%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU494^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 03:37:48 EDT 2024

% Result   : Theorem 3.33s 1.90s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   3 unt;   2 typ;   2 def)
%            Number of atoms       :   13 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   46 (   4   ~;   0   |;   5   &;  30   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :   17 (   4   ^  13   !;   0   ?;  17   :)

% Comments : 
%------------------------------------------------------------------------------
thf(inv_type,type,
    inv: ( $i > $i > $o ) > $i > $i > $o ).

thf(inv_def,definition,
    ( inv
    = ( ^ [A: $i > $i > $o,B: $i,C: $i] : ( A @ C @ B ) ) ) ).

thf(so_type,type,
    so: ( $i > $i > $o ) > $o ).

thf(so_def,definition,
    ( so
    = ( ^ [A: $i > $i > $o] :
          ( ( asymm @ A )
          & ( trans @ A ) ) ) ) ).

thf(1,conjecture,
    ! [A: $i > $i > $o] :
      ( ( so @ A )
     => ( so @ ( inv @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_strict_order_is_strict_order) ).

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

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

thf(16,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU494^1 : TPTP v8.2.0. Released v3.6.0.
% 0.16/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n003.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sun May 19 17:11:54 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.94/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.41/1.08  % [INFO] 	 Parsing done (165ms). 
% 1.59/1.09  % [INFO] 	 Running in sequential loop mode. 
% 2.03/1.34  % [INFO] 	 eprover registered as external prover. 
% 2.03/1.34  % [INFO] 	 cvc4 registered as external prover. 
% 2.03/1.35  % [INFO] 	 Scanning for conjecture ... 
% 2.34/1.46  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.40/1.48  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.40/1.48  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.40/1.48  % [INFO] 	 Type checking passed. 
% 2.40/1.49  % [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 ... 
% 3.33/1.89  % External prover 'e' found a proof!
% 3.33/1.89  % [INFO] 	 Killing All external provers ... 
% 3.33/1.89  % Time passed: 1335ms (effective reasoning time: 796ms)
% 3.33/1.89  % 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)>
% 3.33/1.89  % Axioms used in derivation (0): 
% 3.33/1.89  % No. of inferences in proof: 4
% 3.33/1.90  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1335 ms resp. 796 ms w/o parsing
% 3.33/1.92  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.33/1.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------