%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 01:31:19 EDT 2024

% Result   : Theorem 2.70s 1.94s
% Output   : Refutation 2.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   13 (   1 unt;   5 typ;   0 def)
%            Number of atoms       :   15 (   5 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   32 (   7   ~;   0   |;   0   &;  18   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :    4 (   0   ^   4   !;   0   ?;   4   :)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(x_type,type,
    x: nat ).

thf(y_type,type,
    y: nat ).

thf(more_type,type,
    more: nat > nat > $o ).

thf(less_type,type,
    less: nat > nat > $o ).

thf(1,conjecture,
    ( ~ ( less @ y @ x )
   => ( y = x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).

thf(2,negated_conjecture,
    ~ ( ~ ( less @ y @ x )
     => ( y = x ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ( ~ ( less @ y @ x )
     => ( y = x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ( ~ ( more @ x @ y )
   => ( x = y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

thf(9,plain,
    ( ~ ( more @ x @ y )
   => ( x = y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ( less @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz11) ).

thf(12,plain,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ( less @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(14,plain,
    $false,
    inference(cvc4,[status(thm)],[5,9,12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n007.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Mon May 20 05:54:54 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.99/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.08  % [INFO] 	 Parsing done (149ms). 
% 1.30/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.45  % [INFO] 	 eprover registered as external prover. 
% 1.84/1.45  % [INFO] 	 cvc4 registered as external prover. 
% 1.84/1.46  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.02/1.55  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.02/1.57  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.02/1.57  % [INFO] 	 Type checking passed. 
% 2.02/1.57  % [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 ... 
% 2.70/1.93  % External prover 'cvc4' found a proof!
% 2.70/1.93  % [INFO] 	 Killing All external provers ... 
% 2.70/1.93  % Time passed: 1468ms (effective reasoning time: 837ms)
% 2.70/1.93  % 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)>
% 2.70/1.93  % Axioms used in derivation (2): m, satz11
% 2.70/1.93  % No. of inferences in proof: 8
% 2.70/1.94  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1468 ms resp. 837 ms w/o parsing
% 2.70/1.97  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.70/1.97  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------