%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU460^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 03:37:43 EDT 2024

% Result   : Theorem 3.37s 1.78s
% Output   : Refutation 3.37s
% 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       :   11 (   2 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   33 (   2   ~;   3   |;   0   &;  24   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   2 con; 0-3 aty)
%            Number of variables   :   12 (   4   ^   8   !;   0   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mono_type,type,
    mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).

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

thf(sc_type,type,
    sc: ( $i > $i > $o ) > $i > $i > $o ).

thf(sc_def,definition,
    ( sc
    = ( ^ [A: $i > $i > $o,B: $i,C: $i] :
          ( ( A @ C @ B )
          | ( A @ B @ C ) ) ) ) ).

thf(1,conjecture,
    mono @ sc,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_closure_op_is_monotonic) ).

thf(2,negated_conjecture,
    ~ ( mono @ sc ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(12,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU460^1 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n011.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 : Sun May 19 15:41:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 1.07/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.44/1.10  % [INFO] 	 Parsing done (158ms). 
% 1.44/1.11  % [INFO] 	 Running in sequential loop mode. 
% 1.90/1.32  % [INFO] 	 eprover registered as external prover. 
% 1.90/1.33  % [INFO] 	 cvc4 registered as external prover. 
% 1.90/1.33  % [INFO] 	 Scanning for conjecture ... 
% 2.23/1.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.23/1.44  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.41/1.45  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.41/1.45  % [INFO] 	 Type checking passed. 
% 2.41/1.45  % [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 ... 
% 2.97/1.73  % External prover 'e' found a proof!
% 2.97/1.73  % [INFO] 	 Killing All external provers ... 
% 2.97/1.73  % Time passed: 1197ms (effective reasoning time: 623ms)
% 2.97/1.73  % 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)>
% 2.97/1.73  % Axioms used in derivation (0): 
% 2.97/1.74  % No. of inferences in proof: 4
% 3.37/1.78  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1197 ms resp. 623 ms w/o parsing
% 3.37/1.82  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.37/1.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------