simp,[status(thm)],[13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : SYO003^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n029.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May 20 10:12:09 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 1.01/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.06/1.01  % [INFO] 	 Parsing done (105ms). 
% 1.06/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.25  % [INFO] 	 nitpick registered as external prover. 
% 1.64/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.64/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.83/1.33  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.83/1.33  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.83/1.33  % [INFO] 	 Type checking passed. 
% 1.83/1.33  % [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 ... 
% 2.35/1.56  % [INFO] 	 Killing All external provers ... 
% 2.35/1.56  % Time passed: 1016ms (effective reasoning time: 537ms)
% 2.35/1.56  % 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)>
% 2.35/1.56  % Axioms used in derivation (0): 
% 2.35/1.56  % No. of inferences in proof: 13
% 2.35/1.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1016 ms resp. 537 ms w/o parsing
% 2.35/1.59  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.35/1.59  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------